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| There is therefore now no condemnation to them which are in Christ Jesus, who walk not after the flesh, but after the Spirit.
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| ᎾᏍᎩ ᎢᏳᏍᏗ ᎥᏝ ᎿᎭᏉ ᏩᎭ ᏗᎬᏩᎾᏚᎪᏓᏁᏗ ᎨᏒ ᎾᏍᎩ Ꮎ ᏥᏌ ᎦᎶᏁᏛ ᎬᏩᏯᎢ, ᎾᏍᎩ ᎤᏇᏓᎵ ᎨᏒ ᎾᏂᏍᏓᏩᏕᎬᎾ ᏥᎩ, ᎠᏓᏅᏙᏍᎩᏂ ᏣᏂᏍᏓᏩᏕᎦ.
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Na-s-gi i-yu-s-di v-tla hna-quo wa-ha di-gv-wa-na-du-go-da-ne-di ge-sv na-s-gi na Tsi-sa Ga-lo-ne-dv gv-wa-ya-i, na-s-gi u-que-da-li ge-sv na-ni-s-da-wa-de-gv-na tsi-gi, a-da-nv-do-s-gi-ni tsa-ni-s-da-wa-de-ga.
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| For the law of the Spirit of life in Christ Jesus hath made me free from the law of sin and death.
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| ᎠᏓᏅᏙᏰᏃ ᎬᏂᏛ ᎠᏓᏁᎯ, ᎾᏍᎩ ᎬᏂᏛ ᎦᎶᏁᏛ ᏥᏌ ᏨᏗᏓᎴᎲᏍᎦ, ᎾᏍᎩ ᎠᏓᏅᏙ ᎤᏤᎵ ᏗᎧᎿᎭᏩᏛᏍᏗ ᎠᏊᏓᎴᏒ ᎠᏍᎦᏂ ᎠᎴ ᎠᏲᎱᎯᏍᏗ ᎨᏒ ᎤᎾᏤᎵ ᏗᎧᎿᎭᏩᏛᏍᏗᏱ ᎠᏆᏚᏓᎸᎢ.
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A-da-nv-do-ye-no gv-ni-dv a-da-ne-hi, na-s-gi gv-ni-dv Ga-lo-ne-dv Tsi-sa tsv-di-da-le-hv-s-ga, na-s-gi A-da-nv-do u-tse-li di-ka-hna-wa-dv-s-di a-quu-da-le-sv a-s-ga-ni a-le a-yo-hu-hi-s-di ge-sv u-na-tse-li di-ka-hna-wa-dv-s-di-yi a-qua-du-da-lv-i.
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| For what the law could not do, in that it was weak through the flesh, God sending his own Son in the likeness of sinful flesh, and for sin, condemned sin in the flesh:
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| ᏗᎧᎿᎭᏩᏛᏍᏗᏰᏃ ᎢᎬᏩᏛᏁᏗ ᏂᎨᏒᎾ ᎨᏒᎢ, ᏅᏗᎦᎵᏍᏙᏗᏍᎬ ᎠᏩᎾᎦᎳᎯᏳ ᎨᏒ ᎤᏇᏓᎵ ᎢᏳᏩᏂᏌᏛ,^ ᎤᏁᎳᏅᎯ ᎤᏩᏒ ᎤᏪᏥ ᏧᏅᏎ ᎾᏍᎩᏯ ᏗᏟᎶᏍᏔᏅᎯ ᎠᏍᎦᎾ ᎤᏇᏓᎵ, ᎠᎴ ᎠᏍᎦᏂ ᏧᎬᏩᎴᎢ, ᏚᏭᎪᏓᏁᎴ ᎤᏎᎪᎩᏎ ᎠᏍᎦᏅᎢᏍᏗ ᎨᏒ ᎤᏇᏓᎸ ᎠᏯᎥᎢ;
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Di-ka-hna-wa-dv-s-di-ye-no i-gv-wa-dv-ne-di ni-ge-sv-na ge-sv-i, nv-di-ga-li-s-do-di-s-gv a-wa-na-ga-la-hi-yu ge-sv u-que-da-li i-yu-wa-ni-sa-dv,^ U-ne-la-nv-hi u-wa-sv U-we-tsi tsu-nv-se na-s-gi-ya di-tli-lo-s-ta-nv-hi a-s-ga-na u-que-da-li, a-le a-s-ga-ni tsu-gv-wa-le-i, du-wu-go-da-ne-le u-se-go-gi-se a-s-ga-nv-i-s-di ge-sv u-que-da-lv a-ya-v-i;
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| That the righteousness of the law might be fulfilled in us, who walk not after the flesh, but after the Spirit.
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| ᎾᏍᎩ ᏅᏓᏳᎵᏍᏙᏙᏗᏱ ᏗᎧᎿᎭᏩᏛᏍᏗ ᏂᎦᏪᏍᎬ ᎾᏍᎩᏯ ᏚᏳᎪᏛ ᎢᎦᏛᏁᎰᎲᏍᏗᏱ, ᎠᏴ ᎤᏇᏓᎵ ᎨᏒ ᎢᏗᏍᏓᏩᏕᎩ ᏂᎨᏒᎾ ᏥᎩ, ᎠᏓᏅᏙᏍᎩᏂ ᎢᏗᏍᏓᏩᏕᎩ.
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Na-s-gi nv-da-yu-li-s-do-do-di-yi di-ka-hna-wa-dv-s-di ni-ga-we-s-gv na-s-gi-ya du-yu-go-dv i-ga-dv-ne-ho-hv-s-di-yi, a-yv u-que-da-li ge-sv i-di-s-da-wa-de-gi ni-ge-sv-na tsi-gi, A-da-nv-do-s-gi-ni i-di-s-da-wa-de-gi.
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| For they that are after the flesh do mind the things of the flesh; but they that are after the Spirit the things of the Spirit.
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| ᎾᏍᎩᏰᏃ ᎤᏇᏓᎵ ᏧᎾᏘᏂᏙᎯ ᎤᏇᏓᎵᏉ ᎤᏤᎵ ᎤᎬᏩᎵ ᎤᎾᎦᏌᏯᏍᏙᎢ, ᎾᏍᎩᏍᎩᏂ Ꮎ ᎠᏓᏅᏙ ᏧᎾᏘᏂᏙᎯ ᎠᏓᏅᏙᏉ ᎤᏤᎵ ᎤᎬᏩᎵ ᎤᎾᎦᏌᏯᏍᏙᎢ.
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Na-s-gi-ye-no u-que-da-li tsu-na-ti-ni-do-hi u-que-da-li-quo u-tse-li u-gv-wa-li u-na-ga-sa-ya-s-do-i, na-s-gi-s-gi-ni na A-da-nv-do tsu-na-ti-ni-do-hi A-da-nv-do-quo u-tse-li u-gv-wa-li u-na-ga-sa-ya-s-do-i.
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| For to be carnally minded is death; but to be spiritually minded is life and peace.
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| ᎤᏇᏓᎵᏰᏃ ᎠᎦᏌᏯᏍᏙᏗᏱ ᎠᏲᎱᎯᏍᏗ ᎨᏒ ᏩᎵᏰᎢᎶᎯᎭ; ᎠᏓᏅᏙᏍᎩᏂ ᎠᏕᏌᏯᏍᏙᏗᏱ ᎬᏂᏛ ᎠᎴ ᏅᏩᏙᎯᏯᏛ ᏗᎨᏒ ᏩᎵᏰᎢᎶᎯᎭ.
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U-que-da-li-ye-no a-ga-sa-ya-s-do-di-yi a-yo-hu-hi-s-di ge-sv wa-li-ye-i-lo-hi-ha; a-da-nv-do-s-gi-ni a-de-sa-ya-s-do-di-yi gv-ni-dv a-le nv-wa-do-hi-ya-dv di-ge-sv wa-li-ye-i-lo-hi-ha.
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| Because the carnal mind is enmity against God: for it is not subject to the law of God, neither indeed can be.
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| ᎤᏇᏓᎵᏰᏃ ᎠᎦᏌᏯᏍᏙᏗᏱ ᎨᏒ ᎾᏍᎩ ᎤᏁᎳᏅᎯ ᏗᎦᏘᎴᎩ; ᎥᏝᏰᏃ ᏗᎧᎿᎭᏩᏛᏍᏗ ᎤᏁᎳᏅᎯ ᎤᏤᎵ ᏗᎧᎿᎭᏩᏕᎩ ᏱᎩ, ᎥᏝ ᎠᎴ ᎤᏙᎩᏳᎯ ᎾᏍᎩ ᏰᎵ ᏱᏅᎬᏛᎦ;
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U-que-da-li-ye-no a-ga-sa-ya-s-do-di-yi ge-sv na-s-gi U-ne-la-nv-hi di-ga-ti-le-gi; v-tla-ye-no di-ka-hna-wa-dv-s-di U-ne-la-nv-hi u-tse-li di-ka-hna-wa-de-gi yi-gi, v-tla a-le u-do-gi-yu-hi na-s-gi ye-li yi-nv-gv-dv-ga;
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| So then they that are in the flesh cannot please God.
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| ᎾᏍᎩᏃ ᎤᏇᏓᎵ ᏧᎾᏘᏂᏙᎯ ᎨᏒ ᎥᏝ ᎤᏁᎳᏅᎯ ᎣᏍᏛ ᎤᏰᎸᏗ ᏱᏅᎬᎾᏛᎦ.
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Na-s-gi-no u-que-da-li tsu-na-ti-ni-do-hi ge-sv v-tla U-ne-la-nv-hi o-s-dv u-ye-lv-di yi-nv-gv-na-dv-ga.
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| But ye are not in the flesh, but in the Spirit, if so be that the Spirit of God dwell in you. Now if any man have not the Spirit of Christ, he is none of his.
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| ᏂᎯᏍᎩᏂ ᎥᏝ ᎤᏇᏓᎵ ᏗᏣᏘᏂᏙᎯ ᏱᎩ, ᎠᏓᏅᏙᏍᎩᏂ ᏗᏣᏘᏂᏙᎯ, ᎢᏳᏃ ᎰᏩ ᎤᏁᎳᏅᎯ ᎤᏓᏅᏙ ᏱᏥᏯᎠ. ᎠᎴ ᎢᏳ ᎩᎶ ᎦᎶᏁᏛ ᎤᏓᏅᏙ ᏄᏪᎲᎾ ᎢᎨᏎᏍᏗ, ᎾᏍᎩ Ꮎ ᎥᏝ [ᎦᎶᏁᏛ] ᎤᏤᎵ ᏱᎦᎩ.
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Ni-hi-s-gi-ni v-tla u-que-da-li di-tsa-ti-ni-do-hi yi-gi, A-da-nv-do-s-gi-ni di-tsa-ti-ni-do-hi, i-yu-no ho-wa U-ne-la-nv-hi U-da-nv-do yi-tsi-ya-a. A-le i-yu gi-lo Ga-lo-ne-dv U-da-nv-do nu-we-hv-na i-ge-se-s-di, na-s-gi na v-tla [Ga-lo-ne-dv] u-tse-li yi-ga-gi.
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| And if Christ be in you, the body is dead because of sin; but the Spirit is life because of righteousness.
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| ᎢᏳᏍᎩᏂ ᎦᎶᏁᏛ ᎢᏥᏯᎡᏍᏗ, ᎠᏰᎸ ᎤᏙᎯᏳᎯ ᎤᏲᎱᏒᎯ ᎠᏍᎦᏂ ᏅᏗᎦᎵᏍᏙᏗᎭ; ᎠᏓᏅᏙᏍᎩᏂ ᎬᏃᏛ ᏚᏳᎪᏛ ᎢᏯᏛᏁᏗ ᎨᏒ ᏅᏗᎦᎵᏍᏙᏗᎭ.
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I-yu-s-gi-ni Ga-lo-ne-dv i-tsi-ya-e-s-di, a-ye-lv u-do-hi-yu-hi u-yo-hu-sv-hi a-s-ga-ni nv-di-ga-li-s-do-di-ha; A-da-nv-do-s-gi-ni gv-no-dv du-yu-go-dv i-ya-dv-ne-di ge-sv nv-di-ga-li-s-do-di-ha.
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| But if the Spirit of him that raised up Jesus from the dead dwell in you, he that raised up Christ from the dead shall also quicken your mortal bodies by his Spirit that dwelleth in you.
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| ᎢᏳᏍᎩᏂ ᏥᏌ ᎤᏲᎱᏒ ᏧᎴᏔᏅᎯ ᎤᏓᏅᏙ ᎢᏥᏯᎡᏍᏗ, ᎾᏍᎩ ᎦᎶᏁᏛ ᎤᏲᎱᏒ ᏧᎴᏔᏅᎯ ᎾᏍᏉ ᏙᏓᎬᏃᎯᏍᏔᏂ ᏗᏲᎱᏍᎩ ᏗᏥᏰᎸᎢ ᏓᎬᏔᏂ ᎤᏓᏅᏙ ᎾᏍᎩ ᏥᏥᏯᎠ.
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I-yu-s-gi-ni Tsi-sa u-yo-hu-sv tsu-le-ta-nv-hi U-da-nv-do i-tsi-ya-e-s-di, na-s-gi Ga-lo-ne-dv u-yo-hu-sv tsu-le-ta-nv-hi na-s-quo do-da-gv-no-hi-s-ta-ni di-yo-hu-s-gi di-tsi-ye-lv-i da-gv-ta-ni U-da-nv-do na-s-gi tsi-tsi-ya-a.
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| Therefore, brethren, we are debtors, not to the flesh, to live after the flesh.
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| ᎾᏍᎩ ᎢᏳᏍᏗ ᎢᏓᎵᏅᏟ, ᎡᎩᏚᎦ, ᎥᏝ ᎤᏇᏓᎵ ᏱᎩᏚᎦ, ᎾᏍᎩ ᎤᏇᏓᎵ ᎢᎩᏍᏓᏩᏗᏓᏍᏗᏱ ᎢᏕᎲᎢ.
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Na-s-gi i-yu-s-di i-da-li-nv-tli, e-gi-du-ga, v-tla u-que-da-li yi-gi-du-ga, na-s-gi u-que-da-li i-gi-s-da-wa-di-da-s-di-yi i-de-hv-i.
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| For if ye live after the flesh, ye shall die: but if ye through the Spirit do mortify the deeds of the body, ye shall live.
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| ᎢᏳᏰᏃ ᎢᏤᎲ ᎤᏇᏓᎵ ᎨᏒ ᎢᏥᏍᏓᏩᏗᏙᎮᏍᏗ, ᏙᏓᏥᏲᎱᏏ; ᎢᏳᏍᎩᏂ ᎠᏓᏅᏙ ᎬᏗ ᎠᏰᎸ ᏚᎸᏫᏍᏓᏁᎲ ᎢᏥᎯᎮᏍᏗ, ᏕᏨᏁᏍᏗ.
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I-yu-ye-no i-tse-hv u-que-da-li ge-sv i-tsi-s-da-wa-di-do-he-s-di, do-da-tsi-yo-hu-si; i-yu-s-gi-ni A-da-nv-do gv-di a-ye-lv du-lv-wi-s-da-ne-hv i-tsi-hi-he-s-di, de-tsv-ne-s-di.
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| For as many as are led by the Spirit of God, they are the sons of God.
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| ᎾᏂᎥᏰᏃ ᎩᎶᎢ ᎤᏁᎳᏅᎯ ᎤᏓᏅᏙ ᏧᎾᏘᏂᏙᎯ, ᎾᏍᎩ ᎤᏁᎳᏅᎯ ᏧᏪᏥ.
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Na-ni-v-ye-no gi-lo-i U-ne-la-nv-hi U-da-nv-do tsu-na-ti-ni-do-hi, na-s-gi U-ne-la-nv-hi tsu-we-tsi.
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| For ye have not received the spirit of bondage again to fear; but ye have received the Spirit of adoption, whereby we cry, Abba, Father.
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| ᎥᏝᏰᏃ ᎠᏓᏅᏙ ᎠᏥᎾᏝᎢ ᏔᎵᏁ ᎡᏥᏁᎸᎯ ᏱᎩ, ᎾᏍᎩ ᎢᏥᎾᏰᎯᏍᏗᏱ; ᏧᏪᏥᏍᎩᏂ ᎢᎨᎬᏁᎸᎯ ᎤᎾᏓᏅᏙ ᎡᏥᏁᎸ, ᎾᏍᎩ ᎢᏛᏗᏍᎬ, ᎠᏆ! ᎡᏙᏓ! ᏥᏓᏗᏍᎪᎢ.
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V-tla-ye-no A-da-nv-do a-tsi-na-tla-i ta-li-ne e-tsi-ne-lv-hi yi-gi, na-s-gi i-tsi-na-ye-hi-s-di-yi; tsu-we-tsi-s-gi-ni i-ge-gv-ne-lv-hi u-na-da-nv-do e-tsi-ne-lv, na-s-gi i-dv-di-s-gv, A-qua! E-do-da! tsi-da-di-s-go-i.
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| The Spirit itself beareth witness with our spirit, that we are the children of God:
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| ᎠᏓᏅᏙᏰᏃ ᎤᏩᏒ ᏓᎵᎪᏁᎭ ᏗᎦᏓᏅᏙ ᎬᏂᎨᏒ ᎾᏅᏁᎲ, ᎾᏍᎩ ᎠᏴ ᎤᏁᎳᏅᎯ ᏧᏪᏥ ᎨᏒᎢ.
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A-da-nv-do-ye-no u-wa-sv da-li-go-ne-ha di-ga-da-nv-do gv-ni-ge-sv na-nv-ne-hv, na-s-gi a-yv U-ne-la-nv-hi tsu-we-tsi ge-sv-i.
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| And if children, then heirs; heirs of God, and joint-heirs with Christ; if so be that we suffer with him, that we may be also glorified together.
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| ᎠᎴ ᎢᏳ ᏧᏪᏥ ᏱᎩ, ᎿᎭᏉ ᎢᎦᏘᏰᎯ ᏧᎬᏩᎶᏗ; ᎢᎦᏘᏰᏗ ᏧᎬᏩᎶᏗ ᎤᏁᎳᏅᎯ ᎤᏓᏁᏗ ᎨᏒᎢ, ᎠᎴ ᎦᎶᏁᏛ ᎢᏧᎳᎭ ᎢᎦᏘᏰᏗ; ᎢᏳᏃ ᎰᏩ ᏱᎦᏠᏯᏍᏗᎭ ᎠᎩᎵᏲᎬᎢ, ᎾᏍᏉ ᎢᎦᏠᏯᏍᏙᏗ ᎨᏎᏍᏗ ᎠᏥᎸᏉᏗᏍᎬᎢ.
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A-le i-yu tsu-we-tsi yi-gi, hna-quo i-ga-ti-ye-hi tsu-gv-wa-lo-di; i-ga-ti-ye-di tsu-gv-wa-lo-di U-ne-la-nv-hi u-da-ne-di ge-sv-i, a-le Ga-lo-ne-dv i-tsu-la-ha i-ga-ti-ye-di; i-yu-no ho-wa yi-ga-tlo-ya-s-di-ha a-gi-li-yo-gv-i, na-s-quo i-ga-tlo-ya-s-do-di ge-se-s-di a-tsi-lv-quo-di-s-gv-i.
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| For I reckon that the sufferings of this present time are not worthy to be compared with the glory which shall be revealed in us.
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| ᎦᏓᏅᏖᏍᎬᏰᏃ ᎯᎠ ᎾᏍᎩ ᎪᎯ ᎠᎩᎵᏲᎢᏍᏗ ᎨᏒ ᎥᏝ ᏗᎬᏟᎶᏍᏙᏗ ᏱᎩ ᎦᎸᏉᏗᏳ ᎨᏒ ᎾᏍᎩ ᎡᎩᎾᏄᎪᏫᏎᏗ ᎨᏒᎢ.
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Ga-da-nv-te-s-gv-ye-no hi-a na-s-gi go-hi a-gi-li-yo-i-s-di ge-sv v-tla di-gv-tli-lo-s-do-di yi-gi ga-lv-quo-di-yu ge-sv na-s-gi e-gi-na-nu-go-wi-se-di ge-sv-i.
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| For the earnest expectation of the creature waiteth for the manifestation of the sons of God.
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| ᎤᎵᏂᎩᏛᏰᏃ ᎤᏚᎩ ᎤᏩᏒ ᎠᎦᏁᎳᏅᎯ ᎨᏒ ᎠᎦᏘᏯ ᎨᏥᎾᏄᎪᏫᏒ ᎤᏁᎳᏅᎯ ᏧᏪᏥ.
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U-li-ni-gi-dv-ye-no u-du-gi u-wa-sv a-ga-ne-la-nv-hi ge-sv a-ga-ti-ya ge-tsi-na-nu-go-wi-sv U-ne-la-nv-hi tsu-we-tsi.
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| For the creature was made subject to vanity, not willingly, but by reason of him who hath subjected the same in hope,
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| ᎠᎦᏁᎳᏅᎯᏰᏃ ᎠᏲᎩ ᎾᎬᏁᎴᎢ, ᎥᏝ ᎣᏏᏳ ᎤᏰᎸᏒ ᎢᏳᏍᏗ, ᎣᏏᏳᏍᎩᏂ ᎤᏰᎸᏅ ᎢᏳᏍᏗ ᎾᏍᎩ Ꮎ ᎾᏍᎩ ᎢᏳᏩᏁᎸᎯ, ᎤᏚᎩ ᎤᏮᏗᏱ ᎤᏰᎸᏅ,
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A-ga-ne-la-nv-hi-ye-no a-yo-gi na-gv-ne-le-i, v-tla o-si-yu u-ye-lv-sv i-yu-s-di, o-si-yu-s-gi-ni u-ye-lv-nv i-yu-s-di na-s-gi na na-s-gi i-yu-wa-ne-lv-hi, u-du-gi u-wv-di-yi u-ye-lv-nv,
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| Because the creature itself also shall be delivered from the bondage of corruption into the glorious liberty of the children of God.
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| ᎾᏍᎩ ᎠᎦᏁᎳᏅᎯ ᎤᏩᏒ ᎾᏍᏉ ᎤᏚᏓᎴᏍᏗᏱ ᎠᏲᎩ ᎨᏒ ᎤᎾᏝᎥᎢ, ᎦᎸᏉᏗᏳ ᏂᏗᎨᏥᎾᏝᎥᎾ ᎨᏒ ᎤᏁᎳᏅᎯ ᏧᏪᏥ ᎤᎾᏤᎵᎦ ᏫᏗᎨᏥᎪᏗᏱ.
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Na-s-gi a-ga-ne-la-nv-hi u-wa-sv na-s-quo u-du-da-le-s-di-yi a-yo-gi ge-sv u-na-tla-v-i, ga-lv-quo-di-yu ni-di-ge-tsi-na-tla-v-na ge-sv U-ne-la-nv-hi tsu-we-tsi u-na-tse-li-ga wi-di-ge-tsi-go-di-yi.
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| For we know that the whole creation groaneth and travaileth in pain together until now.
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| ᎢᏗᎦᏔᎭᏰᏃ ᎾᏍᎩ ᎾᏂᎥ ᎨᎦᏁᎳᏅᎯ ᎨᏒ ᎢᏧᎳᎭ ᎤᏂᎵᏰᏗᏍᎬ ᎠᎴ ᎠᏂᎩᎵᏲᎬ ᎪᎯ ᎢᏯᏍᏗ.
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I-di-ga-ta-ha-ye-no na-s-gi na-ni-v ge-ga-ne-la-nv-hi ge-sv i-tsu-la-ha u-ni-li-ye-di-s-gv a-le a-ni-gi-li-yo-gv go-hi i-ya-s-di.
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| And not only they, but ourselves also, which have the firstfruits of the Spirit, even we ourselves groan within ourselves, waiting for the adoption, to wit, the redemption of our body.
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| ᎥᏝ ᎠᎴ ᎤᏅᏒᏉ, ᎢᎬᏒᏍᎩᏂ ᎾᏍᏉ ᎾᏍᎩ ᎢᎬᏱᏱ ᎤᎾᏄᎪᏫᏒᎯ ~ᎠᏓᏅᏙ ᏥᎨᎭ, ᎠᏴ ᎾᏍᏉ ᎢᎬᏒ ᎨᏒ ᎭᏫᏂ ᏕᎩᎵᏰᏗᎭ, ᎢᏗᎦᏘᏴ ᏧᏪᏥ ᎢᎨᎬᏁᏗ, ᎾᏍᎩ ᏗᏗᏰᎸ ᏧᎫᏴᏗᏱ ᏧᏭᏓᎴᏍᏗᏱ.
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V-tla a-le u-nv-sv-quo, i-gv-sv-s-gi-ni na-s-quo na-s-gi i-gv-yi-yi u-na-nu-go-wi-sv-hi ~a-da-nv-do tsi-ge-ha, a-yv na-s-quo i-gv-sv ge-sv ha-wi-ni de-gi-li-ye-di-ha, i-di-ga-ti-yv tsu-we-tsi i-ge-gv-ne-di, na-s-gi di-di-ye-lv tsu-gu-yv-di-yi tsu-wu-da-le-s-di-yi.
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| For we are saved by hope: but hope that is seen is not hope: for what a man seeth, why doth he yet hope for?
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| ᎤᏚᎩᏉᏰᏃ ᎢᎬᎭ ᎡᎩᏍᏕᎸᏗᏱ; ᎤᏚᎩᏍᎩᏂ ᎣᏩᏒ ᎠᎪᎲᎯ ᏥᎨᏐᎢ ᎥᏝ ᎤᏚᎩ ᏲᏩᏐᎢ; ᎪᎱᏍᏗᏰᏃ ᏨᎪᏩᏘᏍᎪᎢ, ᎦᏙᏃ ᎠᏏ ᎤᏚᎩ ᏱᎦᏲᏩᎭ?
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U-du-gi-quo-ye-no i-gv-ha e-gi-s-de-lv-di-yi; u-du-gi-s-gi-ni o-wa-sv a-go-hv-hi tsi-ge-so-i v-tla u-du-gi yo-wa-so-i; Go-hu-s-di-ye-no tsv-go-wa-ti-s-go-i, ga-do-no a-si u-du-gi yi-ga-yo-wa-ha?
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| But if we hope for that we see not, then do we with patience wait for it.
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| ᎢᏳᏍᎩᏂ ᎢᎩᎪᎲᎯ ᏂᎨᏒᎾ ᎨᏒ ᎤᏚᎩ ᏱᎬᎭ, ᎿᎭᏉ ᏗᏛᏂᏗᏳ ᎢᏗᎦᏘᏲ ᎾᏍᎩ.
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I-yu-s-gi-ni i-gi-go-hv-hi ni-ge-sv-na ge-sv u-du-gi yi-gv-ha, hna-quo di-dv-ni-di-yu i-di-ga-ti-yo na-s-gi.
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| Likewise the Spirit also helpeth our infirmities: for we know not what we should pray for as we ought: but the Spirit itself maketh intercession for us with groanings which cannot be uttered.
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| ᎾᏍᎩᏯ ᎾᏍᏉ ᎠᏓᏅᏙ ᎢᎩᏍᏕᎵᎭ ᏗᏗᏩᎾᎦᎳᎯᏳ ᎨᏒᎢ; ᎥᏝᏰᏃ ᏱᏗᎦᏔᎭ ᎢᏳᏍᏗ ᏚᏳᎪᏛ ᎨᏒ ᎢᎩᏔᏲᏍᏗᏱ ᎢᏓᏓᏙᎵᏍᏗᏍᎬᎢ; ᎠᏓᏅᏙᏍᎩᏂ ᎤᏩᏒ ᎢᎦᎵᏍᏗᏰᏓᏁᎭ ᎤᎵᏰᏗᏍᎬ ᎬᏗᎭ ᎾᏍᎩ ᎦᏁᎢᏍᏗ ᏂᎨᏒᎾ ᎨᏒᎢ.
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Na-s-gi-ya na-s-quo A-da-nv-do i-gi-s-de-li-ha di-di-wa-na-ga-la-hi-yu ge-sv-i; v-tla-ye-no yi-di-ga-ta-ha i-yu-s-di du-yu-go-dv ge-sv i-gi-ta-yo-s-di-yi i-da-da-do-li-s-di-s-gv-i; A-da-nv-do-s-gi-ni u-wa-sv i-ga-li-s-di-ye-da-ne-ha u-li-ye-di-s-gv gv-di-ha na-s-gi ga-ne-i-s-di ni-ge-sv-na ge-sv-i.
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| And he that searcheth the hearts knoweth what is the mind of the Spirit, because he maketh intercession for the saints according to the will of God.
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| ᎠᎴ ᎾᏍᎩ Ꮎ ᏗᎪᎵᏰᏍᏗ ᏧᎾᏫ ᎠᎦᏔᎭ ᏄᏍᏛ ᎠᏓᏅᏖᎵᏙᎲ ᎠᏓᏅᏙ ᏅᏗᎦᎵᏍᏙᏗ ᎤᎾᏓᏅᏘ ᏓᎵᏍᏗᏰᏓᏁᎲ ᎾᏍᎩᏯ ᎤᏁᎳᏅᎯ ᎣᏏᏳ ᎤᏰᎸᏗ ᎨᏒᎢ.
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A-le na-s-gi na di-go-li-ye-s-di tsu-na-wi a-ga-ta-ha nu-s-dv a-da-nv-te-li-do-hv A-da-nv-do nv-di-ga-li-s-do-di u-na-da-nv-ti da-li-s-di-ye-da-ne-hv na-s-gi-ya U-ne-la-nv-hi o-si-yu u-ye-lv-di ge-sv-i.
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| And we know that all things work together for good to them that love God, to them who are the called according to his purpose.
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| ᎠᎴ ᎢᏗᎦᏔᎭ ᎾᏍᎩ ᏂᎦᎥ ᏂᏚᎵᏍᏔᏂᏙᎲ ᎤᎾᏖᏆᎶᏒ ᎣᏍᏛ ᎢᏳᎾᎵᏍᏓᏁᏗᏱ ᏚᏂᎸᏫᏍᏓᏁᎲ ᎤᏁᎳᏅᎯ ᎤᏂᎨᏳᎯ, ᎾᏍᎩ Ꮎ ᎨᏥᏯᏅᏛ ᏥᎩ ᎾᏍᎩᏯ ᎤᏓᏅᏖᎸᎢ.
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A-le i-di-ga-ta-ha na-s-gi ni-ga-v ni-du-li-s-ta-ni-do-hv u-na-te-qua-lo-sv o-s-dv i-yu-na-li-s-da-ne-di-yi du-ni-lv-wi-s-da-ne-hv U-ne-la-nv-hi u-ni-ge-yu-hi, na-s-gi na ge-tsi-ya-nv-dv tsi-gi na-s-gi-ya u-da-nv-te-lv-i.
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| For whom he did foreknow, he also did predestinate to be conformed to the image of his Son, that he might be the firstborn among many brethren.
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| ᎾᏍᎩᏰᏃ ᎦᏳᎳ ᏥᏂᏓᎦᏔᎰᎢ, ᎾᏍᎩ ᎾᏍᏉ ᏂᏚᏑᏰᏐ ᎤᏪᏥ ᏄᏍᏛ ᎾᏍᎩᏯ ᎢᏳᎾᎵᏍᏙᏗᏱ, ᎾᏍᎩ ᎢᎬᏱ ᎡᎯ ᎢᏳᎵᏍᏙᏗᏱ ᎤᏂᏣᏘ ᎠᎾᎵᏅᏟ ᎠᏁᎲᎢ.
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Na-s-gi-ye-no ga-yu-la tsi-ni-da-ga-ta-ho-i, na-s-gi na-s-quo ni-du-su-ye-so U-we-tsi nu-s-dv na-s-gi-ya i-yu-na-li-s-do-di-yi, na-s-gi i-gv-yi e-hi i-yu-li-s-do-di-yi u-ni-tsa-ti a-na-li-nv-tli a-ne-hv-i.
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| Moreover whom he did predestinate, them he also called: and whom he called, them he also justified: and whom he justified, them he also glorified.
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| ᎾᏍᎩᏃ ᎦᏳᎳ ᏥᏂᏚᏑᏰᏐᎢ ᎾᏍᎩ ᎾᏍᏉ ᏚᏯᏅᎮᎢ; ᎠᎴ ᎾᏍᎩ ᏧᏯᏅᏛ ᎨᏒᎢ, ᎾᏍᎩ ᎾᏍᏉ ᏚᏭᏓᎴᏎᎢ; ᎠᎴ ᎾᏍᎩ ᏧᏭᏓᎴᏛ ᎨᏒ, ᎾᏍᎩ ᎾᏍᏉ ᎦᎸᏉᏗᏳ ᏂᏚᏩᏁᎴᎢ.
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Na-s-gi-no ga-yu-la tsi-ni-du-su-ye-so-i na-s-gi na-s-quo du-ya-nv-he-i; a-le na-s-gi tsu-ya-nv-dv ge-sv-i, na-s-gi na-s-quo du-wu-da-le-se-i; a-le na-s-gi tsu-wu-da-le-dv ge-sv, na-s-gi na-s-quo ga-lv-quo-di-yu ni-du-wa-ne-le-i.
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| What shall we then say to these things? If God be for us, who can be against us?
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| ᎦᏙᏃ ᏓᏓᏛᏂ ᎯᎠ ᎾᏍᎩ ᏥᏄᏍᏗ? ᎢᏳᏃ ᎤᏁᎳᏅᎯ ᏱᎩᏍᏕᎵᎭ ᎦᎪ ᏱᎦᏡᏓ?
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Ga-do-no da-da-dv-ni hi-a na-s-gi tsi-nu-s-di? i-yu-no U-ne-la-nv-hi yi-gi-s-de-li-ha ga-go yi-ga-tlu-da?
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| He that spared not his own Son, but delivered him up for us all, how shall he not with him also freely give us all things?
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| ᎾᏍᎩ Ꮎ ᏄᎨᏳᏅᎾ ᏥᎨᏎ ᎤᏩᏒ ᎤᏪᏥ, ᏥᏚᏲᏎᏉᏍᎩᏂ ᎠᏴ ᏂᏗᎥ ᎢᎩᏍᏕᎵᏍᎬᎢ, ᎦᏙ ᏱᎦᎵᏍᏙᏓ ᎾᏍᎩ ᏕᎩᏲᎯᏎᎲ ᎠᏎᏉ ᏗᎨᎩᏲᎯᏎᏗ ᏂᎨᏒᎾ ᏱᏂᎦᎵᏍᏓ ᏂᎦᏗᏳ ᎪᎱᏍᏗ?
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Na-s-gi na nu-ge-yu-nv-na tsi-ge-se u-wa-sv U-we-tsi, tsi-du-yo-se-quo-s-gi-ni a-yv ni-di-v i-gi-s-de-li-s-gv-i, ga-do yi-ga-li-s-do-da na-s-gi de-gi-yo-hi-se-hv a-se-quo di-ge-gi-yo-hi-se-di ni-ge-sv-na yi-ni-ga-li-s-da ni-ga-di-yu go-hu-s-di?
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| Who shall lay any thing to the charge of God's elect? It is God that justifieth.
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| ᎦᎪ ᎤᏂᏍᎦᏅᏨ ᏙᏓᎫᎯᏍᏔᏂ ᎤᎾᎴᏅᎯ ᏧᏑᏰᏛ? ᏥᎪ ᎤᏁᎳᏅᎯ, ᎾᏍᎩ ᎤᏄᏓᎴᏍᎩ?
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Ga-go u-ni-s-ga-nv-tsv do-da-gu-hi-s-ta-ni U-na-le-nv-hi tsu-su-ye-dv? tsi-go U-ne-la-nv-hi, na-s-gi u-nu-da-le-s-gi?
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| Who is he that condemneth? It is Christ that died, yea rather, that is risen again, who is even at the right hand of God, who also maketh intercession for us.
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| ᎦᎪ ᏧᏄᎪᏓᏁᎯ? ᎦᎶᏁᏛᏍᎪ, ᎾᏍᎩ ᏧᏂᎱᏎᎢ, ᎥᎥ, ᎠᎴ ᎾᏍᏉ ᎾᏍᎩ ᏥᏚᎴᎯᏌᏅ, ᎾᏍᎩ ᎾᏍᏉ ᎤᏁᎳᏅᎯ ᎠᎦᏗᏏᏗᏢ ᏧᏬᎳ, ᎾᏍᎩ ᎾᏍᏉ ᏥᎦᎵᏍᏗᏰᏓᏁᎭ?
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Ga-go tsu-nu-go-da-ne-hi? Ga-lo-ne-dv-s-go, na-s-gi tsu-ni-hu-se-i, v-v, a-le na-s-quo na-s-gi tsi-du-le-hi-sa-nv, na-s-gi na-s-quo U-ne-la-nv-hi a-ga-di-si-di-tlv tsu-wo-la, na-s-gi na-s-quo tsi-ga-li-s-di-ye-da-ne-ha?
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| Who shall separate us from the love of Christ? shall tribulation, or distress, or persecution, or famine, or nakedness, or peril, or sword?
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| ᎦᎪ ᎢᏴᏛ ᏅᏓᎬᏁᎵ ᎦᎶᏁᏛ ᎢᎩᎨᏒᎢ? ᏥᎪ ᎠᎩᎵᏲᎢᏍᏗ ᎨᏒᎢ, ᎠᎴ ᎤᏪᎵᎯᏍᏗ ᎠᏓᏅᏓᏗᏍᏗ ᎨᏒᎢ, ᎠᎴ ᎤᏲ ᎢᏴᏓᏛᏁᏗ ᎨᏒᎢ, ᎠᎴ ᎤᏓᎪᏄᎶᎯᏍᏗ ᎨᏒᎢ, ᎠᎴ ᏗᎩᏰᎸᎭ ᎨᏒᎢ, ᎠᎴ ᎤᎾᏰᎯᏍᏗ ᎨᏒᎢ, ᎠᎴ ᎠᏰᎳᏍᏗ-ᎦᏅᎯᏛ?
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Ga-go i-yv-dv nv-da-gv-ne-li Ga-lo-ne-dv i-gi-ge-sv-i? tsi-go a-gi-li-yo-i-s-di ge-sv-i, a-le u-we-li-hi-s-di a-da-nv-da-di-s-di ge-sv-i, a-le u-yo i-yv-da-dv-ne-di ge-sv-i, a-le u-da-go-nu-lo-hi-s-di ge-sv-i, a-le di-gi-ye-lv-ha ge-sv-i, a-le u-na-ye-hi-s-di ge-sv-i, a-le a-ye-la-s-di--ga-nv-hi-dv?
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| As it is written, For thy sake we are killed all the day long; we are accounted as sheep for the slaughter.
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| ᎾᏍᎩᏯ ᎯᎠ ᏥᏂᎬᏅ ᏥᎪᏪᎳ, ᏂᎯ ᎨᏒ ᏅᏗᎦᎵᏍᏙᏗᎭ ᏙᎩᎢᎭ ᏂᎪᎯᎸᎢ; ᎤᏂᏃᏕᎾᏉ ᏗᎯᏍᏗ ᎾᏍᎩᏯ ᎣᎩᏰᎸᎠ;
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Na-s-gi-ya hi-a tsi-ni-gv-nv tsi-go-we-la, Ni-hi ge-sv nv-di-ga-li-s-do-di-ha do-gi-i-ha ni-go-hi-lv-i; u-ni-no-de-na-quo di-hi-s-di na-s-gi-ya o-gi-ye-lv-a;
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| Nay, in all these things we are more than conquerors through him that loved us.
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| ᎠᏎᏃ ᎯᎠ ᎾᏍᎩ ᏂᎦᏛ ᏧᏓᎴᏅᏛ ᎨᏒ ᎢᏓᏓᏎᎪᎩᏍᎩ ᎠᎴ ᎤᏟ ᎢᎦᎢ, ᎾᏍᎩ Ꮎ ᎢᎩᎨᏳᎯᏳ ᎢᏳᎵᏍᏔᏅᎯ ᏥᎩ ᎢᏳᏩᏂᏌᏛ.
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A-se-no hi-a na-s-gi ni-ga-dv tsu-da-le-nv-dv ge-sv i-da-da-se-go-gi-s-gi a-le u-tli i-ga-i, na-s-gi na i-gi-ge-yu-hi-yu i-yu-li-s-ta-nv-hi tsi-gi i-yu-wa-ni-sa-dv.
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| For I am persuaded, that neither death, nor life, nor angels, nor principalities, nor powers, nor things present, nor things to come,
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| ᎤᎵᏂᎩᏛᏰᏃ ᎠᏉᎯᏳᎭ, ᎾᏍᎩ ᎥᏝ ᎠᏲᎱᎯᏍᏗ ᎨᏒᎢ, ᎠᎴ ᎠᏛᏂᏗᏍᏗ ᎨᏒᎢ, ᎠᎴ ᏗᏂᎧᎿᎭᏩᏗᏙᎯ, ᎠᎴ ᏄᏂᎬᏫᏳᏌᏕᎩ, ᎠᎴ ᎨᏥᎸᏉᏗ, ᎠᎴ ᎪᎱᏍᏗ ᎪᎯ ᏤᎭ, ᎠᎴ ᎪᎱᏍᏗ ᎠᏏ ᎤᎾᏄᎪᎢᏍᏗ ᏥᎩ,
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U-li-ni-gi-dv-ye-no a-quo-hi-yu-ha, na-s-gi v-tla a-yo-hu-hi-s-di ge-sv-i, a-le a-dv-ni-di-s-di ge-sv-i, a-le di-ni-ka-hna-wa-di-do-hi, a-le nu-ni-gv-wi-yu-sa-de-gi, a-le ge-tsi-lv-quo-di, a-le go-hu-s-di go-hi tse-ha, a-le go-hu-s-di a-si u-na-nu-go-i-s-di tsi-gi,
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| Nor height, nor depth, nor any other creature, shall be able to separate us from the love of God, which is in Christ Jesus our Lord.
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| ᎥᏝ ᎠᎴ ᎦᎸᎳᏗᏳ ᎨᏒᎢ, ᎠᎴ ᎭᏫᏂᏳ ᎨᏒᎢ, ᎥᏝ ᎠᎴ ᏅᏩᏓᎴ ᎠᏁᎳᏅᎯ ᎨᏒᎢ, ᏰᎵ ᎢᏴᏛ ᎢᎬᏩᏁᏗ ᏱᎨᏎᏍᏗ ᎤᏁᎳᏅᎯ ᎢᎩᎨᏳᏒᎢ, ᎾᏍᎩ ᎦᎶᏁᏛ ᏥᏌ ᎤᎬᏫᏳᎯ ᎢᎦᏤᎵ ᏅᏓᏳᏓᎴᏅᎯ ᏥᎩ.
|
|---|
V-tla a-le ga-lv-la-di-yu ge-sv-i, a-le ha-wi-ni-yu ge-sv-i, v-tla a-le nv-wa-da-le a-ne-la-nv-hi ge-sv-i, ye-li i-yv-dv i-gv-wa-ne-di yi-ge-se-s-di U-ne-la-nv-hi i-gi-ge-yu-sv-i, na-s-gi Ga-lo-ne-dv Tsi-sa U-gv-wi-yu-hi i-ga-tse-li nv-da-yu-da-le-nv-hi tsi-gi.
|
|---|


The objective of this lesson is to understand the concepts of Scope and Encapsulation in JavaScript. Please check the console to see the results.


Jeb's first match was him facing a sneaky opponent that had instinctively good timing for finding points. Unfortunately, Jeb gave up a few points in the beginning and was forced to look for points aggressively. Jeb showed much better control and movement later, but his opponent was able to end with a bigger lead than the match reflected when Jeb tried hard to tie at the end (11-18 L). The way Jeb is fighting and moving about, I feel like the match would have been completely different if the opponent hadn't got the early lead. Working on blocking effectively will make a big difference against this type of opponent in the future.


In this post I am giving a quick overview of how to create editable plots in PowerPoint from R. These plots are comprised of simple vector-based shapes and thus allow you to change labels, colours, or text position in seconds. Your project managers will love it!
Motivation
R allows us to create great visualisations, but in most data science settings these need to be presented to key stakeholders and decision makers in presentations or “slideuments”. Having to make small changes to previously compiled slots can be time consuming and frustrating. A solution to this common problem is to keep your plots and graphs editable as a group of vector shapes in PowerPoint. This way project managers or data scientists themselves can make small changes without having to re-execute a single line of code.
Solution
We will use a tidyverse approach for creating the plot. Furthermore, the
officer
package enables us to smoothly interact with PowerPoint, and the rvg
package is required to save our plots as editable vector graphs.
library(tidyverse)
library(officer)
library(rvg)
For demonstration purposes, let’s create a plot using the diamonds dataset.
NB: I am saving the ggplot object to a variable name, but also displaying the
plot when executing the lines by appending the ; ggp
at the end.
# Using diamonds dataset which is shipped with R
ggp <- diamonds %>%
# Let's simplify things by only considering natural number carats
mutate(carat = floor(carat)) %>%
group_by(carat, cut, clarity, color) %>%
summarise(price = mean(price)) %>%
# Create a plot of price by carat, colour, cut, and clarity
ggplot(aes(x = carat, y = price, fill = color)) +
geom_bar(stat = 'identity') +
facet_grid(cut ~ clarity) +
# Simplify the plot layout a little
theme_bw() +
guides(fill = FALSE) +
theme(panel.grid.major.x = element_blank(),
panel.grid.minor.x = element_blank()); ggp
Now we can use officer
to create a new PowerPoint document and
rvg::ph_with_vg
to drop our ggplot object in there.
# Create a new powerpoint document
doc <- read_pptx()
doc <- add_slide(doc, 'Title and Content', 'Office Theme')
# Add the plot
doc <- ph_with_vg(doc, ggobj = ggp, type = 'body')
# Write the document to a file
print(doc, target = 'plot.pptx')
Now open the document in PowerPoint. Right-click and ungroup the plot. Voila! You should be able to select individual elements, for example the data bars in the plot, change their colour, move them around, change the text in labels, and much more. Have a look at the plot below. A cookie for you if you can find all ten edits that I made in the example.
As always, hope this is helpful. And FYI, I am still looking for a way to
achieve the same result using Python
. If you know one, collect some bounty
here


Tool comming soon...
For more information please visit https://www.synapse.org/#!Synapse:syn2785778/wiki/70252
For more information about the community please visit http://dreamchallenges.org


title = "Leaderboard" url = "/leaderboard" layout = "in-gallery-screen" hidden = "0" [Leaderboard] ==
{{ "now"|date("l F jS, Y") }}


| Package | Description |
|---|---|
| org.bouncycastle.asn1 |
A library for parsing and writing ASN.1 objects.
|
| org.bouncycastle.asn1.anssi | |
| org.bouncycastle.asn1.bc |
ASN.1 classes specific to the Bouncy Castle APIs.
|
| org.bouncycastle.asn1.bsi |
ASN.1 classes specific to the Bundesamt für Sicherheit in der Informationstechnik (BSI) standards.
|
| org.bouncycastle.asn1.cmp |
Support classes useful for encoding and supporting PKIX-CMP as described RFC 4210.
|
| org.bouncycastle.asn1.cms |
Support classes useful for encoding and supporting Cryptographic Message Syntax as described in PKCS#7 and RFC 3369 (formerly RFC 2630).
|
| org.bouncycastle.asn1.cms.ecc |
Support classes for CMS ECC - RFC 5753/3278.
|
| org.bouncycastle.asn1.crmf |
Support classes useful for encoding and supporting PKIX-CRMF as described RFC 4211.
|
| org.bouncycastle.asn1.cryptopro |
Support classes for CRYPTO-PRO related objects - such as GOST identifiers.
|
| org.bouncycastle.asn1.dvcs |
Support classes useful for encoding and processing Data Validation and Certification Server (DVCS) protocols as described in RFC 3029.
|
| org.bouncycastle.asn1.eac |
ASN.1 classes specific to the Bundesamt für Sicherheit in der Informationstechnik (BSI) Technical Guideline Advanced Security Mechanisms for Machine Readable Travel Documents.
|
| org.bouncycastle.asn1.esf |
Support classes useful for encoding and supporting [ESF] RFC3126
Electronic Signature Formats for long term electronic signatures.
|
| org.bouncycastle.asn1.ess |
Support classes useful for encoding and supporting Enhanced Security Services for S/MIME as described RFC 2634 and RFC 5035.
|
| org.bouncycastle.asn1.gnu |
ASN.1 classes specific to the GNU APIs and applications.
|
| org.bouncycastle.asn1.iana |
ASN.1 classes specific to the Internet Assigned Numbers Authority (IANA).
|
| org.bouncycastle.asn1.icao |
ICAO ASN.1 classes for electronic passport.
|
| org.bouncycastle.asn1.isismtt |
Support classes for the ISIS-MTT Project.
|
| org.bouncycastle.asn1.isismtt.ocsp |
Support classes for the ISIS-MTT profile for OCSP.
|
| org.bouncycastle.asn1.isismtt.x509 |
Support classes for the ISIS-MTT X.509 Certificate Extensions.
|
| org.bouncycastle.asn1.iso | |
| org.bouncycastle.asn1.kisa |
Support classes for the Korea Information Security Agency (KISA) standard - SEED algorithm.
|
| org.bouncycastle.asn1.microsoft |
Support for Microsoft specific ASN.1 classes and object identifiers.
|
| org.bouncycastle.asn1.misc |
Miscellaneous object identifiers and objects.
|
| org.bouncycastle.asn1.mozilla |
Support classes useful for encoding objects used by mozilla.
|
| org.bouncycastle.asn1.nist |
Support classes for NIST related objects.
|
| org.bouncycastle.asn1.ntt |
ASN.1 classes relevant to the standards produced by Nippon Telegraph and Telephone.
|
| org.bouncycastle.asn1.ocsp |
Support classes useful for encoding and supporting OCSP objects.
|
| org.bouncycastle.asn1.oiw |
Objects and OID for the support of ISO OIW.
|
| org.bouncycastle.asn1.pkcs |
Support classes useful for encoding and supporting the various RSA PKCS documents.
|
| org.bouncycastle.asn1.sec |
Classes for support of the SEC standard for Elliptic Curve.
|
| org.bouncycastle.asn1.smime |
Support classes useful for encoding and supporting S/MIME.
|
| org.bouncycastle.asn1.teletrust |
Support classes for TeleTrust related objects.
|
| org.bouncycastle.asn1.tsp |
Support classes useful for encoding and supporting Time Stamp Protocol as described RFC 3161.
|
| org.bouncycastle.asn1.ua |
Support classes for the Ukrainian DSTU standard.
|
| org.bouncycastle.asn1.util |
An ASN.1 dump utility.
|
| org.bouncycastle.asn1.x500 |
Support classes for the creation and processing of object based on X.500 names.
|
| org.bouncycastle.asn1.x500.style |
Template classes for the common styles used for converting X.500 names to strings and back.
|
| org.bouncycastle.asn1.x509 |
Support classes useful for encoding and processing X.509 certificates.
|
| org.bouncycastle.asn1.x509.qualified |
Support classes useful for encoding and processing messages based around RFC3739
|
| org.bouncycastle.asn1.x509.sigi |
Support classes for the German SigI (Signature Interoperability Specification) standard.
|
| org.bouncycastle.asn1.x9 |
Support classes useful for encoding and supporting X9.62 elliptic curve.
|
| Package | Description |
|---|---|
| org.bouncycastle.jcajce | |
| org.bouncycastle.jcajce.io | |
| org.bouncycastle.jcajce.spec | |
| org.bouncycastle.jcajce.util | |
| org.bouncycastle.jce |
Utility classes for use with the JCE.
|
| org.bouncycastle.jce.exception | |
| org.bouncycastle.jce.interfaces |
Interfaces for supporting Elliptic Curve Keys, El Gamal, and PKCS12 attributes.
|
| org.bouncycastle.jce.netscape | |
| org.bouncycastle.jce.spec |
Parameter specifications for supporting El Gamal, and Elliptic Curve.
|
| Package | Description |
|---|---|
| org.bouncycastle.crypto |
Base classes for the lightweight API.
|
| org.bouncycastle.crypto.agreement |
Basic key agreement classes.
|
| org.bouncycastle.crypto.agreement.jpake |
Support classes for Password Authenticated Key Exchange by Juggling (J-PAKE) key exchange.
|
| org.bouncycastle.crypto.agreement.kdf |
Support classes for KDF based key derivation functions.
|
| org.bouncycastle.crypto.agreement.srp |
Support classes for Secure Remote Password (SRP) protocol.
|
| org.bouncycastle.crypto.commitments |
Classes for supporting commitment calculation.
|
| org.bouncycastle.crypto.digests |
Message digest classes.
|
| org.bouncycastle.crypto.ec |
Utility classes for support Elliptic Curve cryptographic transforms.
|
| org.bouncycastle.crypto.encodings |
Block encodings for asymmetric ciphers.
|
| org.bouncycastle.crypto.engines |
Basic cipher classes.
|
| org.bouncycastle.crypto.examples |
Simple examples of light weight API usage.
|
| org.bouncycastle.crypto.generators |
Generators for keys, key pairs and password based encryption algorithms.
|
| org.bouncycastle.crypto.io |
Classes for doing "enhanced" I/O with Digests and MACs.
|
| org.bouncycastle.crypto.kems |
Key Encapsulation Mechanisms.
|
| org.bouncycastle.crypto.macs |
Classes for creating MACs and HMACs.
|
| org.bouncycastle.crypto.modes |
Modes for symmetric ciphers.
|
| org.bouncycastle.crypto.modes.gcm |
GCM mode support classes.
|
| org.bouncycastle.crypto.paddings |
Paddings for symmetric ciphers.
|
| org.bouncycastle.crypto.params |
Classes for parameter objects for ciphers and generators.
|
| org.bouncycastle.crypto.parsers |
Helper classes for parsing "on the wire" public keys.
|
| org.bouncycastle.crypto.prng |
Lightweight psuedo-random number generators and SecureRandom builders.
|
| org.bouncycastle.crypto.prng.drbg |
SP800-90A deterministic random bit generators, can be used stand alone or in conjunction with SP800SecureRandomBuilder class.
|
| org.bouncycastle.crypto.signers |
Basic signers.
|
| org.bouncycastle.crypto.tls |
A lightweight TLS API.
|
| org.bouncycastle.crypto.util |
Some general utility/conversion classes.
|
| Package | Description |
|---|---|
| org.bouncycastle.math | |
| org.bouncycastle.math.ec |
Math support for Elliptic Curve.
|
| org.bouncycastle.math.ec.custom.djb |
Experimental implementation of curve25519.
|
| org.bouncycastle.math.ec.custom.sec |
Custom implementations of (most of) the curves over Fp from the SEC specification.
|
| org.bouncycastle.math.ec.endo | |
| org.bouncycastle.math.ec.tools | |
| org.bouncycastle.math.field | |
| org.bouncycastle.math.raw |
Math support for raw multi-precision calculations.
|
| org.bouncycastle.util |
General purpose utility classes used throughout the APIs.
|
| org.bouncycastle.util.encoders |
Classes for producing and reading Base64 and Hex strings.
|
| org.bouncycastle.util.io |
General purpose I/O helper classes and wrappers.
|
| org.bouncycastle.util.io.pem |
Classes for reading and writing raw PEM objects.
|
| org.bouncycastle.util.test |
Light weight test API.
|
| Package | Description |
|---|---|
| org.bouncycastle.asn1.test |
Test programs for the ASN.1 package.
|
| org.bouncycastle.crypto.agreement.test | |
| org.bouncycastle.crypto.ec.test | |
| org.bouncycastle.crypto.prng.test | |
| org.bouncycastle.crypto.test |
Example code and test classes for the lightweight API.
|
| org.bouncycastle.crypto.test.cavp | |
| org.bouncycastle.crypto.tls.test | |
| org.bouncycastle.jce.provider.test | |
| org.bouncycastle.jce.provider.test.nist | |
| org.bouncycastle.jce.provider.test.rsa3 |
| Package | Description |
|---|---|
| org.bouncycastle.pqc.crypto | |
| org.bouncycastle.pqc.crypto.gmss | |
| org.bouncycastle.pqc.crypto.gmss.util | |
| org.bouncycastle.pqc.crypto.mceliece | |
| org.bouncycastle.pqc.crypto.ntru | |
| org.bouncycastle.pqc.crypto.rainbow | |
| org.bouncycastle.pqc.crypto.rainbow.util |
| Package | Description |
|---|---|
| org.bouncycastle.pqc.asn1 |
| Package | Description |
|---|---|
| org.bouncycastle.pqc.math.linearalgebra | |
| org.bouncycastle.pqc.math.ntru.euclid | |
| org.bouncycastle.pqc.math.ntru.polynomial | |
| org.bouncycastle.pqc.math.ntru.util |
| Package | Description |
|---|---|
| org.bouncycastle.pqc.crypto.test | |
| org.bouncycastle.pqc.jcajce.provider.test | |
| org.bouncycastle.pqc.math.ntru.euclid.test | |
| org.bouncycastle.pqc.math.ntru.polynomial.test | |
| org.bouncycastle.pqc.math.ntru.util.test |


Chapter 3 Growth curves
3.1 Between person models and cross sectional data
You already know this, but it gives us a chance to review regression
\[ {Y}_{i} = b_{0} + b_{1}X_{1} + b_{2}X_{2} + b_{3}X_{3}+... +\epsilon_{i} \]
\[ \hat{Y}_{i} = b_{0} + b_{1}X_{1} + b_{2}X_{2} + b_{3}X_{3}+... \]
Parameters are considered fixed where one regression value corresponds to everyone. I.e., that association between X1 and Y is the same for everyone.
Each person has a Y, denoted by the subscript i, and each has a residual associated with them, also designated by i.
library(readr,)
example <- read_csv("~/Box Sync/5165 Applied Longitudinal Data Analysis/Longitudinal/example.csv")
example$ID <- as.factor(example$ID)
Lets look at some data
library(tidyverse)
library(ggplot2)
gg1 <- ggplot(example,
aes(x = week, y = SMN7)) + geom_point() + stat_smooth(method = "lm")
print(gg1)
What happens if we run a regression?
regression <- lm(SMN7 ~ week, data = example)
summary(regression)
##
## Call:
## lm(formula = SMN7 ~ week, data = example)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.099294 -0.039929 -0.005938 0.032715 0.169885
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.100161 0.005261 19.039 <2e-16 ***
## week 0.004087 0.002563 1.595 0.112
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.05562 on 214 degrees of freedom
## (9 observations deleted due to missingness)
## Multiple R-squared: 0.01174, Adjusted R-squared: 0.007124
## F-statistic: 2.543 on 1 and 214 DF, p-value: 0.1123
3.2 Within person models e.g., 2-level models
library(tidyverse)
gg2 <- ggplot(example,
aes(x = week, y = SMN7, group = ID)) + geom_point() + stat_smooth(method = "lm", se = FALSE)
gg3 <- gg2 + stat_smooth(data = example, aes(x = week, y = SMN7, group=1, colour="#990000"), method = "lm", size = 3, se=FALSE)
print(gg3)
Each person has multiple assessments, so we now need to distinguish between people and their assessments. Failing to distinguish would lead to violation of independence, an important assumption of the standard regression model.
As seen in the graph above, what we have now is both individual level slopes as well as an average level slope. The average level slope is going to be the average of the individual level slopes, which will look like our average slope ignoring all dependencies. Same for the intercept.
## Joining, by = "ID"
regressions <- example2 %>%
group_by(ID) %>%
do(tidy(lm(SMN7 ~ week, data = .)))
head(regressions)
## # A tibble: 6 x 6
## # Groups: ID [3]
## ID term estimate std.error statistic p.value
## <fctr> <chr> <dbl> <dbl> <dbl> <dbl>
## 1 6 (Intercept) 0.04375163 0.019715849 2.2191095 0.26953127
## 2 6 week -0.01149513 0.016432601 -0.6995322 0.61139970
## 3 29 (Intercept) 0.11040000 NaN NaN NaN
## 4 29 week -0.03303298 NaN NaN NaN
## 5 48 (Intercept) 0.11333779 0.006560796 17.2750049 0.03681099
## 6 48 week 0.03097069 0.003240913 9.5561620 0.06637719
We also have variation around that mean. This variation is lost when we have a between subjects only model that ignores the individual level. This variation will be called Random Effects
Note, there is another source of error, the within-subjects error that can be seen in the below graph. This error is assumed to be random. We will discuss this error more in depth later.
example3 <- example2 %>%
filter(ID == "66")
gg4 <- ggplot(example3, aes(x = week, y = SMN7, group = ID)) + geom_point() + stat_smooth(method = "lm")
gg4
3.2.1 thinking about random effects
3.2.2 random effects
Within subjects variability in either staring value or slope is referenced in terms of random effects. How do we represent this in our equation? Easy, we just say that the typical regression parameters we have are not the same for everyone – that they are random (in contrast to fixed).
In general, when would we want to use random effects? If there is some sort of selection (random or not) of many possible values of the predictor (e.g., stimuli are 3 random depression drugs, three semi random chosen levels of a drug). With longitudinal data this is people.
What situations are necessary for random effects? For longitudinal models, there needs to be multiple assessments per your grouping category (people, schools, neighborhoods).
Random as in they are sampled from some population and thus can vary. This means that your parameters (traditional regression parameters) are estimates and thus have error associated with them. This error is not like like a standard residual, which represents error for your overall model. Nor is it like the standard error for a point estimate. Random effects can best be thought of as deviation of individual regression lines from the group regression line (though it technically is not this).
To facilitate the multiple assessments per person we will now use both i and j subscripts. We will see that the random effects are part of the overall error term in the model. Counterintutitively, the main focus of these types of models will be the fixed effects, with less attention paid to the random effects. That said, the random effects are necessary to account for dependency in the data. One can think about these models as normal fixed effects regressions, with the random effects there to account for the longitudinal nature of the data. They are made up of a number of standard regression equations, each for a single individual. Doing so side steps the trouble of having correlated errors, and thus allows us to interpret our findings without concern.
3.2.3 Empty model equation
Level 1 \[ {Y}_{ij} = \beta_{0j} +\varepsilon_{ij} \] Note that we have multiple responses per individual j, noted with an i to refer to specific times. Level 1 is considered the within person model.
Also note that the intercept has a subscript. In typical regression it does not. This suggests that not everyone has the same intercept.
The residuals at this level are thought of as measurment error OR as something that can be explained by time varying predictors.
Level 2 \[ {\beta}_{0j} = \gamma_{00} + U_{0j} \] Level 2 takes the intercept (or other parameter) at level 1 and breaks it down into an equation for each individual, j. An overall group average (the gamma) and a residual term specific to deviation around the intercept (see below).
And two variance components: 1. a random effect of the intercept \[ {U}_{0j} \sim \mathcal{N}(0, \tau_{00}^{2}) \] The subscript of the \(U_{0j}\) refers to the number of the parameter where 0 is the intercept, 1 is the first regression coefficient, and so on. The second refers to the individual, j.
This random effect is normally distributed with a mean of zero and a variance of \(\tau\)
- the residual error term \[ {R}_{ij} \sim \mathcal{N}(0, \sigma^{2}) \] Much like in normal regression there is an error term for all of the variation we cannot account for. What is unique here is that we took that normal variation and split it into two components. One that is attributable to variation around the intercept \({U}_{0j}\) and a catch all residual.
Technically this is not a growth model, nor one that is inherently longitudinal. However, it does serve as a nice starting point to identify random effects.
3.2.4 Putting it together
\[ {Y}_{ij} = \gamma_{00} + U_{0j} + \varepsilon_{ij} \]
Random as in they are sampled from some population and thus can vary. This means that your parameters (traditional regression parameters) are estimates and thus have error associated with them. This error is not like like a standard residual, which represents error for your overall model. Nor is it like the standard error for a point estimate. Random effects can best be thought of as deviation of individual regression lines from the group regression line.
To facilitate the multiple assessments per person we will now use both i and j subscripts. We will see that the random effects are part of the overall error term in the model. Counterintutitively, the main focus of these types of models will be the fixed effects, with less attention paid to the random effects. That said, the random effects are necessary to account for dependency in the data. One can think about these models as normal fixed effects regressions, with the random effects there to account for the longitudinal nature of the data. They are made up of a number of standard regression equations, each for a single individual. Doing so side steps the trouble of having correlated errors, and thus allows us to interpret our findings without concern.
3.2.5 Empty model
Level 1 \[ {Y}_{ij} = \beta_{0j} +\varepsilon_{ij} \] Note that we have multiple responses per individual j, noted with an i to refer to specific times. Level 1 is considered the within person model.
Also note that the intercept has a subscript. In typical regression it does not. This suggests that not everyone has the same intercept.
Level 2 \[ {\beta}_{0j} = \gamma_{00} + U_{0j} \] Level 2 takes the intercept (or other parameter) at level 1 and breaks it down into an equation for each individual, j. An overall group average (the gamma) and a residual term specific to deviation around the intercept (see below).
And two variance components: 1. a random effect of the intercept \[ {U}_{0j} \sim \mathcal{N}(0, \tau_{00}^{2}) \] The subscript of the \(U_{0j}\) refers to the number of the parameter where 0 is the intercept, 1 is the first regression coefficient, and so on. The second refers to the individual, j.
This random effect is normally distributed with a mean of zero and a variance of \(\tau\)
- the residual error term \[ {R}_{ij} \sim \mathcal{N}(0, \sigma^{2}) \] Much like in normal regression there is an error term for all of the variation we cannot account for. What is unique here is that we took that normal variation and split it into two components. One that is attributable to variation around the intercept \({U}_{0j}\) and a catch all residual.
Technically this is not a growth model, nor one that is inherently longitudinal. However, it does serve as a nice starting point to identify random effects.
3.2.6 Putting it together
\[ {Y}_{ij} = \gamma_{00} + U_{0j} + \varepsilon_{ij} \]
3.2.7 ICC
ICC:
\[\frac{U_{0j}}{U_{0j}+ \varepsilon_{ij}}\]
- % variation between vs within person variance
3.3 Adding time
Level 1:
\[ {Y}_{ij} = \beta_{0j} + \beta_{1j}X_{ij} + \varepsilon_{ij} \]
Note how similar this looks like to a normal regression equation. Again, the differences are due to those pesky subscripts. Like before, think of this as a normal regression equation at the level of a person. Each person would have one of these equations with, in addition to a unique Y, X and residual, a unique \(\beta_{0}\) and \(\beta_{1}\).
Level 2:
\[ {\beta}_{0j} = \gamma_{00} + U_{0j}\]
Level 2 takes the parameters at level 1 and decomposes them into a fixed component that reflects that average and then the individual deviations around that fixed effect.
\[ {\beta}_{1j} = \gamma_{10} \]
The new level 2 term refers to the first predictor in the level 1 regression equation ie the slope. This slope is fixed in that the level 2 equation only has a gamma term and no U residual term.
Putting it together: \[ {Y}_{ij} = \gamma_{00} + \gamma_{10} (X_{1j})+ U_{0j} + \varepsilon_{ij} \]
Note that in computing a single individuals Y, it depends on the two fixed effects, the Xj, and the random effect for the intercept.
3.3.1 What does this look like graphically?
And how does this differ from the random intercept model?
What does this look like graphically?
Can you draw out the sources of error? The random effects for each participant? The fixed effects?
3.3.2 Adding a random slope?
What happens when we add a random slope? Level 1:
\[ {Y}_{ij} = \beta_{0j} + \beta_{1j}X_{1j} + \varepsilon_{ij} \] Level 2:
\[ {\beta}_{0j} = \gamma_{00} + U_{0j}\]
\[ {\beta}_{1j} = \gamma_{10} + U_{1j} \]
\[ {Y}_{ij} = \gamma_{00} + \gamma_{10}(X_{ij})+ U_{0j} + U_{1j}(X_{ij}) + \varepsilon_{ij} \]
Can think of a persons score divided up into a fixed component as well as the random component.
These random effects are likely related to one another. For example, if someone starts high on a construct they are then less likely to increase across time. This negative correlation can be seen in the residual structure, where the random effects are again normally distributed with a mean of zero, but this time one must also consider covariance in addition to variance.
\[ \begin{pmatrix} {U}_{0j} \\ {U}_{1j} \end{pmatrix} \sim \mathcal{N} \begin{pmatrix} 0, & \tau_{00}^{2} & \tau_{01}\\ 0, & \tau_{01} & \tau_{10}^{2} \end{pmatrix} \]
Note that it is possible to have a different error structure, one where there is no relationship between the intercept and the slope. We will discuss this more later in the semester. Right now just know that the default is to have correlated random effects.
We also have the within subject variance term that accounts for deviations that are not accounted for by time variable and other level 1 predictors.
\[ {R}_{ij} \sim \mathcal{N}(0, \sigma^{2}) \]
Note that it is possible to model these level 1 residuals with different structures. This specification implies that there is no correlation across an individuals residuals, once you account for level 1 predictors (ie growth trajectories). Having a specific level 1 autoregressive or other type of pattern is common in other treatments of longitudinal models (panel models) but is not necessary with growth models (but possible).
This is the basic format of the growth model. It will be expanded later on by adding variables to the level 1 model and to the level 2 model. Adding to the level 1 model is only possible with repeated variables.
Level 1 regression coefficients are added to the level 2 model. These coefficients are decomposed into a fixed effect, a random effect (possibly), and between person predictors. As with any regression model, each of these only have a single error term.
3.4 Individaul level random effects
3.4.1 Calculation of individaul level random effects
Random effects are often thought in terms of variance components. We can see this if we think of individual level regressions for each person where we then have a mean and a variance for both the intercept or the slope. The greater the variance around the intercept and the slope means that not everyone starts at the same position and not everyone changes at the same rate.
If you want to look at a specific person’s random effect you can think of it as a deviation from the fixed effect where subject 6’s intercept can be thought of as
\[ {\beta}_{06} = \gamma_{00} \pm U_{06}\] e.g 2.2 = 3 - .8
3.4.2 How are these random effects calculated?
It isn’t as straightforward as calculating a slope for each person and then using the difference between that slope and the average slope. Instead, the estimates are partially pooled towards the overall mean of the sample, the fixed effect. We do this to get a better estimate of the parameters, the same way that using regression to predict y-hat given an X is better than binning X and calculating y-hat. More information = better.
Why not full pooling? Because it ignores individaul differences in change.
The result is that the variance of the change trajectories (using MLM) will be smaller than the variance of the fitted linear models.
3.4.3 random effects and residual (standard) assumptions
Joint normal distribution of random effects
Normally distributed residual
Constant variance over time
Random effects and residual are uncorrelated
Both have a mean of zero
Random effects and residual size will depend on predictors in the model.
3.4.4 Random effect decomposition
Think of the original total variance in a scatter plot of our DVs. Adding random effects takes that variance and trims it down.
The intercept only MLM seperates it into a level 1 variance (which at this stage is treated as error) and a level 2 random intercept variance.
Creating a random slopes model takes the Level 1 residual variance and creates a new “pile” of explained variance.
3.5 working with models in R
3.5.1 basic lmer code
The basic function we will work with is lmer from the lme4 package
library(lme4)
## Loading required package: Matrix
##
## Attaching package: 'Matrix'
## The following object is masked from 'package:tidyr':
##
## expand
The package was developed to be similar to the lm function. The code will be similar to the formula for the combined model
Code for empty model
lmer(Y ~ 1 + (1 | subjects), data=example)
Level 1 \[ {Y}_{ij} = \beta_{0j} +\varepsilon_{ij} \] Level 2 \[ {\beta}_{0j} = \gamma_{00} + U_{0j} \]
Combined \[ {Y}_{ij} = \gamma_{00} + U_{0j} + \varepsilon_{ij} \]
1 is the way to reference the intercept. All additional fixed effects go outside the parentheses. Inside the parentheses are the random effects and residual terms. To the right of the vertical line is our level 1 residual term, which references the grouping variable. In this case, as with almost all longitudinal work, is the subject ID. To the left of the vertical line is the random effects we want to estimate. Right now this estimates only one random effect, one for the intercept.
It is possible to suppress a random intercept by putting a zero instead of a 1. If you do not put anything there the 1 is implied.
lmer(y ~ 1 + time + (1 + time | subjects), data=data)
lmer(y ~ time + (time | subjects), data=data)
# both are equivalent
3.5.2 Example
mod.1 <- lmer(SMN7 ~ 1 + (1 | ID), data=example)
summary(mod.1)
## Linear mixed model fit by REML ['lmerMod']
## Formula: SMN7 ~ 1 + (1 | ID)
## Data: example
##
## REML criterion at convergence: -714.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.1575 -0.4728 -0.0232 0.4512 3.2750
##
## Random effects:
## Groups Name Variance Std.Dev.
## ID (Intercept) 0.001823 0.04270
## Residual 0.001302 0.03608
## Number of obs: 225, groups: ID, 91
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.106972 0.005106 20.95
3.5.3 How to calculate ICC?
0.001823/(0.001823 + 0.001302)
## [1] 0.58336
3.6 Exploring beyond the summary
class(mod.1)
## [1] "lmerMod"
## attr(,"package")
## [1] "lme4"
3.6.1 what do the random effects look like?
library(sjPlot)
sjp.lmer(mod.1, facet.grid = FALSE,
sort = "sort.all")
Best Linear Unbiased Predictor = BLUP.  Lets calculate ID 6 intercept random effect
#coef = fixef + raneff
# coef for ID = 6 is 0.04724795
0.106972 -0.0597240676
## [1] 0.04724793
To get residuals and fitted scores
library(broom)
example.aug<- augment(mod.1, data = example)
## Warning: Deprecated: please use `purrr::possibly()` instead
## Warning: Deprecated: please use `purrr::possibly()` instead
## Warning: Deprecated: please use `purrr::possibly()` instead
## Warning: Deprecated: please use `purrr::possibly()` instead
## Warning: Deprecated: please use `purrr::possibly()` instead
# .fitted = predicted values
# .resid = residuals/errors
# .fixed = predicted values with no random effects
3.7 Adding time to the MLM
3.7.1 fixed slope
mod.2f <- lmer(SMN7 ~ 1 + week + (1 | ID), data=example)
summary(mod.2f)
## Linear mixed model fit by REML ['lmerMod']
## Formula: SMN7 ~ 1 + week + (1 | ID)
## Data: example
##
## REML criterion at convergence: -675.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.2308 -0.4868 -0.0377 0.4542 3.2337
##
## Random effects:
## Groups Name Variance Std.Dev.
## ID (Intercept) 0.001815 0.04261
## Residual 0.001300 0.03606
## Number of obs: 216, groups: ID, 88
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.104041 0.005733 18.147
## week 0.001331 0.001755 0.758
##
## Correlation of Fixed Effects:
## (Intr)
## week -0.426
What does this look like graphically?
3.7.2 Random slope
mod.2 <- lmer(SMN7 ~ 1 + week + (week | ID), data=example)
summary(mod.2)
## Linear mixed model fit by REML ['lmerMod']
## Formula: SMN7 ~ 1 + week + (week | ID)
## Data: example
##
## REML criterion at convergence: -678.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.9333 -0.4702 -0.0040 0.4699 2.6797
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## ID (Intercept) 1.688e-03 0.041081
## week 5.998e-05 0.007745 0.11
## Residual 1.114e-03 0.033380
## Number of obs: 216, groups: ID, 88
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.1047192 0.0054662 19.158
## week 0.0004891 0.0019133 0.256
##
## Correlation of Fixed Effects:
## (Intr)
## week -0.339
How does the intercept change from the random intercpet only model? It may change because the intercept is now conditional on time ie after accounting for time. It is not the predicted outcome when time = 0. You can think of the previous intercept as the grand mean of person means. If our week variable here changed across time then there would be a larger change in the intercept.
How do you interpret week?
How did the random effects change?
<IP_ADDRESS> Why treating time is so important
Time with a different scale. How do we interpret? And what changes?
example$week.n <- (example$week - 30)
mod.2n <- lmer(SMN7 ~ 1 + week.n + (week.n | ID), data=example)
summary(mod.2n)
## Linear mixed model fit by REML ['lmerMod']
## Formula: SMN7 ~ 1 + week.n + (week.n | ID)
## Data: example
##
## REML criterion at convergence: -678.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.9333 -0.4702 -0.0040 0.4699 2.6797
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## ID (Intercept) 5.770e-02 0.240217
## week.n 5.998e-05 0.007745 0.99
## Residual 1.114e-03 0.033380
## Number of obs: 216, groups: ID, 88
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.1193933 0.0557850 2.140
## week.n 0.0004891 0.0019133 0.256
##
## Correlation of Fixed Effects:
## (Intr)
## week.n 0.996
3.8 Random effects
3.8.1 Calcualtion of random effect confidence interval
Conveys the predicted range around each fixed effect in which 95% of the sample individauls are predicted to fall.
95% random effect = fixed effect plus minus 1.96 * random standard deviation
How to calcualte? 1. Intercept \[ \gamma_{00} \pm 1.96 * \tau_{U_{0j}} \]
0.1193933 + (1.96 * 0.240217)
## [1] 0.5902186
0.1193933 - (1.96 * 0.240217)
## [1] -0.351432
- Slope \[ \gamma_{10} \pm 1.96 * \tau_{U_{1j}} \]
0.0004891 + (1.96 * 0.007745)
## [1] 0.0156693
0.0004891 - (1.96 * 0.007745)
## [1] -0.0146911
3.8.2 Individaul level random effects
Are the intercept random effects the same as the model with only the intercept?  Lets calculate ID 6 intercept random effect
#coef = fixef + raneff
# 0.04724795
0.106972 -0.0597240676
## [1] 0.04724793
To get residuals and fitted scores
library(broom)
example.aug<- augment(mod.1, data = example)
## Warning: Deprecated: please use `purrr::possibly()` instead
## Warning: Deprecated: please use `purrr::possibly()` instead
## Warning: Deprecated: please use `purrr::possibly()` instead
## Warning: Deprecated: please use `purrr::possibly()` instead
## Warning: Deprecated: please use `purrr::possibly()` instead
# .fitted = predicted values
# .resid = residuals/errors
# .fixed = predicted values with no random effects
3.8.3 adding time
mod.2 <- lmer(SMN7 ~ 1 + week + (week | ID), data=example)
summary(mod.2)
## Linear mixed model fit by REML ['lmerMod']
## Formula: SMN7 ~ 1 + week + (week | ID)
## Data: example
##
## REML criterion at convergence: -678.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.9333 -0.4702 -0.0040 0.4699 2.6797
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## ID (Intercept) 1.688e-03 0.041081
## week 5.998e-05 0.007745 0.11
## Residual 1.114e-03 0.033380
## Number of obs: 216, groups: ID, 88
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.1047192 0.0054662 19.158
## week 0.0004891 0.0019133 0.256
##
## Correlation of Fixed Effects:
## (Intr)
## week -0.339
Random effects another way
re2 <- ranef(mod.2)
head(re2)
## $ID
## (Intercept) week
## 6 -0.0565693876 -0.0036946488
## 29 -0.0084812502 -0.0012399695
## 34 -0.0065599139 -0.0036267334
## 36 -0.0071058058 0.0047521215
## 37 -0.0075835906 0.0003777806
## 48 0.0376074895 0.0079898155
## 53 -0.0198932735 -0.0015608785
## 54 0.0012968175 -0.0046566304
## 58 0.0003752814 -0.0054295218
## 61 -0.0252286991 -0.0013741827
## 66 -0.0169264910 0.0022286289
## 67 -0.0044351198 0.0020522124
## 71 -0.0479007926 0.0002822149
## 75 0.0214734474 0.0025669329
## 76 -0.0011779173 0.0005878693
## 78 0.0159038244 0.0031438858
## 79 -0.0045545372 0.0005645243
## 80 -0.0178969517 -0.0007156657
## 81 0.0531021721 0.0082153576
## 82 0.0041632658 0.0008113125
## 85 -0.0522903314 -0.0013886487
## 86 -0.0374677321 -0.0020088964
## 87 -0.0353031581 -0.0042626635
## 89 -0.0190640130 -0.0008531461
## 91 0.0154744432 -0.0021927932
## 92 -0.0051270484 -0.0012824204
## 93 0.0377896360 0.0055463318
## 94 -0.0531789999 -0.0005574516
## 96 0.0253571389 -0.0004375991
## 97 -0.0465464370 -0.0019519248
## 98 -0.0387554767 -0.0027543679
## 99 0.0097850196 0.0016153839
## 101 0.0407311481 0.0116027111
## 103 -0.0191071264 -0.0013253683
## 104 -0.0465610719 -0.0034348580
## 105 -0.0453195741 -0.0021916503
## 106 0.0000399538 -0.0015452066
## 110 0.0526597916 -0.0065614779
## 112 -0.0054830896 -0.0041408032
## 114 -0.0518752910 -0.0023741320
## 115 -0.0006017030 0.0004675098
## 116 0.0079162240 -0.0002937992
## 120 0.0315638227 0.0021827362
## 122 0.0784520272 0.0030226010
## 125 0.0556521820 -0.0004022564
## 127 -0.0103573035 0.0009944533
## 129 -0.0438343313 -0.0011904028
## 135 0.0451700269 -0.0027840979
## 136 -0.0325726528 -0.0027537699
## 137 -0.0430719716 -0.0026649436
## 140 -0.0138988286 -0.0009470076
## 141 0.0782760199 0.0011254590
## 142 0.0765600112 0.0071699889
## 143 0.0088016978 0.0001783473
## 144 0.0005025170 0.0007246050
## 146 -0.0519054115 -0.0030655524
## 149 -0.0131560770 0.0001910980
## 150 0.0132910150 -0.0028905846
## 152 -0.0171937714 -0.0013668613
## 153 0.0486487108 0.0022931844
## 155 -0.0221220162 -0.0004933714
## 156 -0.0204142314 -0.0004524692
## 159 -0.0478271856 -0.0015437565
## 160 0.0034589214 0.0001562946
## 162 0.0877114808 0.0058969641
## 163 0.0157575910 0.0011486111
## 165 0.0324401589 0.0013198877
## 167 -0.0005438261 -0.0009082554
## 169 0.0657639666 0.0011933574
## 171 -0.0347569068 -0.0047509419
## 174 0.0279792237 -0.0004754973
## 182 -0.0052334591 -0.0081368313
## 187 -0.0560957612 -0.0019685294
## 189 0.0345643054 0.0020406710
## 190 -0.0016206743 -0.0003743260
## 193 0.0585379718 0.0071783218
## 194 0.0042424182 0.0066149744
## 201 0.0118765581 -0.0001338794
## 204 0.0379964146 0.0055305720
## 205 0.0400395330 -0.0029403941
## 208 0.0003049287 0.0043102513
## 209 -0.0336676597 -0.0004229467
## 211 0.0185609056 -0.0003189818
## 214 -0.0367595828 -0.0001671127
## 219 0.0454155727 0.0143718855
## 222 -0.0194792229 -0.0063357893
## 223 -0.0171899695 -0.0051032913
## 229 -0.0425480075 -0.0060015683
random_params <- tidy(mod.2, effect = "ran_modes")
head(random_params)
## level group term estimate std.error
## 1 101 ID (Intercept) 0.1454503656 0.018681947
## 2 101 ID week 0.0120918470 0.006503031
## 3 103 ID (Intercept) 0.0856120912 0.020552512
## 4 103 ID week -0.0008362324 0.007484226
## 5 104 ID (Intercept) 0.0581581457 0.020564594
## 6 104 ID week -0.0029457221 0.007470732
Using simulations to get better estimates of confidence around our estimates
library(merTools)
## Loading required package: arm
## Loading required package: MASS
##
## Attaching package: 'MASS'
## The following object is masked from 'package:dplyr':
##
## select
##
## arm (Version 1.9-3, built: 2016-11-21)
## Working directory is /Users/jackson/Box Sync/5165 Applied Longitudinal Data Analysis/Longitudinal
FEsim(mod.2)
## term mean median sd
## 1 (Intercept) 0.1049237738 0.104749324 0.005445517
## 2 week 0.0003563293 0.000391386 0.001891124
re.sim <- REsim(mod.2)
head(re.sim)
## groupFctr groupID term mean median sd
## 1 ID 6 (Intercept) -0.056524049 -0.056520728 0.01853646
## 2 ID 29 (Intercept) -0.009123963 -0.008834185 0.02100222
## 3 ID 34 (Intercept) -0.008829130 -0.006406428 0.01971477
## 4 ID 36 (Intercept) -0.007868465 -0.006664865 0.02263075
## 5 ID 37 (Intercept) -0.008726581 -0.008822561 0.01890025
## 6 ID 48 (Intercept) 0.039487076 0.040242828 0.02003486
This can be used to create CIs for each individaul random effect (and fixed effect). What is the confidence interval around person 6’s intercept estimate compared to person 2000 who has 25 repeated measurements?
3.8.4 caterpillar plots
Look through these different methods of getting random effects. Note that they are not all exactly the same.
caterpillar plots
p1 <- plotREsim(re.sim)
p1
3.8.5 Density of individaul random effects
p1.gg1 <- re.sim %>%
filter(term == "(Intercept)")
ggplot(p1.gg1, aes(mean)) +
geom_density()
p1.gg2 <- re.sim %>%
filter(term == "week")
ggplot(p1.gg2, aes(mean)) +
geom_density()
3.9 comparing to a standard linear model
lm.1 <- lm(SMN7 ~ 1 + week, data=example)
summary(lm.1)
##
## Call:
## lm(formula = SMN7 ~ 1 + week, data = example)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.099294 -0.039929 -0.005938 0.032715 0.169885
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.100161 0.005261 19.039 <2e-16 ***
## week 0.004087 0.002563 1.595 0.112
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.05562 on 214 degrees of freedom
## (9 observations deleted due to missingness)
## Multiple R-squared: 0.01174, Adjusted R-squared: 0.007124
## F-statistic: 2.543 on 1 and 214 DF, p-value: 0.1123
3.10 Other types of models
Depending on your DV, you might not want to have a Gaussian sampling distribution. Instead you may want something like a Poisson or a negative binomial if you are using some sort of count data. You can do this somewhat with lme4. However, the BRMS package – which uses Bayesian estimation – has many more possibilities: geometric, log normal, weibull, exponential, gamma, Beta, hurdle Poisson/gamma/negative binomial, zero inflated beta/Poisson/negative binomial, cumulative. Maybe we will fit some of these later in the semester.
3.11 Matrix notation (as a way to help understand what is going on)
\[ y_{i} = X_{i}\beta + Z_{i}b_{i} + \varepsilon_{i} \] Lets assume we have four time points.  Uses a likelihood function that describes the probability of observing the sample data as a function of the parameters. Attempts to maximize the function.
REML vs ML
Differences account for the fact that fixed effects are being estimated simultaously with th variance parameters. REML accounts for uncertainty in the fixed effects before estimating residual variance. REML attempts to maximize the likelihood of the residuals whereas ML the sample data.
If you use REML you should be careful in testing fixed effects against eachother (more down below)
3.13 Testing significance (adapted from Ben Bolker)
Methods for testing single parameters From worst to best:
- Wald Z-tests. Easy to compute. However, they are asymptotic approximations, assuming both that (1) the sampling distributions of the parameters are multivariate normal and that (2) the sampling distribution of the log-likelihood is (proportional to) χ2.
- Wald t-tests
- Likelihood ratio test.
- Markov chain Monte Carlo (MCMC) or parametric bootstrap confidence intervals
3.13.1 P values are not included
Authors are not convinced of the utility of the general approach of testing with reference to an approximate null distribution. In general, it is not clear that the null distribution of the computed ratio of sums of squares is really an F distribution, for any choice of denominator degrees of freedom. While this is true for special cases that correspond to classical experimental designs (nested, split-plot, randomized block, etc.), it is apparently not true for more complex designs (unbalanced, GLMMs, temporal or spatial correlation, etc.).
tl;dr: it gets messy with more complex models
If you really want p values
# library(lmerTest)
3.13.2 Likelhiood ratio test
How much more likely the data is under a more complex model than under the simpler model (these models need to be nested to compare this).
Log Likelihood (LL) is derived from ML estimation. Larger the LL the better the fit.
Deviance compares two LLs. Current model and a saturated model (that fits data perfectly).
Deviance = -2[LL current - LL saturated]
LL saturated = 1 for MLMs (probability it will perfectly recapture data). log of 1 is 0. So this term drops out.
Deviance = -2LL current model.
Comparing 2 models is called a likelihood ration test. Need to have: 1. same data 2. nested models (think of constraining a parameter to zero)
Distributed as chi-square with df equal to constraint differences between models.
mod.2r <- lmer(SMN7 ~ 1 + week + ( 1 | ID), data=example)
summary(mod.2r)
## Linear mixed model fit by REML ['lmerMod']
## Formula: SMN7 ~ 1 + week + (1 | ID)
## Data: example
##
## REML criterion at convergence: -675.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.2308 -0.4868 -0.0377 0.4542 3.2337
##
## Random effects:
## Groups Name Variance Std.Dev.
## ID (Intercept) 0.001815 0.04261
## Residual 0.001300 0.03606
## Number of obs: 216, groups: ID, 88
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.104041 0.005733 18.147
## week 0.001331 0.001755 0.758
##
## Correlation of Fixed Effects:
## (Intr)
## week -0.426
anova(mod.2, mod.2r)
## refitting model(s) with ML (instead of REML)
## Data: example
## Models:
## mod.2r: SMN7 ~ 1 + week + (1 | ID)
## mod.2: SMN7 ~ 1 + week + (week | ID)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod.2r 4 -686.93 -673.43 347.46 -694.93
## mod.2 6 -685.45 -665.20 348.73 -697.45 2.5248 2 0.283
3.13.3 Likelihood tests for random effects
Not listed in the output because it is hard to do this with variances. Remember variances do not have values below zero and thus the distributions get a wonky quickly. Needs mixture distributions (Cannot be easily done with chi square, for example)
Can Do anova comparisons, though that falls to many similar problems as trying to do a Wald test.
The sampling distribution of variance estimates is in general strongly asymmetric: the standard error may be a poor characterization of the uncertainty. Thus the best way to handle is to do bootstrapped estimates.
3.13.4 AIC and BIC
AIC (Akaike’s Information Criterion) and the BIC (Bayesian Information Criterion) where “smaller is better.” This is the opposite of LL/Deviance As with the other types, these may give you wonky findings depending on some factors as they are related to LLs.
AIC = 2(number of parameters) + (−2LL) BIC = ln(n)(number of parameters) + (−2LL)
BIC penalizes models with more parameters more than AIC does.
3.13.5 MCMC
library(rstanarm)
library(brms)
library(mcmcsamp)
#library(mcmcsamp)
3.13.6 Bootstraps
Parametric bootstrap:
confint(mod.1, method="boot", nsim=1000)
## Computing bootstrap confidence intervals ...
## 2.5 % 97.5 %
## .sig01 0.03437900 0.05119232
## .sigma 0.03201764 0.04051648
## (Intercept) 0.09665969 0.11679542
summary(mod.1)
## Linear mixed model fit by REML ['lmerMod']
## Formula: SMN7 ~ 1 + (1 | ID)
## Data: example
##
## REML criterion at convergence: -714.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.1575 -0.4728 -0.0232 0.4512 3.2750
##
## Random effects:
## Groups Name Variance Std.Dev.
## ID (Intercept) 0.001823 0.04270
## Residual 0.001302 0.03608
## Number of obs: 225, groups: ID, 91
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.106972 0.005106 20.95
# uses SDs of random effects
# sigma = residual standard error
Comparing two models. fit the reduced model, then repeatedly simulate from it and compute the differences between the deviance of the reduced and the full model for each simulated data set. Compare this null distribution to the observed deviance difference. This procedure is implemented in the pbkrtest package.
library(pbkrtest)
#pb <- PBmodcomp(mod.2,mod.2r)
3.14 Predictions and prediction intervals
Predict function is deterministic and uses only the fixed effects (i.e. does not include random effects in the predictions). It does not do prediction in the typical sense where you are predicting new individual’s scores.
Simulate is non-deterministic because it samples random effect values for all subjects and then samples from the conditional distribution. Simulation is needed to create true predictions.
3.14.1 Predictions and prediction intervals
Predict function is deterministic and uses only the fixed effects (i.e. does not include random effects in the predictions). It does not do prediction in the typical sense where you are predicting new individuals’s scores.
Simulate is non-deterministic because it samples random effect values for all subjects and then samples from the conditional distribution. Simulation is needed to create true preditions.
Short of a fully Bayesian analysis, bootstrapping is the gold-standard for deriving prediction intervals/bands (ie where would a new person score given X), but the time required is typically high.
In order to generate a proper prediction (for either a new person or a new observation within a person), a prediction must account for three sources of uncertainty in mixed models:
- the residual (observation-level) variance,
- the uncertainty in the fixed coefficients, and
- the uncertainty in the variance parameters for the random effects
Does so by: 1. extracting the fixed and random coefficients 2. takes n draws from the multivariate normal distribution of the fixed and random coefficients (separately) 3. calculates the linear predictor for each row in newdata based on these draws, and 4. incorporates the residual variation
then: 5. returns newdata with the lower and upper limits of the prediction interval and the mean or median of the simulated predictions
library(merTools)
# see also their shiny app: shinyMer(mod.1)
PI <- predictInterval(merMod = mod.2, newdata = example, level = 0.9, n.sims = 100, stat = "median", include.resid.var = TRUE)
head(PI)
## fit upr lwr
## 1 0.05308425 0.1183595 -0.00207539
## 2 0.03924973 0.1016941 -0.02471092
## 3 0.04589482 0.1067277 -0.02701423
## 4 0.09898698 0.1629537 0.02230258
## 5 0.09481121 0.1548031 0.02872763
## 6 0.09965338 0.1668796 0.04177601
Nice for bringing in confidence bands around your prediction (And we might use this later)
Broom offers the fitted (predicted) values already if you just want to plot your trajectory. But note that these are not typical prediction intervals (what happens if you get a new participant with a certain value of X). The bands fit in ggplot are for predicted \(\mu\)|X
Broom offers the fitted (predicted) values already if you just want to plot your trajectory. But note that these are not typical prediction intervals (what happens if you get a new particpant with a certain value of X). The bands fit in ggplot are for predicted \(\mu\)|X
P.gg <- ggplot(example.aug, aes(x= week, y = .fitted)) + geom_point() + stat_smooth(method = "lm")
P.gg
## Warning: Removed 9 rows containing non-finite values (stat_smooth).
## Warning: Removed 9 rows containing missing values (geom_point).
Can also explicitly simulate new data (rather than rely on another function to do so), which will be useful for power calculations later. In the simulated data, the subject means are different from the means in the original data because simulate samples by-subject random effect values using the variance components in the fitted model.
sim.1<- simulate(mod.2)
head(sim.1)
3.15 Coefficient of determination equivalents
Issue is: should you include or exclude variation of different random-effects terms?
Can do a more Psuedo R2 by taking the difference in variance between model 1 and model 2 and deviding it by model 1.
E.g,. residual variance in varying intercept model subtracted from growth model devided by intercept only model.
(sigma(mod.1) - sigma(mod.2)) / sigma(mod.1)
## [1] 0.07480908
Proportion of variance explained by time.
3.15.1 batch analyses
Can easily do a lot of models simulataniously. You do not need to use for loops.
Check out dplyr::do as well as purrr::map.
3.16 Now you try:
1.Run linear models on all of your subjects (a basic regression). What is the average intercept, the average slope?
Now run a mlm/lmer model with only a random intercept. What is the ICC? What does residual variance look like compared to linear model? Create a graph to show this effect.
Introduce a fixed slope term. What is the difference in terms of the fixed effects estimates between this estimate and the previous? Of the residual standard error? Create a graph to show both fixed effects estimates and the CIs around them.
Run an additional model with a random slope. How does this change compare to the previous model? Should you keep the random slope or not?
Interpret the correlation between the slope and the intercept.
Create a density plot of the random effects from your final model.
Create a catepilar plot of the random effects. Is there any person that seems odd in terms of a large standard errors around intercept and slope estimates?
Create a plot of the trajectory, along with a spaghetti plot of each person’s individual slope. Set the alpha level (transparency) on the individual slopes to make them easier to see.
Create a plot of the trajectory, along with a spagehtti plot of each person’s individual slope. Set the alpha level (transperancy) on the individual slopes to make them easier to see.


50pop
There’s this great story from the book “Art and Fear”:
The ceramics teacher announced on opening day that he was dividing the class into two groups.
All those on the left side of the studio, he said, would be graded solely on the quantity of work they produced, all those on the right solely on its quality.
His procedure was simple: on the final day of class he would bring in his bathroom scales and weigh the work of the “quantity” group: 50 pounds of pots rated an “A”, 40 pounds a “B”, and so on.
Those being graded on “quality”, however, needed to produce only one pot — albeit a perfect one — to get an “A”.
Well, came grading time and a curious fact emerged: the works of highest quality were all produced by the group being graded for quantity.
It seems that while the “quantity” group was busily churning out piles of work-and learning from their mistakes — the “quality” group had sat theorizing about perfection, and in the end had little more to show for their efforts than grandiose theories and a pile of dead clay.
So the name “50pop” is an acronym for “50 pounds of pots” - a reminder to keep churning out those ideas.


Gin is a spirit that is typically triple distilled, based upon neutral grain spirits, and cut with distilled water. In most cases, the grain spirits have been created through a double or triple column still distillation. Then the grain spirit is distilled a final time in a pot still with botanicals including juniper, oil of juniper, coriander, orange peel, lemon peel, anise, cassia, bitter almonds, caraway, cocoa, angelica root, orris root and many other ingredients. For proprietary reasons, producers zealously guard their botanical recipes.
Nonetheless, it is possible to learn a great deal about any gin and its recipe from the flavors and aromas. Juniper is distinctly peppery and herbal.  Some of the most highly prized juniper berries are grown and aged for several years in Tuscany.
Citrus peel adds lemon, orange and lime elements; that seems obvious. Coriander, the seed of the cilantro plant, adds an herbal aroma, but also brings a tart, even grapefruit-like flavor to the gin. Cassia brings a somewhat bitter note, something like tonic water. Other ingredients may offer floral notes, vegetal notes, even tea flavors; flowers, vegetables and tea might also be a part of the recipe.
Gin can be made anywhere that distillation occurs. Still, there are four approximate types of gins, and those gin types tend to come from certain places.
For more than a century, gin producers around the world have looked to London Dry Gin as the benchmark gin style. While it can be made anywhere—it needn’t come from London—the style is nonetheless still strongly associated with Great Britain. Juniper and/or citrus tend to dominate the botanical profile. Alcohol range is from 37.5 to 55 percent by volume; the traditional strength is 47 percent.
Genever or Hollands gin is produced in the Netherlands, Belgium and small parts of France and Germany. It has some yellowish color, may be distinctly sweet, in opposition to London Dry, and can be powerful and oily. Made mostly from the pot-stilled barley/rye distillate known as “malt wine,” usually with neutral grain spirits blended in, it’s always more malty/grainy/cereally than herbal or fruity/spicy. Alcohol range is from 35 to 50 percent by volume.
Plymouth, England is home to a single gin distillery, Blackfriars, and a distinctive style called Plymouth. Plymouth Gin is lower in alcohol than London Dry varieties but owns an earthy richness that is unique. Alcohol is 41.2 percent.
So-called “New” or “International Style” gins are as diverse as the many places from which they derive. Alcohol range is from 40 to 55 percent by volume. Typically, other botanicals than juniper tend to dominate.
If gin is a juniper flavored grain-based spirit (and it is), then there would be nothing wrong with proclaiming Arnaud de Villanova as gin’s inventor. He is credited with developing the European practice of distillation in the thirteenth century A.D., perhaps acquiring the skills developed centuries earlier by Muslim scholars, Geber and Avicenna. Importantly, his first products were grain spirits distilled with juniper berries. Why? Juniper has long been known to possess healthful properties (that’s why we drink gin now, right?). Masks made of juniper were believed by some to offer protection from the plague. Juniper is likewise believed to aid when ailments of the kidneys strike.
But Villanova’s gin was more or less a one-off. In the end, it was the Dutch who invented the spirit we know as gin. The word is theirs, as well. They call juniper genever in Dutch; the British turned that word into “geneva” and then abbreviated it to “gin.” For the Dutch, alcohol’s preservative abilities were ideally suited to retain the character of the spices and fruits they were trading.
Throughout much of the fifteenth, sixteenth, and seventeenth centuries, the Dutch were masters of the high seas and, as such, pioneered and dominated international trade and commerce. All the major European powers, namely, the British, Spanish, Portuguese and Dutch, vied to create the fastest and most direct route to the spice regions of eastern Asia. The stories of their competitions and subsequent ruthless methods once they arrived in places like the Moluccas (where cloves grow) have filled bookshelves. The Dutch East India Company was particularly successful.
While Dutch ships entered the port of Rotterdam, much of their cargo was loaded to an upriver suburb called Schiedam. Consequently, Schiedam’s warehouses were bulging with fruits, spices and other raw goods and materials. By the seventeenth century, four hundred pot stills were in use to convert those goods into something with a bit more longevity. Juniper was a prime ingredient for their genever, but many other ingredients found their way into the increasingly complex brew. Genever was reportedly healthful and, man, it was potent. The British called the drink Dutch Courage because they frequently hired Dutch mercenaries to do some of their military dirty work. The Dutch mercenaries were known to drink copious amounts of genever and were notoriously effective in their ferocity.
But the British and many of Continental Europe’s monarchs did not get along in the late 1600s. So, the English Crown decreed that any British subject could distill this so-called Dutch Courage, in the hope that the increasingly thirsty British people would stop buying French brandy and that perhaps Holland’s genever might be supplanted as well. As history depicts, the plan worked.
By the early 1700s, Dutch Courage had become “Mother’s Ruin.” The ravages and dislocations of the Industrial Revolution were at least partially blamed on gin, which had swept through England’s burgeoning cities like liquid crack. Gin was accused of being evil. With distilleries working in seemingly half the back rooms of London churning out inexpensive, semi-poisonous spirit from the cheapest materials available, that description wasn’t far-fetched.
After the “Gin Craze” burnt itself out in England, gin became celebrated as something essentially British. England shut down home distilling through Parliamentary laws and built beautiful gin palaces to lure the populace into a more controlled—and taxable—setting. Gin Punch became one of the sporting drinks of the upper class at home while for the protectors of the Empire in the far-flung tropical regions of India and Africa gin and quinine-water became the tonic drink (as in, medicinal) of choice.
By the early 1800s, English gin’s style had distinguished itself from the malty, rich Dutch style. Where the Dutch worked to make the best, most flavorful (pot-still) base spirit they could and then flavored it simply with juniper and small amounts of other spices, the English relied on a base spirit that was rectified—that is, redistilled and filtered to remove as many traces of the base material as possible—which was then flavored with a complex mix of botanicals and then, usually, sweetened. This style was known as Old Tom gin.
In the 1830s, Charles Tanqueray created the distinct style of London Dry Gin, altogether crisper and lighter than the genevers and even the hitherto-dominant Old Tom gins. With the introduction of continuous stills, the distilleries in the Lowlands of Scotland were fired up. Ironically, much of the grain whisky they made (and still make) wasn’t intended for Scotch whisky but instead for the gin distilleries of England. With the help of the neutral spirit they provided, London Dry Gin had become by the end of the nineteenth century the preeminent, defining style, produced by dozens of distilleries, each with its own proprietary blend of botanicals.
This explosion wasn’t occurring just in Britain. In the U.S., distillers began making the new London Dry style, which was much cheaper to produce than the malt-rich Dutch style. In Ireland, Cork’s Watercourse Distillery had a tradition of gin-making dating back to 1798, with its own special botanical formula, but didn’t launch its Cork Dry Gin, or “C.D.C. Gin” (so called after its maker, the Cork Distilleries Company), until 1941, when the distillery installed a column still that enabled it to make a true dry gin.
After a century of widespread popularity, gin has struggled since the explosion of vodka in the 1970s. In the last decade though, gin, perhaps sensing imminent doom, has begun to revisit its roots. Now, after three decades of decline, there are suddenly dozens of new brands. Some of the gins in the market are rootier, more idiosyncratic, and Plymouth Gin, an icon among English gins that almost disappeared, is reborn. Genever is coming back to the world stage after a century of eclipse (naval embargos during the first World War and German occupation during the second effectively destroyed its foreign markets). While finding a bottle sometimes requires an exhaustive search, there is good news from Bols, which has recently reintroduced their classic genever to the global market. There are even contemporary versions of Old Tom Gin available again, if with limited distribution. Bottom line is: gin is back!
With the recent explosion of Gin as a category, there seems to be a certain amount of misinformation about the regulations regarding it, so let’s set the record straight. First, since gin is originally a European product, these are the EU rules, and as such, American gins do not necessarily need to follow these rules. That said, most American distillers seem to have embraced these regulations as their own, perhaps out of respect for their forebears or perhaps because they hope to sell some spirit in the European Community.
Today, we classify Gin by both geographic origin and style. It should be pointed out that although London Gins began as products of that city, today, the name London Gin, or London Dry Gin, is a style that can be made anywhere, as long as the producer adheres to some very strict rules. This is contrary to the regulations for Plymouth Gin, which must be made in the town of Plymouth, England, and Genever/Genievre/Jenever, which must be made in The Netherlands or Belgium, and as such are considered PDOs, or Geographic Indications of Origin, and have their own sets of rules and regulations.
There are currently nine other PDOs for Gin in the EU: two of which are German, one each from Spain and Lithuania, and the remaining five from Slovakia.
There are also classifications for the use of the word Gin, which are, in ascending order of specificity, from just calling it Gin, to Distilled Gin, to London Distilled Gin (insert the word Dry as preferred), which is a type of Distilled Gin, that must be distilled to a minimum of 70 percent, then redistilled in a traditional (pot) still with botanicals that are all natural plant materials, of which the juniper must be predominant.
New Western Dry Gins are basically defined, according to Ryan Magarian’s thesis on the subject of Gin and its style sub-categories, as Gins that, while embracing Juniper, focus as much or more on their complement of other botanicals, although no specific rules or legislation has yet been universally approved for this designation.
While we can argue about the origins of the Martini, there is no argument that it was originally a gin drink. In the nineteenth century, the gin most Americans imbibed was Hollands, not Old Tom or London Dry. But in the last quarter of the 1800s, the trend was toward lighter, dryer drinks.
Old Tom gin began to edge out genever. Mix Old Tom with vermouth and you have a Martini. Make that vermouth dry and switch the Old Tom for Plymouth or London dry gin, and you have a dry Martini, which was introduced in the 1890s. We’re still drinking it now.
In America, during the manmade drought of Prohibition (1919- 1933), aged spirits were very expensive, if not downright unavailable. But homemade bathtub gin was as popular as the Charleston. It’s not hard to explain why that dance was all the rage, but gin was only a quick step away from moonshine. Gin demanded no long barrel aging and no exotic ingredients—just bootleg moonshine and some juniper extract purchased from Sears Roebuck’s, J.C. Penney’s or Montgomery Ward’s mail-order catalogues (all ranked such juniper products amongst their top ten sellers). Dozens of gin-based cocktails date from these years and have become classics. But gin’s spicy, ever-changing aromas and flavors are still too much for some drinkers and may provide too much of a challenge for lazy bartenders who find it easier to throw some juice together with vodka and call it a new classic.
Unlike vodka, gin is all about the aromas and flavors that are derived from botanicals. Compared to tasting vodka, gin is easy and straightforward. You smell it and you look for spices, fruits, vegetables and anything else you can think of, and if it’s an interesting gin, you’ll find a lot of each present.
But as with vodka, a good taster looks to the base spirit. Is it rich, smooth, textured, or oily (in a good way)? Or is it hot, spiky and bitter? Some distillers, as if they were still making bathtub gin, figure that the botanicals will cover up lazy distillation. They won’t. The best way to find flavor and identify differences is to put a few gins next to each other. Smell, taste and compare them. While putting words to the differences still requires some artistic license, you will definitely find differences.
Gin should be clean and dry and not bitter and not sweet, unless it is a genever or genever-styled gin. A good genever seems sweet from its powerfully malty character, and can indeed be gently sweet.


Shine Chad'z rating: ***1/2 (out of 4 = very good) 1996, PG-13, 105 minutes [1 hour, 45 minutes] [drama] starring: Geoffrey Rush (adult David Helfgott), Noah Taylor (teenage David Helfgott), Armin Mueller-Stahl (Mr. Peter Helfgott), Lynn Redgrave (Gillian), written by Scott Hicks, Jan Sardi, produced by Jane Scott, directed by Scott Hicks.
You don't have to be a musician to understand the power music can have. It's something so forceful it rivals love. "Shine" proves this to be true as it is a story of a gifted pianist torn between his loyalty and honor to his father and his love for his music. The film's most moving element is not the drama, but the music itself.
As the film opens we meet an eccentric man wandering in the rain, he is the main character, David Helfgott as an adult (Rush). Through a series of flashbacks we are told the story of how he came to be where he is now. As a small child he displayed a great ability for playing the piano. He enters a talent competition and although he amazes everyone, he does not win first prize. Later, one of the judges stops by his house to give him a "special" prize, but this insults his Orthodox Jewish father, Mr. Peter Helfgott (Mueller-Stahl) because he is essentially given a prize for losing. Mr Helfgott is a Holocaust survivor, he refuses handouts, and teaches his children, "Only the strong survive."
Most of the first half is plotless, however, many events occur to create for detailed characterization and atmosphere. Some of these things are short and subtle, but really add up, such as a scene in which David (played by Noah Taylor from age 14 - 20) flirts with a girl but his father purposely calls him away. Other examples include: when David's sister crawls through a hole in the fence to talk to a boy, Mr. Helfgott seals up the hole; and when David tries to get back at his father by ruining his bath, he is beaten. I find family conflict and domestic violence to be some of the most powerful, dramatic elements in cinema, and this film makes perfect use of them.
The love/hate relationship between David and his father reaches a boiling point when he is offered a full scholarship to a musical college in London. David decides to go even after his father threatens to completely disown him.
I never thought I'd see a parallel to "Star Wars" in a film such as this, but a Luke Skywalker/Obi-Wan Kenobi type of relationship seems to form between David and his new teacher at college. The teacher describes the power of music in such a way it seems supernatural - music becomes to David what The Force is to Luke Skywalker.
There are many wonderful scenes in which David's musical ability speaks volumes on its own, but could it be too much for him to handle? His entire life has revolved around the piano, and it finally catches up with him as he suffers a mental breakdown after performing his best concert ever.
The second half of the film is quite strange and jumbled. Geoffrey Rush delivers an outstanding performance as a mentally challenged adult David, but the film doesn't give much explanation to his condition. Then again, an explanation nor a plot is really necessary from this point on, as it becomes a simpler story about David's day-to-day struggle for happiness.
David starts playing the piano again and many things start to happen in his life. He meets a woman named Gillian (Redgrave) and they get married. David's father also makes an appearance in a typical coming of terms scene - but has he finally forgiven him? It's difficult to tell, but I think that's the point. In fact, most everything that happens during his adult life is open to interpretation. The scenes themselves are easy to follow (and quite funny at times), and it seems something monumental is going to happen.
The only thing I didn't like about "Shine" was the sudden ending and the choppy storytelling throughout the second half. But despite these minor flaws, the film works as a good and original drama that combines the power of music with the human spirit.
Please visit Chad'z Movie Page @ http://members.aol.com/ChadPolenz E-mail<EMAIL_ADDRESS>(C)1997 Chad Polenz
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Get a US unlocked Galaxy S9+ for just $480 ($120 off)
by Corbin DavenportThe Galaxy S11 is only a few months away, but the S10 is still an excellent phone. The S9 is also still hanging in there, especially since it will probably get Android 10 at some point. Now you can get the United States version of the S9+ for just $474.99 from Amazon, a $120 savings from the usual price of ~$600.
The model on sale has a Snapdragon 845 processor, 6GB of RAM, 64GB of internal storage (there's a microSD card slot for expansion), a 6.2-inch 1440x2960 AMOLED screen with HDR10 support, an IP68 water/dust resistance. There are two 12MP rear cameras (one wide, one telephoto), and an 8MP shooter on the front. It was updated to Android 9 Pie earlier this year.
Unlike most of the deals we see on Samsung phones, this one is for the United States version of the S9+, not an international variant. That means you get Samsung's full warranty, support for all major networks in the US, and full Samsung Pay functionality.
Buy:
Amazon


Akan names are derived from Ghanian culture.Frequently in Ghana ,children are given their first names as a 'day name' which corresponds to the day in the week they were birn depending on their gender.


I have always had some symptoms of ADHD and at the age of 21,I decided to consult a psychiatrist. He gave me Efalex and later Xanax (alprozalam) in case it was anxiety. When both failed he prescribed Ritalin (methylphenidate) for me.
The first time I took 10mg and after 30 t0 60 minutes, I started feeling my heart beeting a lot and after some time I felt euphoric. Everything seemed so good. I was doing exams at the moment and under the effect of Ritalin, I succeeded to study an entire four hours without stopping. I actually found studying a very pleasurable thing while under Ritalin ' s effect.
The next day I felt the same with a 10mg pill. On the third day, I
again took a 10mg pill and felt the same. However when it's effect
finished I decided to take another one and it worked as well. The following morning I took another pill during the exam. It worked fine.
However starting from the fourth day, Ritalin never produced its miraculous effect again. Instead of feeling euphoric, it started to make me anxious and restless. I increased dosages up to 60mg but it was even worse. I have tried paroxetine with it, alcohol, benzodiazepines, but it was all in vain. Ritalin never worked again!
I started taking paroxetine everyday, and occasionally after having taken paroxetine (20mg/day) for a long time, I stop it suddenly. After a day or two I start feeling dizzy, and like having a fever. To my amusement during this SSRI withdrawal syndrome, sometimes Ritalin starts making me euphoric again (not as much as the first times).
Can anyone explain this ?
All I know, is that Ritalin intially seemed to be a panacea and the ultimate drug, but it turned out to be disappointing.
Experience Reports are the writings and opinions of the individual authors who submit them.
Some of the activities described are dangerous and/or illegal and none are recommended by Erowid.


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Description
This object implements the NcHaloDensityProfile class for a Navarro-Frenk-White (NFW) density profile.
As described NcHaloDensityProfile, we just need to implement the dimensionless 3D density $\hat{\rho}(x)$
[which refers to the virtual function nc_halo_density_profile_eval_dl_density()
].
In particular, the NFW profile is given by
\begin{equation}
\hat{\rho}(x) = \frac{1}{x(1 + x)^2},
\end{equation}
where $x = r/r_s$ and $r_s$ is the scale radius.
Both the mass $M_\Delta$ and the scale profile $\rho_s$ are written in terms of the integral
$I_{x^2\hat\rho}(c_\Delta)$ [virtual function nc_halo_density_profile_eval_dl_spher_mass()
].
The respective NFW implementation provides
\begin{equation}
I_{x^2\hat\rho}(x) = \ln(1 + x) - \frac{x}{1 + x}.
\end{equation}
The NFW dimensionless surface mass density [virtual function nc_halo_density_profile_eval_dl_2d_density()
] is
\begin{equation}
\hat{\Sigma}(X) = \frac{2}{X^2 -1} \left[1 - \frac{\arctan (\sqrt{X^2 -1})}{\sqrt{X^2 - 1}}\right].
\end{equation}
For $X^2 - 1 < 0$ the equation above can be written in terms of $\mathrm{arctanh}(\sqrt{1 - X^2})/\sqrt{1 - X^2}$.
If $\vert X - 1 \vert < 10^{-6}$ or $X < 10^{-6}$, $\hat{\Sigma} (X)$ is computed using
the Taylor series expansion at $1$ or $0$ respectively (with sufficient terms in order to obtain double precision).
The NFW enclosed mass is [virtual function nc_halo_density_profile_eval_dl_cyl_mass()
]
\begin{equation}
\hat{\overline{\Sigma}} (< X) = 2 \left[\frac{\arctan (\sqrt{X^2 - 1})}{\sqrt{X^2 - 1}} + \ln (X / 2)\right],
\end{equation}
Similar expressions in terms of $\mathrm{arctanh}$ and approximations, as described above, are used here.
References: Navarro (1996), Wright (2000), astro-ph/0206508 and arxiv:1010.0744.
Functions
nc_halo_density_profile_nfw_class_set_ni ()
void
nc_halo_density_profile_nfw_class_set_ni
(gboolean num
);
This function substitutes the child methods by the parent ones if num is TRUE. It enforces the computations to be performed by numerical integration.
WARNING: this function modifies the behavior object. It should be used for testing only!
nc_halo_density_profile_nfw_new ()
NcHaloDensityProfileNFW * nc_halo_density_profile_nfw_new (const NcHaloDensityProfileMassDef mdef
,const gdouble Delta
);
This function returns the NcHaloDensityProfileNFW implementation of
NcHaloDensityProfile setting “mass-def” to mdef
and “Delta” to Delta
.


NAVO Registry Publishing Interface - Individual Resource Management
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