# Embedded Model Control of Networked Control Systems: an Experimental Case-
study - Stability analysis and further results

Luca Nanu , Carlos Perez Montenegro , Luigi Colangelo , Carlo Novara
Department of Mechanical and Aerospace Engineering, Polytechnic of Turin,
Corso Duca degli Abruzzi 24, Turin, 10129, Italy. Mail address:
<EMAIL_ADDRESS>Polytechnic of Turin, Corso Duca degli Abruzzi 24,
Turin, 10129, Italy. Mail address<EMAIL_ADDRESS>of
Electronics and Telecommunications Engineering, Polytechnic of Turin, Corso
Duca degli Abruzzi 24, Turin, 10129, Italy. Mail address:
<EMAIL_ADDRESS>of Electronics and Telecommunications
Engineering, Polytechnic of Turin, Corso Duca degli Abruzzi 24, Turin, 10129,
Italy. Mail address<EMAIL_ADDRESS>
###### Abstract

In Networked Control Systems (NCS), the absence of physical communication
links in the loop leads to relevant issues, such as measurement delays and
asynchronous execution of the control commands. These issues may lead to
unwanted control behaviours. This ArXiv paper is intended to give additional
results to the work presented in [1]. The last one presents an original
approach, based on the Embedded Model Control, to deal with experimental
scenarios characterized by asynchronous control timing. The effectiveness of
the proposed approach is demonstrated with a differential-drive robot, first
with high-fidelity simulations and finally with several experimental tests.

Specifically, the present work aims to study the stability analysis of the EMC
experimental setup and to give further experimental results, to complement
those presented in the main paper, [1].

##  1 Introduction

At the beginning, the present paper provides additional studies on the
stability analysis for the specific experimental test case with the
differential-drive robot presented in [1], with the introduction of the
asynchronous control timing.

Furthermore, additional results are studied in the final part of the present
paper, comprising:

(a) an experimental test comparing the estimated output and the measured
output for the DC motor speed. In this test, it is evident how the model error
is very small, thus verifying the effectiveness of the EMC observer state
estimation;

(b) a set of experimental tests in which the EMC control unit is tested in
several critical conditions concerning the asynchronous timing, in order to
explore the control space and to highlight the boundaries of the control
action;

(c) further benchmarking tests, between EMC and a Proportional-Integrative
(PI) control.

##  2 Mobile robot application: EMC Stability analysis

This section gives a stability proof of the EMC control unit applied to the
experimental differential-drive robot setup. In addition, the stability
analysis of the EMC unit in a general control scenario is already treated in
[2].

The EMC unit is split into sub-models and a stability analysis is made for
each of them. The idea is that the EMC unit can guarantee internal and
bounded-input-bounded-output (BIBO) stability of the closed-loop system if all
the sub-models are internal and BIBO stable.

###  2.1 Internal model stability proof

The internal model of the EMC unit can be formulated in the form of state
equations as follows, [3]

$\displaystyle\mathbf{x}(k+1)=\begin{bmatrix}\mathbf{x}_{c}\\\
\mathbf{x}_{d}\end{bmatrix}(k+1)=\underbrace{\begin{bmatrix}\mathbf{A}_{c}&\mathbf{H}_{c}\\\
0&\mathbf{A}_{d}\end{bmatrix}}_{\mathbf{A}}\mathbf{x}(k)\ +$ (1)
$\displaystyle+\underbrace{\begin{bmatrix}\mathbf{B}_{c}\\\
\mathbf{B}_{d}\end{bmatrix}}_{\mathbf{B}}\mathbf{u}(k)+\underbrace{\begin{bmatrix}\mathbf{G}_{c}\\\
\mathbf{G}_{d}\end{bmatrix}}_{\mathbf{G}}\mathbf{\overline{w}}(k),$
$\displaystyle\mathbf{y}_{m}(k)=\underbrace{\begin{bmatrix}\mathbf{C}_{c}\
\mathbf{C}_{d}\end{bmatrix}}_{\mathbf{C}}\mathbf{x}(k),$

where $\mathbf{x}_{c}$ and $\mathbf{x}_{d}$ refer to the controllable (or
canonical) and rejector states, respectively.

On the other side, the matrices $\mathbf{A},\mathbf{B},\mathbf{C}$, are
related respectively to: (i) the state $\mathbf{x}$, (ii) the control input
$\mathbf{u}$, and (iii) the estimated output from the internal model
$\mathbf{y}_{m}$. In addition the matrix $\mathbf{G}$ is present, for the
estimation of the noise vector $\mathbf{\overline{w}}$. In particular, the
matrix $\mathbf{A}$ is made by the sub-matrices: $\mathbf{A}_{c}$, related to
$\mathbf{x}_{c}$, $\mathbf{A}_{d}$ related to $\mathbf{x}_{d}$, and
$\mathbf{H}_{c}$, which considers the interactions of $\mathbf{x}_{d}$ on
$\mathbf{x}_{c}$. Similarly, we have the sub-matrices $\mathbf{B}_{c}$ and
$\mathbf{B}_{d}$ for $\mathbf{B}$ matrix, $\mathbf{G}_{c}$ and
$\mathbf{G}_{d}$ for $\mathbf{G}$ matrix, $\mathbf{C}_{c}$ and
$\mathbf{C}_{d}$ for $\mathbf{C}$ matrix.

Equation (1) for the internal model can be converted from time to frequency
domain, as follows

$\displaystyle\mathbf{X}(z)=$
$\displaystyle\underbrace{\\{z\mathbb{I}-\left[\mathbf{A}-\mathbf{GLC}\right]\\}^{-1}}_{\mathbf{X}_{zi}(z)}\mathbf{X}(0)+$
(2)
$\displaystyle+\underbrace{\mathbf{B}\\{z\mathbb{I}-\left[\mathbf{A}-\mathbf{GLC}\right]\\}^{-1}}_{\mathbf{X}_{zs,1}(z)}\mathbf{U}(z)+$
$\displaystyle+\underbrace{\mathbf{GL}\\{z\mathbb{I}-\left[\mathbf{A}-\mathbf{GLC}\right]\\}^{-1}}_{\mathbf{X}_{zs,2}(z)}\mathbf{Y}(z)$

where $\mathbf{X}_{zi}(z)$ denotes the zero-input response of the closed-loop
system when $\mathbf{U}(z)=\mathbf{Y}(z)=0$, $\mathbf{X}_{zs,1}(z)$ the zero
state response when $\mathbf{X}(0)=\mathbf{Y}(z)=0$ and $\mathbf{X}_{zs,2}(z)$
the zero state response when $\mathbf{X}(0)=\mathbf{U}(z)=0$.

Both the internal and BIBO stability of the internal model can be studied by
imposing $\det\\{z\mathbb{I}-\left[\mathbf{A}-\mathbf{GLC}\right]\\}^{-1}$
equal to a characteristic polynomial $(z-p_{1})(z-p_{2})\dots(z-p_{n})$, where
$n$ is the $\mathbf{A}$ matrix dimension: in order to guarantee the asymptotic
stability, the poles $\left[p_{1},p_{2},\dots,p_{n}\right]$ must lie inside
the unitary circle. From the equation above it is clear that the stability
finally depends on the observer matrix $\mathbf{L}$ components’ design, which
will be discussed in Section 2.5.

###  2.2 Plant stability proof

The plant of the DC motor, i.e. the mathematical description of the DC motor
physical behaviour, must guarantee BIBO stability. Equation (3) define the
state equations for the DC motor

$\displaystyle\begin{cases}&\omega(k+1)=\left(-\frac{1}{\tau_{m}}T_{s}+1\right)\omega(k)+\frac{T_{s}}{\tau_{m}k^{\prime}_{v}}V_{a}(k)+d(k),\\\
&x_{d1}(k+1)=(T_{s}+1)x_{d1}(k)+T_{s}\left[x_{d2}(k)+\overline{w}_{2}(t)\right],\\\
&x_{d2}(k+1)=(T_{s}+1)x_{d2}(k)+T_{s}\overline{w}_{3}(k),\end{cases}$ (3)
$\displaystyle d(k)=T_{s}\left[\overline{w}_{1}(k)+x_{d1}(k)\right],$
$\displaystyle\omega(0)=\omega_{0},\quad x_{d1}(0)=x_{d10},\quad
x_{d2}(0)=x_{d20},$

where $\omega$ is the DC motor output speed, $\tau_{m}$ is the DC motor
mechanical time constant, $k^{\prime}_{v}$ is the back electromotive force
constant specifically found for the studied motor,
$[\overline{w}_{1},\overline{w}_{2},\overline{w}_{3}]$ are the components of
the noise vector $\mathbf{\overline{w}}$, $[x_{d1},x_{d2}]$ are the components
of the disturbance state $\mathbf{x}_{d}$, $T_{s}$ is the sampling time.

Equation (3) can be translated in frequency domain and reshaped in a matrix
form, i.e.

$\displaystyle
W_{{}_{M}}(z)=\frac{Y(z)}{U(z)}=\frac{\beta_{0}(z+1)}{z^{2}+\alpha_{1}z+\alpha_{0}},$
(4) $\displaystyle\beta_{0}=\frac{T^{2}}{k_{v}(\tau_{m}T+2\tau_{m}\tau_{a})},$
$\displaystyle\alpha_{0}=\frac{T^{2}-\tau_{m}T+2\tau_{m}\tau_{a}}{\tau_{m}T+2\tau_{m}\tau_{a}},$
$\displaystyle\alpha_{1}=\frac{T^{2}-4\tau_{m}\tau_{a}}{\tau_{m}T+2\tau_{m}\tau_{a}}$

The worst case for the stability corresponds to the lowest sampling time
possible. For example, by considering for $T_{s}$ a range of $[0.01,0.03]\
$\mathrm{s}$$, the lowest sampling time corresponds to $T_{s}=0.01\ s$: hence
the parameters become
$\beta_{0}=0.1313,\alpha_{0}=-0.1471,\alpha_{1}=-0.4835$.

The motor transfer function can be alternatively expressed as

$W_{{}_{M}}(z)=\frac{\beta_{0}(z+1)}{\left(z-d_{0}\right)\left(z-d_{1}\right)}$
(5)

where the two poles are $d_{0}=0.695,d_{1}=-0.212$, both inside the unitary
circle, leading to asymptotic BIBO stability of the motor plant transfer-
function.

###  2.3 Reference dynamics stability proof

The reference dynamics equations are recalled from [1]

$\displaystyle\overline{\mathbf{x}}(k+1)=\mathbf{A}_{{}_{R}}\overline{\mathbf{x}}(k)+\mathbf{B}_{{}_{R}}\overline{\mathbf{r}}(k),$
(6)
$\displaystyle\overline{\mathbf{y}}(k)=\mathbf{C}_{{}_{R}}\mathbf{\overline{x}}(k),$
$\displaystyle\mathbf{A}_{{}_{R}}=\mathbf{A}_{c}-\mathbf{B}_{c}\mathbf{K}_{{}_{R}},$
$\displaystyle\mathbf{B}_{{}_{R}}=\mathbf{B}_{c}\mathbf{N}_{{}_{R}},\quad\mathbf{C}_{{}_{R}}=\mathbf{C}_{c}.$

The reference trajectory $\mathbf{\overline{r}}(k)$ is obtained by exploiting
a static-state feedback, with as nominal control input
$\overline{\mathbf{u}}(k)=-\mathbf{K}_{{}_{R}}\overline{\mathbf{x}}(k)+\mathbf{N}_{{}_{R}}\overline{\mathbf{r}}(k)$,
where $\mathbf{K}_{{}_{R}}=k_{{}_{R}}$ and $\mathbf{N}_{{}_{R}}=n_{{}_{R}}$
are the reference generator gains.

The reference dynamics internal and BIBO stability can be studied by
exploiting (6) into frequency domain:

$\mathbf{\overline{X}}(z)=\underbrace{z\left[z\mathbb{I}-\mathbf{A}_{{}_{R}}\right]^{-1}}_{\mathbf{\overline{X}}_{zi}(z)}\mathbf{X}(0)+\underbrace{\mathbf{B}_{{}_{R}}\left[z\mathbb{I}-\mathbf{A}_{{}_{R}}\right]^{-1}}_{\mathbf{\overline{X}}_{zs}(z)}\mathbf{\overline{R}}(z)$
(7)

where $\mathbf{\overline{X}}_{zi}(z)$ denotes the zero-input response (hence
when $\mathbf{R}(z)=0$), $\mathbf{\overline{X}}_{zs}(z)$ the zero state
response when $\mathbf{X}(0)=0$, $\mathbf{\overline{R}}$ the reference
trajectory input $\mathbf{\overline{r}}$ translated in frequency domain. The
stability depends on the term
$\left[z\mathbb{I}-\mathbf{A}_{{}_{R}}\right]^{-1}$. Indeed, by applying the
pole-placement technique, the continuous-time eigenvalue
$\mathbf{A}_{{}_{R}}=a_{{}_{R}}$ is user-defined to lie in the right-half
plane, to guarantee stability in frequency-domain.

###  2.4 Control law stability proof

The controller block is part of an external closed-loop system, including a PI
controller and the internal model controllable dynamics.

The EMC control law is made up by three terms: (i) the feed-forward component
$\overline{\mathbf{u}}$, (ii) the state feedback
$\mathbf{u}_{trk}=\mathbf{K}_{{}_{C}}\overline{\mathbf{e}}$, and (iii) the
disturbance rejection term $\mathbf{u}_{d}=\mathbf{M}\mathbf{x}_{d}$. Ergo,
being $\mathbf{\overline{e}}$ the tracking error, the full command expression
holds:

$\begin{split}\mathbf{u}(k)&=\overline{\mathbf{u}}(k)+\mathbf{K}_{{}_{C}}\overline{\mathbf{e}}(k)-\mathbf{M}\mathbf{x}_{d}(k),\\\
\overline{\mathbf{e}}(k)&=\left(\overline{\mathbf{x}}(k)-\mathbf{Q}\mathbf{x}_{d}(k)\right)-\mathbf{x}_{c}(k).\end{split}$
(8)

The control block state equations are defined as follows, [1]

$\displaystyle\begin{bmatrix}\mathbf{x}_{1}\\\
\mathbf{x}_{2}\end{bmatrix}(k+1)=\mathbf{A}_{ctrl}\begin{bmatrix}\mathbf{x}_{1}\\\
\mathbf{x}_{2}\end{bmatrix}(k)+\mathbf{B}_{ctrl}\mathbf{\overline{e}}(k),$ (9)
$\displaystyle\mathbf{A}_{ctrl}=\begin{bmatrix}-\mathbf{A}_{c}-k_{p}\mathbf{B}_{c}&k_{i}\mathbf{B}_{c}\\\
-1&1\end{bmatrix},$
$\displaystyle\mathbf{B}_{ctrl}=\begin{bmatrix}k_{p}\mathbf{B}_{c}\\\
1\end{bmatrix},$ $\displaystyle\mathbf{A}_{c}=-\frac{T_{s}}{\tau_{m}}+1,\ \
\mathbf{B}_{c}=\frac{T_{s}}{\tau_{m}k^{\prime}_{v}}$

where $\mathbf{x}_{1}=\mathbf{x}_{c}$ is the already defined controllable
state of the internal model and $\mathbf{x}_{2}$ is the augmented state
introduced by the PI controller.

Both the internal and BIBO stability can be studied following (9), translated
in frequency domain:

$\displaystyle\mathbf{X}_{ctrl}(z)=$
$\displaystyle\underbrace{z\left[z\mathbb{I}-\mathbf{A}_{ctrl}\right]^{-1}}_{\mathbf{X}_{ctrl,zi}(z)}\mathbf{X}_{ctrl}(0)+$
(10)
$\displaystyle+\underbrace{\mathbf{B}_{ctrl}\left[z\mathbb{I}-\mathbf{A}_{ctrl}\right]^{-1}}_{\mathbf{X}_{ctrl,zs}(z)}\mathbf{\overline{e}}(z)$

where $\mathbf{X}_{ctrl,zi}(z)$ denotes the zero-input response (hence when
the tracking error $\mathbf{\overline{e}}(z)=0$), $\mathbf{X}_{ctrl,zs}(z)$
the zero state response when $\mathbf{X}_{ctrl}(0)=0$. Similarly as before,
the stability analysis depends on the term
$\left[z\mathbb{I}-\mathbf{A}_{ctrl}\right]^{-1}$, which can be solved by
applying the pole-placement technique.

The disturbance rejection input term $\mathbf{u}_{d}=\mathbf{M}\mathbf{x}_{d}$
can be designed to guarantee the stability by finding a suitable matrix
$\mathbf{M}$. This matrix can be obtained by following the Sylvester-Francis
equation, [3, 4].

###  2.5 Noise estimator stability proof

The noise estimator block goal is to achieve the closed-loop stabilization of
the predictor as well as to ensure a suitable disturbance estimation
capability, i.e. estimate the noise vector $\mathbf{\overline{w}}$. The noise
estimator block governing equations are as follows

$\displaystyle\mathbf{\overline{w}}(k)$
$\displaystyle=\begin{bmatrix}\overline{w}_{1}\\\ \overline{w}_{2}\\\
\overline{w}_{3}\end{bmatrix}(k)=\mathbf{L}\mathbf{e}_{m}(k)=\begin{bmatrix}l_{1}\\\
l_{2}\\\ l_{3}\end{bmatrix}\mathbf{e}_{m}(k),$ (11)
$\displaystyle\mathbf{e}_{m}(k)$
$\displaystyle=\mathbf{y}(k)-\mathbf{y}_{m}(k).$

In (11), $\mathbf{y}_{m}$ is the estimated output of the internal model,
$\mathbf{y}$ is the measurement output of the plant, while $\mathbf{L}$
collects the closed-loop predictor gains $l_{k}\mbox{, }k\,{=}\,1,\dots,3$,
for the specific DC motor case. As a result, the closed-loop predictor model
can be determined by designing and tuning the $l_{k}$ gains trading-off
between the closed-loop stability and the estimation performance.

A static-feedback is selected for the design of noise estimator, and its
stability analysis is already studied in [1], Appendix B.

###  2.6 Asynchronous sampling time stability remarks

From the experimental design perspective, the discrete-time eigenvalues of the
control unit naturally change at each time-step. This is directly related to
the nature of the NCS environment, characterised by highly variable sampling
times. As a result, the adopted design solution was based on the design of a
set of continuous-time eigenvalues first, focusing on expected stability and
performance level. In particular, $\mu_{{}_{K}}$ are the control law
continuous-time eigenvalues, $\mu_{{}_{R}}$ the reference dynamics eigenvalues
and finally $\mu_{{}_{N}}$ the predictor eigenvalues. Indeed, such a
continuous-time set of eigenvalues, $\mu_{i},\,i\,{=}\,1,\dots,n$, do not
depend on the variable sampling time and can be then converted, at every time-
step, into discrete-time eigenvalues
$\lambda_{i}=e^{\mu_{i}T_{s,k}},\,i\,{=}\,1,\dots,n$, being $T_{s,k}$ the
generic sampling time of the $k^{th}$ time-step.

In Figure 1 the discrete-time domain eigenvalues are presented, for reference
dynamics $\lambda_{{}_{R}}=e^{\mu_{{}_{R}}T_{s}}$, control law
$\lambda_{{}_{K}}=e^{\mu_{{}_{K}}T_{s}}$ and predictor
$\lambda_{{}_{N}}=e^{\mu_{{}_{N}}T_{s}}$: it can be seen that, for the defined
variation of $T_{s}$, spanning from $0.01$\mathrm{s}$$ to $0.03$\mathrm{s}$$,
the values are always inside the unitary circle, thus guaranteeing asymptotic
stability.

Figure 1: Experimental results: polar plot of the stability conditions of the
control system, for $T_{s}=[0.01,0.03]\ s$

##  3 Additional experimental results

In this section experimental tests are presented, which give additional
results for the work in [1].

###  3.1 EMC mobile robot test - NCS disturbance rejection effectiveness

Figure 3 presents an experimental test with the right motor of the
differential-drive robot (the results are analogous for the left motor), in
the case of EMC disturbance rejection active. The motor output speed must
follow a reference trajectory with the values of
$6\text{\,}\mathrm{rad}\text{\,}{\mathrm{s}}^{-1}$ and
$-$4\text{\,}\mathrm{rad}\text{\,}{\mathrm{s}}^{-1}$$, with a first-order
dynamics in two different time periods. The sampling time is asynchronous and
defined in the range $T_{s}=[0.01,0.03]\ $\mathrm{s}$$, as it can be seen in
Figure 2. The measured $\mathbf{y}$ and the estimated $\mathbf{y}_{m}$ outputs
are compared to understand the internal model observer estimation
capabilities, quantified by the model error
$\mathbf{e}_{m}=\mathbf{y}-\mathbf{y}_{m}$, which is shown in Figure 4. The
model error results to be in the range of the DC motor encoder maximum angular
speed resolution error, $e_{enc}=0.8726\ $\mathrm{rad}\text{/}\mathrm{s}$$.
This implies a remarkable and effective estimation performances, as it can be
visually appreciated in Figure 3, where $\mathbf{y},\mathbf{y}_{m}$ basically
overlap.

Figure 2: Experimental results: asynchronous timestamp with range
$T_{s}=[0.01,0.03]\ $\mathrm{s}$$ Figure 3: Experimental results: DC motor
output speed estimation ($\mathbf{y}_{m}$) and comparison with reference
($\mathbf{\overline{y}}$) and measured ($\mathbf{y}$) values - Disturbance
rejection case Figure 4: Experimental results: Tracking error $\mathbf{e}_{m}$

###  3.2 EMC mobile robot test - Critical asynchronous sampling times

Figure 5 shows the estimated output of the EMC internal model
$\mathbf{y}_{m}$, for several asynchronous sampling times $T_{s}$; spanning
from a fixed minimum value of $10$ ms, to a variable maximum value of
$[50,100,150,200]$ ms. For this experimental test, the reference motor speed
is imposed to a fixed value of $\mathbf{\overline{y}}=6$ rad/sec. The
estimation of $\mathbf{y}_{m}$ is effective and characterized by a negligible
model error $\mathbf{e}_{m}$, until a maximum value $T_{s}=150$ ms, which is
sufficiently high to cover a wide range of NCS delay and package loss
variations. Only for higher sampling times, $T_{s}>150$ ms, the model output
$\mathbf{y}_{m}$ starts to show a degradation in estimation performance.

Figure 5: Experimental results: $\mathbf{y}_{m}$ for several variable time-
stamps $T_{s}$

###  3.3 EMC mobile robot test - EMC and PI comparison

In [1] a comparison between the EMC and a complete PID controller is made.
However other experimental tests are conducted by considering a partial
Proportional-Integral (PI) controller. Such a benchmark is adopted because, in
a set of experimental tests, it is found that the absence of the derivative
term led to more satisfactory control behaviours. The experimental comparison
between the EMC and PI controllers, in critical varying time conditions, is
shown in Figures from 6 to 8. The adopted variable timestamp is in the range
of $T_{s}=[10-150]$ ms, which introduces high delays in the control system and
simulates an NCS scenario. The EMC and PI controller parameters are listed in
Table 1.

Table 1: EMC and PI controllers experimental test parameters Parameter | Value
---|---
Experimental test time step $T_{s}\ [$\mathrm{s}$]$ | $[0.01,0.15]$
EMC Ref. dynamics eigenvalues $\mu_{{}_{R}}$ | $\left[-2.5647\right]$
EMC Feedback eigenvalues $\mu_{{}_{K}}$ | $\left[-2.5647,-2.5647\right]$
EMC Predictor eigenvalues $\mu_{{}_{N}}$ | $\left[-14.3842,-14.3842,-14.3839\right]$
PI proportional gain $K_{P}$ | 1.35
PI integral gain $K_{I}$ | 11.25

In Figure 6 the EMC control unit and a Proportional-Integral controller were
compared in the mentioned experimental scenario. The measured output is
$\mathbf{y}$ and the reference to be tracked is $\mathbf{\overline{y}}$. The
PI controller results to have difficulties to track the reference output
speed, even in steady-state conditions. Instead the EMC, after an initial
transient with acceptable delays and overshoots, is able to follow
$\mathbf{\overline{y}}$ with small errors.

Such a behaviour is validated by Figure 7, where the Root Mean Square Error
(RMSE) between $\mathbf{\overline{y}}$ and $\mathbf{y}$ is computed. In the
EMC case, the error is $RMSE_{EMC}=0.40594\
$\mathrm{rad}\text{\,}{\mathrm{s}}^{-1}$$: significantly lower than the one
for the PI controller, $RMSE_{PI}=0.88376\
$\mathrm{rad}\text{\,}{\mathrm{s}}^{-1}$$.

Finally in Figure 8 the tracking control inputs for both the controllers were
studied. In the EMC the control input $\mathbf{u}_{trk}$ is lower in magnitude
compared to the PI control input, and presents a more stable behaviour in
steady-state conditions.

This experimental behaviour is driven by the structure of the EMC control
block. Indeed, the EMC control input has 2 key parts: the feedback
$\mathbf{u}_{trk}$, leveraging the tracking error, and the disturbance
rejection signal $\mathbf{u}_{d}$. The last term, $\mathbf{u}_{d}$, is driven
by the disturbance dynamics estimated by the state observer, and counteracts
all the disturbances affecting the plant behaviour; up to a certain bandwidth
(set by the observer eigenvalues) [3]. This contributes in discharging the
tracking control input $\mathbf{u}_{trk}$, i.e. the feedback part of the
control law, whose main tasks becomes counteracting residual effects not
estimated by the observer [2]. Conversely, in the PI unit the control is only
managed by $\mathbf{u}_{trk}$, hence leading to the unexpected control
oscillations.

Figure 6: EMC and PI output speed comparison - Experimental test with
timestamp $T_{s}=[10-150]$ ms Figure 7: EMC and PI comparison: tracking error
$\mathbf{\overline{e}}$ with RMSE - Experimental tests with timestamp
$T_{s}=[10-150]$ ms Figure 8: EMC and PI comparison: tracking control input
$\mathbf{u}_{trk}$ \- Experimental tests with timestamp $T_{s}=[10-150]$ ms

##  4 Conclusion

This work is intended to give additional studies and results to the main work
Embedded Model Control of Networked Control Systems: an Experimental Case-
study, [1]. In this main work, the Embedded Model Control (EMC) methodology is
applied to design a complete digital control unit for a differential-drive
mobile robot controlled in a network controlled system (NCS), thus operating
in a scenario characterised by a varying sampling time and asynchronous
command execution.

At the beginning, this complementary paper presents a study on the stability
analysis of the EMC, in the case of the differential-drive robot setup; namely
the setup explored in [1]. Furthermore, experimental tests are added to those
presented in [1]. The first test verified the EMC asynchronous timing
disturbance rejection capabilities, in the case of the differential-drive
robot setup. The second experiment aimed to test the EMC in critical
asynchronous NCS scenarios, with high delays of the timestamp. The EMC
resulted to have satisfactory control behaviours until high ranges of variable
timestamp, thus validating the high practical applicability of the EMC
control. Another experiment benchmarked the proposed EMC asynchronous
architecture with a Proportional-Integral controller (a design showing a more
satisfactory control behaviour than other control architectures, e.g. PID).
The experimental benchmarking study showed that the EMC has a better tracking
performance than the PI controller, thanks to the presence of the new
disturbance rejection control term.

## References

  * [1] L. Nanu, C. Perez Montenegro, L. Colangelo, C. Novara, Embedded Model Control of Networked Control Systems: an Experimental Case-study, Control Engineering Practice (to be published) (2023).
  * [2] C. Novara, E. Canuto, D. Carlucci, Control of systems with sector-bounded nonlinearities: robust stability and command effort minimization by disturbance rejection, Control Theory and Technology 14 (3) (2016) 209–223.
  * [3] E. Canuto, Embedded Model Control: Outline of the theory, ISA Transactions 46 (3) (2007) 363–377.  doi:10.1016/j.isatra.2007.01.006.
URL http://linkinghub.elsevier.com/retrieve/pii/S0019057807000481

  * [4] W. Acuña-Bravo, A. G. Molano-Jiménez, E. Canuto, Embedded model control, performance limits: A case study, DYNA 84 (201) (2017) 267.  doi:10.15446/dyna.v84n201.59165.
URL http://revistas.unal.edu.co/index.php/dyna/article/view/59165


# Profile Update: The Effects of Identity Disclosure on Network Connections
and Language

Minje Choi  School of Information, University of Michigan  Daniel M. Romero
School of Information, University of Michigan  Computer Science and
Engineering Division, University of Michigan  Center for the Study of Complex
Systems, University of Michigan  David Jurgens  School of Information,
University of Michigan  Computer Science and Engineering Division, University
of Michigan

###### Abstract

Our social identities determine how we interact and engage with the world
surrounding us. In online settings, individuals can make these identities
explicit by including them in their public biography, possibly signaling a
change to what is important to them and how they should be viewed. Here, we
perform the first large-scale study on Twitter that examines behavioral
changes following identity signal addition on Twitter profiles. Combining
social networks with NLP and quasi-experimental analyses, we discover that
after disclosing an identity on their profiles, users (1) generate more tweets
containing language that aligns with their identity and (2) connect more to
same-identity users. We also examine whether adding an identity signal
increases the number of offensive replies and find that (3) the combined
effect of disclosing identity via both tweets and profiles is associated with
a reduced number of offensive replies from others.

##  1 Introduction

Our social identities such as age, gender, or occupation play a crucial role
in shaping how we express thoughts and opinions through language, and in turn,
how others interact with us. In social media platforms such as Twitter, the
identity that one chooses to associate oneself with can influence behaviors
such as the topics one engages with or the ties one forms. One can choose to
explicitly disclose their identity through various means, but the effects and
consequences of such actions are largely unknown. In this paper, we perform a
large-scale study to understand how explicitly disclosing social identities
leads to changes in the interactions of one’s social network.

Figure 1: Identity disclosure in Twitter profiles

Identity disclosure and management is an essential part of online behavior
(Joinson et al., 2010; Pavalanathan and De Choudhury, 2015), as individuals
navigate what aspects of themselves are salient to others. In more public
platforms like Twitter, individuals must weight how to present themselves
based on the mix of audiences who may find them (Marwick and boyd, 2011;
Bazarova and Choi, 2014; Duguay, 2016). People may explicitly express social
identities in social media by including phrases related to the identity in
profile descriptions, as shown in Figure 1. Profile descriptions, similar to
posts, also contain rich textual features associated with the user’s social
identity (Li et al., 2014; Priante et al., 2016; Wilson and Wun, 2020; Wang et
al., 2019). Crucially, these profiles are not static: Individuals add and
remove identity markers from their bios to emphasize new or specific aspects
of themselves, such as political affiliations (Jones, 2021) or gender pronouns
(Tucker and Jones, 2023; Jiang et al., 2022).

Disclosed social identities can affect how they are perceived and targeted by
other users. Prior studies have drawn connections between the disclosure of
identities—especially marginalized or minority identities—and identity-based
hate or cyberbullying, therefore hindering people from fully expressing
themselves and sometimes even forcing them to hide identities online (Haimson
et al., 2015; Jhaver et al., 2018). However, not all identities are
marginalized and the potential varied outcomes for identity disclosure are yet
to be quantified.

To understand the effects of identity disclosure, we conduct a large-scale
quasi-experimental study on hundreds of thousands of users who updated their
profiles to disclose a particular social identity. We observe that while
overall tweet activity levels remain stable post-disclosure, their tweets
contain significantly higher volumes of identity-relevant language, which we
further dissect into topic and style properties. We demonstrate that this
disclosure is also associated with social network changes: users actively
engage more with similar-identity individuals following disclosure. Finally,
we examine the number of offensive replies received from others during pre-
and post-disclosure periods, where we show that contrary to existing studies
(Chan, 2022; Meyer, 2003), the addition of identity signals in profiles did
not lead to increased levels of received offensiveness, even for identity
categories known to be prone to targeted offensiveness such as sexual and
gender minorities. Overall, our findings suggest profile-based identity
disclosure is an active process signaling future behavior changes in the
priorities of a user.

##  2 Social Identities and Self-disclosure

Prior work has examined identity disclosure from the perspectives of language,
networks, and social interactions, particularly in online spaces. We build on
the previous studies to formulate hypotheses that examine whether disclosure
of social identities leads to changes in behaviors of both the user themself
and how they are perceived by others.

Figure 2: Schematic diagram of data collection, identity classifiers,
propensity score matching, and analyses on research questions. AlwaysPositive,
AlwaysNegative, IdentityAdded, NotAdded and Control represent sets of users
with specific profile and identity statuses.

###  2.1 Social Identities and Language

Sociolinguistics has long associated language with social identities of the
speaker (Labov, 1966; Eckert, 2000; Pomerantz, 2007). Specifically, Bucholtz
and Hall (2005) propose a framework for understanding identity through
linguistic interaction, where they suggest that identities can be indexed
through linguistic aspects such as style, stances, and labels (Schilling-
Estes, 2004). This framework also posits that the display of identity through
language can be an intentional form of agency to meet social goals (Duranti,
2008). From this perspective, we can assert that the intention to disclose
one’s social identity can be reflected through their language, which may be
indicative of the identity.

Our first hypothesis examines the relationship between identity disclosed
through language and through profile updates. We hypothesize that the
modification of one’s profile to disclose a particular social identity will
motivate the user to tune their linguistic style to accommodate their
presented identity.
H1 The addition of a social identity on a Twitter profile will lead to posting
more identity-aligned tweets compared to a reference group.

###  2.2 Networked Effects of Identity Disclosure

People present themselves to others by controlling the amount of information
available to maintain a publicly desirable image, a concept known as
impression management (Goffman, 1959). This management helps achieve socially
desirable goals such as maintaining reputation (Schlenker and Britt, 1999;
Zivnuska et al., 2004). In social networking platforms such as Twitter or
Instagram, the downstream effects of impression management can be translated
into measurable outcomes such as maintaining connections with “friends” in the
platform who can provide desirable effects such as social support or access to
information (Lampe et al., 2007; Yan et al., 2022). We thus expect that the
addition of social identity in one’s profile reflects a desire to connect with
like-minded others, which results in an increased effort to forge connections
with people of the same identity.
H2 The addition of a social identity on a Twitter profile will directly lead
to establishing more network connections with users of the same identity
compared to a reference group.

###  2.3 Consequences of Identity Disclosure

Identity disclosure can lead to undesirable consequences. Privacy is a major
risk of disclosure in online spaces (Ampong et al., 2018). Also, the
disclosure of minority or marginalized identities can lead to being targeted
for online harassment. For example, nonbinary users consider disclosing their
identity on social media a stressful event (Haimson et al., 2015; Haimson and
Veinot, 2020).

As our final hypothesis, we test whether disclosure of one’s identity can lead
to increased hostility directed at the user. Specifically, we measure if a
user becomes a target of offensive content following the addition of their
identity on the profile.
H3 The addition of a social identity on a Twitter profile will result in
receiving more offensive replies compared to a reference group.

##  3 Identifying Identity Change in Profiles

Here, we describe our pipeline for identifying instances of Twitter users
disclosing social identities on their profiles. An overview of the data
collection and processing is shown in Figure 2.

###  3.1 Identifying Twitter Profile Changes

We first identify a set of users who have added signals of their social
identity to their Twitter profiles. This information is unobtainable using
just the Twitter API as it only returns a user’s profile information at the
time of the API call and does not provide a chronological timeline of profile
changes. We instead use the Twitter Decahose dataset which contains a 10%
sample of the entire Twitter activities over a period of over 12 months. We
identify all activities of every user between April 2020 and April 2021. Each
tweet or retweet object includes various metadata, one of which is the user’s
profile description at the time of the tweet. We collect all instances of user
profiles for our Twitter users and sort them in chronological order, enabling
us to identify when a user changed their profile. We remove verified accounts
and users whose language is set to a language other than English, resulting in
15,215,776 users and 73,048,466 unique profiles.

###  3.2 Categorizing Social Identities

Deciding what counts as a social identity can be challenging. Here, we start
from an initial set of social categories based on two relevant studies.
Priante et al. (2016) categorized social identities into five groups: personal
relationships, vocations/avocations, political affiliations, ethnic/religious
groups, and stigmatized groups. Meanwhile, Yoder et al. (2020) used 11
identity categories: age, ethnicity/nationality, fandoms, gender, interests,
location, personality type, pronouns, relationship status, sexual orientation,
and zodiac. Using this list of categories as a starting point, one author
manually inspected each n-gram and assigned it to a category when applicable.
The n-grams within each category were additionally grouped into subcategory
levels, e.g., the gender category consists of three subcategories: men, women,
and nonbinary. A total of 221 n-grams were assigned to a category and
subcategory.

We also create subcategory-level identities within each category, which is the
basic unit of social identity in this study. This process results in a total
of ten categories (Table 1) and 44 subcategories of identities (Appendix Table
2). Further details on the subcategories are in Appendix Section A.

After categorizing n-grams into identity categories and subcategories, we
follow the approach from prior work (Yoder et al., 2020; Pathak et al., 2021)
and construct regular expressions for each category and subcategory based on
the n-grams to improve precision. For example, when constructing regular
expressions for age, we ensure that the corresponding phrases include
identifiers such as ‘years old’ or ‘y/o’.

Category | # users
---|---
Age | 12,737
Education | 23,201
Ethnicity | 16,507
Gender pronouns | 59,893
Occupation | 68,694
Personal | 41,107
Political | 26,609
Relationship | 20,167
Religion | 11,169
Sexuality (LGBTQ+) | 3,772
Total | 283,793
Table 1: The number of users who updated their Twitter profiles to disclose
social identities. Refer to Table 2 in the Appendix for counts at subcategory
level.

Next, we identify a set of users who have changed their profiles to disclose
their social identity. We run our regular expressions on every unique profile
to determine whether a profile is associated with a particular identity. We
assign multiple labels if a user’s profile is associated with multiple
identity categories (e.g. “18yo — he/him — father of two wonderful children”),
but leave out profiles that our method labels as belonging to multiple
subcategories within the same category when they are meant to be mutually
exclusive (e.g. age - “18yo — 30y/o”, political affiliation - “devout democrat
— conservative”). Based on the mapped identities per profile, we can identify
all users who satisfy the following two conditions: (1) each user has made
only one change in their profile during the 1 year observation period, and (2)
the only change is the addition of a new social identity—i.e., the phrase
indicating identity should only exist in the changed profile and not the
previous version. This filtering results in a set of 283,793 users who added a
single new social identity through Twitter profiles, which we refer to as
IdentityAdded. Tables 1 and 2 contain category- and subcategory-level counts.

We validate the quality of our pipeline for capturing instances of identity
disclosure through an annotation task. For each subcategory, three annotators
are provided twenty samples which each consist of two subsequent profiles, one
pre- and one post-change. The twenty samples include ten positive samples from
IdentityAdded as well as ten negative samples, which vary from (1) no
disclosure in either, (2) disclosure in both, and (3) disclosure only in pre-
change. The resulting Krippendorff’s $\alpha$ was 0.74, indicating a high
level of agreement that the changes detected by our approach do constitute
meaningful self-disclosure of identity. We then evaluate our pipeline by
evaluating it on the majority vote from the annotations, from which we saw
that 41/44 identities achieved an F1 score higher than 0.5 (Appendix Tables 3
and 4). We therefore removed the three identities with low performance:
education:student, ethnicity:korean, and occupation:art.

###  3.3 Propensity Score Matching

Since our research questions center around behavioral changes following social
identity disclosure through profiles, a meaningful measurement can be made by
comparing against a control group that displays similar behaviors but does not
disclose social identities through profile updates. We adopt propensity score
matching (PSM), a quasi-experimental method widely adopted in observational
studies involving observational social media data (Yuan et al., 2023; Choi et
al., 2023).

Apart from the IdentityAdded users we also identify 849,901 users who (1) made
one profile update during the 1-year observation period but (2) did not
include any phrases of social identity in their profiles before or after the
update, which we refer to as NotAdded users. For each user in IdentityAdded
and NotAdded, we identify the following covariates obtained at the date of the
profile change: number of days since account creation, number of friends,
number of followers, number of total posts, number of tweets and retweets
posted during one month prior to the time of profile update. Further details
of the matching can be found in Appendix Section C.

As a result of the matching process, we are left with 283,566 treated users
and 1,228,945 matched users. We refer to the resulting matched set as Control
users. Figure 9 in the Appendix shows that the distribution containing the
standardized mean difference of every covariate reduces sharply after
matching, demonstrating the diminished effect caused by confounding
covariates.

###  3.4 Estimating Treatment Effects

Our setting of treated and control variables allows us to perform a widely
used causal inference method known as difference-in-differences (DiD; Abadie,
2005). Though DiD is most commonly used when the outcome variable is a
continuous variable, it can be applied to different types of outcomes such as
count variables (Cameron and Trivedi, 2013; Mark et al., 2013). Accordingly,
we use the following equation:

$\textrm{log}\left(y_{i,t}\right)=\beta_{0}+\beta_{1}X_{i}+\beta_{2}\left(T=1\right)+\beta_{3}\left(t\geq\textrm{tr}\right)+\beta_{4}\left(T=1\right)\left(t\geq\textrm{tr}\right)$

where $y_{i,t}$ is the outcome variable at time $t$ for user $i$, $T=1$ is a
binary assignment status to treatment group, and $t>=\textrm{tr}$ is whether
time $t$ is beyond treatment period. $X_{i}$ is the time-invariant covariates
of $i$, which consist of the number of friends, followers, and total posts.
All experiments are modeled as a negative binomial regression using
generalized estimating equations (GEE) in statsmodels. Because our hypothesis
testing are done on multiple identities, we apply the Bonferroni-Holm
correction (Holm, 1979) to account for false positives when reporting
significance test results from the regressions.

##  4 How does Identity Disclosure affect Language?

To understanding behavioral changes following identity disclosure, we first
study whether users change their language following profile updates to include
a social identity. We hypothesize that the addition of an identity signal
provides a certain level of boost to represent their identity more through the
content they produce and engage with.

#### Measuring Identity-specific Language

We first construct classifiers to measure the amount of identity alignment
from a tweet. Based on existing findings that posts and profile descriptions
in online platforms are reflective of one’s social identity (e.g., Priante et
al., 2016; Preoţiuc-Pietro and Ungar, 2018), we assume that if a user has
disclosed a social identity on their profile description for a sufficiently
long time, then the text created by the user contains topical and stylistic
features indicative of the disclosed identity. Accordingly, we first identify
users who did not update their profile during our observation period, and
identify cases where their profile did (AlwaysPositive) or did not
(AlwaysNegative) include an identity (refer to Figure 2). We then aggregate
the tweets created by each user and assign positive or negative labels to the
tweets based on the user’s identity existence. Each classifier is a RoBERTa
(Liu et al., 2019) model pretrained from tweets and further finetuned on the
labeled tweet dataset. Further training details and examinations on classifier
performances can be found in Appendix Section B.

#### Experiment Setting

We use the scores from the classifiers to measure levels of identity-specific
language from both the content that users post (tweets) and engage with
through sharing (retweets). Using the identity classifiers, we obtain scores
for every tweet and retweet generated by each IdentityAdded and Control user
between one month before and after the profile update. We then count the
number of tweets with an inferred identity score higher than 0.5 and aggregate
them into two periods, before and after the profile update. We consider these
as the total number of identity-relevant tweets the user tweeted or retweeted
before or after treatment. We also count the number of total tweets regardless
of identity score, which captures overall activity levels. We run separate
regressions with the number of total tweets/retweets and identity-specific
tweets/retweets as outcome variables, and include the number of total
activities as a control variable when modeling identity-specific activities.

Figure 3: Effect sizes of identity disclosure on tweet and retweet-level
activities. The x-axis indicates percentage increase in number of tweets
following identity disclosure. Significant positive and negative values that
pass the correction test are marked in red (positive) and blue (negative).
While identity disclosure does not lead to increased activity levels, there
are significant increases in the number of tweets and retweets that contain
identity-specific language

#### Results

Figure 3 shows the effects of adding profiles on four different types of tweet
activity counts: the number of total tweets (Figure 3(a)) and retweets (Figure
3(b)) versus identity-aligning tweets (Figure 3(c)) and retweets (Figure
3(d)). We can first observe that, contrary to prior work Lampe et al. (2007),
the additional disclosure of social identity via profiles does not lead to
greater overall activity levels compared to profile updates without such
disclosure (Figures 3(a) and 3(b)). In fact, we observe the opposite for
several types of identities, most notably drops of both tweet and retweet
levels in binary gender pronouns and student status. The only statistically
significant increases we observe arise from disclosing political statuses.

On the other hand, we observe statistically significant increases in the
number of tweets posted and retweeted which contain identity-specific
language, across almost every category (Figures 3(c) and 3(d)). Though there
exists variance among categories, in general, we observe that identity-
specific tweets increased by around 20-40% and identity-specific retweets
increased by around 10-30%, indicating that though the content volume does not
change, the percent of identity-related content within that volume increases
substantially. Further comparisons within identity categories reveal
interesting findings. For instance, we observe that for both tweets and
retweets, the increase following identity disclosure of men is lower than that
of women and nonbinary genders. One possible reason is women and nonbinary
gender users may undergo harder decisions to disclose their identity, which
results in a greater change in their behavior following disclosure. Similarly,
our results on ethnicity disclosures show larger identity-specific activities
for African identities compared to the American identity, suggesting the level
of language change may differ by identity types.

Figure 4: Changes in style and topic differences between AlwaysPositive users
and IdentityAdded users before and after identity disclosure. Style becomes
more similar after the disclosure compared to topics, where the relative
distances are much smaller.

#### Identity-specific language: topic or style?

To further understand which aspects of language change following identity
disclosure, we compare the tweets through two components of language: topic
and style. We examine whether having a IdentityAdded user disclose their
identity results in their language becoming more similar to that of a
AlwaysPositive user regarding each component. Further details for computing
the distances can be found in Appendix Section D.

Figure 4 shows changes in the distance between the language of users who
change towards disclosing their identity to those who always have had the
identity visible. While topic differences remain relatively unchanged, the
difference in style between the two user groups are reduced following identity
disclosure for all categories apart from age. Though users do not
significantly shift their topics of interest, they tune their language to
appear more similar to the style associated with the identity that they choose
to disclose.

##  5 Does identity disclosure in profiles lead to network rewiring towards
same-identity connections?

Figure 5: Effect sizes of identity disclosure on out- and in-degree network
sizes. Users reach out to those of the same identity following disclosure
(out-degree), but not all identities receive increased attention from others
in return (in-degree)

In our next analysis, we investigate whether the addition of identities leads
to bridging more connections with like-minded others. To do so, we collect the
ego networks of every IdentityAdded and Control user where an edge between two
users $u$ and $v$ is defined when $u$ replies to or retweets a tweet posted by
$v$. We divide a user’s network activities by pre- and post-treatment where we
look at a timespan of 12 weeks. We use the same set of regular expressions
from the profiles of all users included in the networks and extract any social
identities from their profiles during the 12-week period. The subset of
connected users who have adopted the same identity as the ego user at any
point will be considered same-identity nodes. Thus, in our subsequent diff-in-
diff analysis, the outcome variable is the number of same-identity nodes
before and after the identity disclosure.

#### Results

Figure 5 displays the treatment effect on the out- and in-degree of the
network when restricted to users of the same identity. We can observe that
across most categories, the out-degree of same-identity neighbors
significantly increases after identity disclosure in profiles (Figure 5(a)).
This indicates that the users who choose to disclose their identities also
choose to connect to more people that share the same identity.

We next look at the in-degree level changes, which is a stronger indicator of
how the addition of identity is viewed by others (Figure 5(b)). We observe
that the in-degree of same-identity groups is less likely to increase compared
to the out-degree, which indicates that inbound connections are less likely to
be made compared to outbound connections, as the former requires others to
actually be motivated to establish new connections with the user who has made
a profile change.

Additional results, shown in the Appendix, highlight identity-specific
changes. Figure 12 contains the effect sizes of the total out- and in-degree
network sizes following disclosure, revealing that the overall network size
only increases for political identities. These results support our claim that
users choose to strategically rewire their connections more towards those of
the same identity while keeping overall network sizes stable instead of merely
being more open in general. Figure 13 shows changes in connection levels
towards different identities in the same category. We find that gender
pronouns is the only category to increase in both in-degree and out-degree for
all identities, which is in line with existing work that showed tie clustering
among such pronouns (Tucker and Jones, 2023). Last of all, we compare changes
in cross-partisan connections for conservative and liberal users, where we
observe significant increases of outbound connections from those who disclose
their liberal identity to conservative users, but not the other way round.

##  6 Does identity disclosure lead to receiving more offensive content?

In our final research question, we investigate possible negative consequences
of disclosing one’s identity, namely whether identity disclosure leads to
increased targeted offensive content.

#### Experiment Setting

For each IdentityAdded and Control user, we use the 10% sample dataset to
collect a history of the tweets posted by the user during one month before and
after the time of their profile update, as well as all replies received from
other users during this period. Next, we use a publicly available classifier
for detecting offensiveness from Hugging Face (Barbieri et al.,
2020)111https://huggingface.co/cardiffnlp/twitter-roberta-base-offensive to
obtain offensiveness scores of both the tweets posted and the replies from
others. We then formulate an equation to model the expected number of
offensive replies

$\textrm{log}\left(y_{i,t}\right)=\beta_{0}+\beta_{1}X_{i}+\beta_{2}\left(T=1\right)+\beta_{3}\left(t\geq\textrm{tr}\right)+\beta_{4}\left(T=1\right)\left(t\geq\textrm{tr}\right)+\color[rgb]{0,0,1}\textrm{log}\left(\beta_{5}\textrm{n}_{id}\right)+\color[rgb]{1,0,0}\textrm{log}\left(\beta_{6}\textrm{n}_{id}\right)\left(T=1\right)\left(t\geq\textrm{tr}\right)$.
The added term $\textrm{log}\left(\beta_{5}\textrm{n}_{id}\right)$ indicates
the log-normalized number of identity-specific tweets posted by the user and
$\textrm{log}\left(\beta_{6}\textrm{n}_{id}\right)\left(T=1\right)\left(t\geq\textrm{tr}\right)$
is the interaction effect between identity disclosure via profile and
identity-specific tweets.

#### Results

Figure 6(a) ($\beta_{4}$) first shows that identity disclosure through
profiles increases offensiveness for only a handful of categories -
ethnicity:American, gender:men, personal:socialmedia, and political:activism.
However, when we observe changes in offensiveness levels caused by increased
identity of tweets (Figure 6(b) ($\beta_{5}$)), we can see that significant
effects can be seen from several categories. Interestingly, the disclosure of
identity through tweets leads to reduced levels of offensiveness from others
for the three studied gender types, as well as for occupations and religion
types. Meanwhile, we observe increased levels of offensive replies from all
three types within the political category, hinting that this may be due to
heated political conversations that often correlate with offensiveness.
Lastly, the interaction effect of identity disclosure via both tweet and
profile (Figure 6(c)) ($\beta_{6}$) suggests that the combined effect from
disclosure through both channels reduces levels of offensiveness for every
category where increased identity disclosure through tweets was associated
with increased offensiveness. One potential explanation is that disclosing
identity through both profile and tweet could create a sense of consistency,
which helps reduce levels of hostility towards that identity group.

Figure 6: Effect size of identity disclosure on the number of offensive
replies received. (left) identity addition to profile, (middle) number of
identity-specific tweets per week, (right) interaction effect of identity
disclosure through profile and number of identity-specific tweets per week

##  7 Discussion

Our findings indicate that disclosing social identities, regardless of
category, follows similar behaviors in that both the content produced and
connections made by the user become more aligned with the announced identity.
We can assume that at the heart of such disclosure lies the innate desire to
express oneself and find comfort among like-minded peers. It is also notable
that instead of just becoming more active overall, users maintain similar
levels of activity and connectivity while channeling their effort towards more
identity-aligned decisions. This comes at the expense of interactions with
those unassociated with the identity, and coupled with existing findings that
more people are disclosing their identity on Twitter (Pathak et al., 2021;
Jones, 2021), could even signal that our Twitter networks might become more
homogeneous over time.

Another interesting finding regarding the effects of disclosure was that
identity disclosure via profiles did not result in significant increases in
offensive replies targeted to the user for marginalized categories such as
nonbinary gender, LGBTQ+ sexualities or minority ethnicities. While our
results do not and are not meant to deny the existence of identity-targeted
hate in social media platforms that is a major source of harm, we take a more
positive view suggesting that the consequences of disclosing identity through
profiles may not be as severe as anticipated, and that disclosure should be
promoted and more widely accepted.

##  8 Conclusion

We conduct a case study for identifying whether added disclosure of one’s
social identity through profile updates leads to subsequent changes in
linguistic style and network connections, and whether the disclosure leads to
increased offensiveness from others. We propose methods for measuring identity
disclosure through both profile- and tweet-level language and apply them to
quasi-experimental difference-in-differences methods to show that identity
disclosure through labels leads to increased disclosure in subsequent
language. Furthermore, we also observe that identity disclosure can lead to
increased connections with like-minded identities, which is much more
prevalent from the outward versus inward ties. Finally, we observe that,
contrary to existing concerns, the negative effect of increased offensiveness
from disclosing a social identity via profiles does not exist for most
identities, and that the combined disclosure from both profile- and tweet-
levels led to reduced targeted offensiveness levels. Overall, our results
suggest that the decision to disclose one’s social identity can be encouraged,
with negative effects appearing less than is concerned. The code and annotated
data for the study will be available at
https://github.com/minjechoi/twitter_identity.

##  9 Limitations and Ethical Considerations

One limitation that our analysis is focuses only on Twitter. The amount of
disclosure may differ by type of platform depending on why people use it
(Jaidka et al., 2018; van Dijck, 2013). Identity may be visible through means
other than the profile text. One example would be a profile image, which can
indicate demographic features such as age, gender, and ethnicity (Yoder et
al., 2020).

#### Identity-unaware offensiveness classifiers

To conduct the experiment on offensiveness levels after identity disclosure,
we use finetuned classifiers trained on an external Twitter corpus (Barbieri
et al., 2020). The black-box nature of these classifiers and datasets contain
the risk of predicting text features of some identities as more offensive than
others without sufficient understanding of contexts surrounding the identity,
such as African-American English (Sap et al., 2019; Harris et al., 2022). In
fact, our correlation results between the scores of the offensive classifier
and identity-specific classifiers on a large corpus (Figure 10 in the
Appendix) may lead to conclusions such as identity-specific language from
nonbinary genders being more likely to be offensive than men or women, or the
identity-specific language of Mexicans being the most offensive compared to
other ethnicities.

#### Purpose of identity classifier

It is possible that one may associate the regular expression-based pipelines
for identifying profile disclosures and the identity classifier models with
purposes such as detecting whether a user possesses a hidden identity trait
based on their prior Twitter history. We argue that our models are not served
for that purpose. Rather, our categorization of users is entirely based on
self-declared phrases indicative of social identities, which we examine
through a meticulous verification process. Our results are driven from purely
observational data aggregated at a scale of hundreds or thousands of users,
which removes the possibility of identification.

#### Results on the disclosure of marginalized identities

One of the findings of our study is that the disclosure of social identities
via profile changes did not result in increased levels of targeted
offensiveness, even for marginalized identity groups such as specific gender
or ethnicity groups. One possible limitation is that our study is based on
users who have willingly made the decision at some point to update their
profile and make their identity visible to their friends and to the public,
and those who did update may have been in a situation where they felt more
comfortable to disclose in the first place. This creates a selection bias that
might interfere with the generalizability of our findings to the general
population of Twitter users, and thus further caution should be made when
estimating the reactions following disclosure in online spaces. Nevertheless,
we conclude from our findings that identity disclosure through profiles can be
an effective means of expressing oneself and connecting with like-minded
others, and would encourage users to do so if seeking such outcomes.

## References

  * Abadie (2005) Alberto Abadie. 2005.  Semiparametric difference-in-differences estimators.  _The review of economic studies_ , 72(1):1–19.
  * Ampong et al. (2018) George Oppong Appiagyei Ampong, Aseda Mensah, Adolph Sedem Yaw Adu, John Agyekum Addae, Osaretin Kayode Omoregie, and Kwame Simpe Ofori. 2018.  Examining self-disclosure on social networking sites: A flow theory and privacy perspective.  _Behavioral Sciences_ , 8(6):58.
  * Barbieri et al. (2020) Francesco Barbieri, Jose Camacho-Collados, Luis Espinosa Anke, and Leonardo Neves. 2020.  Tweeteval: Unified benchmark and comparative evaluation for tweet classification.  In _Findings of the Association for Computational Linguistics: EMNLP 2020_ , pages 1644–1650, Online. Association for Computational Linguistics.
  * Bazarova and Choi (2014) Natalya N Bazarova and Yoon Hyung Choi. 2014.  Self-disclosure in social media: Extending the functional approach to disclosure motivations and characteristics on social network sites.  _Journal of Communication_ , 64(4):635–657.
  * Bianchi et al. (2021a) Federico Bianchi, Silvia Terragni, and Dirk Hovy. 2021a.  Pre-training is a hot topic: Contextualized document embeddings improve topic coherence.  In _Proceedings of the 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing (Volume 2: Short Papers)_ , pages 759–766, Online. Association for Computational Linguistics.
  * Bianchi et al. (2021b) Federico Bianchi, Silvia Terragni, Dirk Hovy, Debora Nozza, and Elisabetta Fersini. 2021b.  Cross-lingual contextualized topic models with zero-shot learning.  In _Proceedings of the 16th Conference of the European Chapter of the Association for Computational Linguistics: Main Volume_ , pages 1676–1683, Online. Association for Computational Linguistics.
  * Bucholtz and Hall (2005) Mary Bucholtz and Kira Hall. 2005.  Identity and interaction: a sociocultural linguistic approach.  _Discourse Studies_ , 7(4-5):585–614.
  * Cameron and Trivedi (2013) A Colin Cameron and Pravin K Trivedi. 2013.  _Regression analysis of count data_ , volume 53.  Cambridge university press.
  * Chan (2022) Randolph CH Chan. 2022.  Gender nonconformity, peer victimization, and internalizing problems among youth: Differential moderating effects of school climate by sex assigned at birth.  _Psychology of violence_.
  * Choi et al. (2023) Minje Choi, David Jurgens, and Daniel M. Romero. 2023.  Analyzing the engagement of social relationships during life event shocks in social media.  _Proceedings of the International AAAI Conference on Web and Social Media_ , 17(1):149–160.
  * cjadams et al. (2019) cjadams, Daniel Borkan, inversion, Jeffrey Sorensen, Lucas Dixon, Lucy Vasserman, and nithum. 2019.  Jigsaw unintended bias in toxicity classification.
  * cjadams et al. (2017) cjadams, Jeffrey Sorensen, Julia Elliott, Lucas Dixon, Mark McDonald, nithum, and Will Cukierski. 2017.  Toxic comment classification challenge.
  * Cohen (2013) Jacob Cohen. 2013.  _Statistical power analysis for the behavioral sciences_.  Academic press.
  * Deaux et al. (1995) Kay Deaux, Anne Reid, Kim Mizrahi, and Kathleen A Ethier. 1995.  Parameters of social identity.  _Journal of personality and social psychology_ , 68(2):280.
  * Duguay (2016) Stefanie Duguay. 2016.  “he has a way gayer facebook than i do”: Investigating sexual identity disclosure and context collapse on a social networking site.  _New media & society_, 18(6):891–907.
  * Duranti (2008) Alessandro Duranti. 2008.  _A companion to linguistic anthropology_.  John Wiley & Sons.
  * Eckert (2000) P. Eckert. 2000.  _Language Variation as Social Practice: The Linguistic Construction of Identity in Belten High_.  Language in Society. Wiley.
  * Goffman (1959) Erving Goffman. 1959.  _The presentation of self in everyday life._ Doubleday.
  * Haimson et al. (2015) Oliver L Haimson, Jed R Brubaker, Lynn Dombrowski, and Gillian R Hayes. 2015.  Disclosure, stress, and support during gender transition on facebook.  In _Proceedings of the 18th ACM conference on computer supported cooperative work & social computing_, pages 1176–1190.
  * Haimson and Veinot (2020) Oliver L Haimson and Tiffany C Veinot. 2020.  Coming out to doctors, coming out to “everyone”: Understanding the average sequence of transgender identity disclosures using social media data.  _Transgender Health_ , 5(3):158–165.
  * Harris et al. (2022) Camille Harris, Matan Halevy, Ayanna Howard, Amy Bruckman, and Diyi Yang. 2022.  Exploring the role of grammar and word choice in bias toward african american english (aae) in hate speech classification.  In _2022 ACM Conference on Fairness, Accountability, and Transparency_ , pages 789–798.
  * Hartmann et al. (2023) Jochen Hartmann, Mark Heitmann, Christian Siebert, and Christina Schamp. 2023.  More than a feeling: Accuracy and application of sentiment analysis.  _International Journal of Research in Marketing_ , 40(1):75–87.
  * Holm (1979) Sture Holm. 1979.  A simple sequentially rejective multiple test procedure.  _Scandinavian journal of statistics_ , pages 65–70.
  * Jaidka et al. (2018) Kokil Jaidka, Sharath Guntuku, and Lyle Ungar. 2018.  Facebook versus twitter: Differences in self-disclosure and trait prediction.  _Proceedings of the International AAAI Conference on Web and Social Media_ , 12(1).
  * Jenks (1967) George F Jenks. 1967.  The data model concept in statistical mapping.  _International yearbook of cartography_ , 7:186–190.
  * Jhaver et al. (2018) Shagun Jhaver, Sucheta Ghoshal, Amy Bruckman, and Eric Gilbert. 2018.  Online harassment and content moderation: The case of blocklists.  _ACM Transactions on Computer-Human Interaction (TOCHI)_ , 25(2):1–33.
  * Jiang et al. (2022) Julie Jiang, Emily Chen, Luca Luceri, Goran Murić, Francesco Pierri, Ho-Chun Herbert Chang, and Emilio Ferrara. 2022.  What are your pronouns? examining gender pronoun usage on twitter.
  * Joinson et al. (2010) Adam N Joinson, Ulf-Dietrich Reips, Tom Buchanan, and Carina B Paine Schofield. 2010\.  Privacy, trust, and self-disclosure online.  _Human–Computer Interaction_ , 25(1):1–24.
  * Jones (2021) Jason Jeffrey Jones. 2021.  A dataset for the study of identity at scale: Annual prevalence of american twitter users with specified token in their profile bio 2015–2020.  _PLOS ONE_ , 16(11):1–17.
  * Kang and Hovy (2021) Dongyeop Kang and Eduard Hovy. 2021.  Style is NOT a single variable: Case studies for cross-stylistic language understanding.  In _Proceedings of the 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing (Volume 1: Long Papers)_ , pages 2376–2387, Online. Association for Computational Linguistics.
  * Labov (1966) William Labov. 1966.  The social stratification of english in new york city.
  * Lampe et al. (2007) Cliff AC Lampe, Nicole Ellison, and Charles Steinfield. 2007.  A familiar face (book) profile elements as signals in an online social network.  In _Proceedings of the SIGCHI conference on Human factors in computing systems_ , pages 435–444.
  * Li et al. (2014) Jiwei Li, Alan Ritter, and Eduard Hovy. 2014.  Weakly supervised user profile extraction from Twitter.  In _Proceedings of the 52nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)_ , pages 165–174, Baltimore, Maryland. Association for Computational Linguistics.
  * Liu et al. (2019) Yinhan Liu, Myle Ott, Naman Goyal, Jingfei Du, Mandar Joshi, Danqi Chen, Omer Levy, Mike Lewis, Luke Zettlemoyer, and Veselin Stoyanov. 2019.  Roberta: A robustly optimized bert pretraining approach.  _arXiv preprint arXiv:1907.11692_.
  * Mark et al. (2013) Barbara A Mark, David W Harless, Joanne Spetz, Kristin L Reiter, and George H Pink. 2013.  California’s minimum nurse staffing legislation: results from a natural experiment.  _Health services research_ , 48(2pt1):435–454.
  * Marwick and boyd (2011) Alice E Marwick and danah boyd. 2011.  I tweet honestly, i tweet passionately: Twitter users, context collapse, and the imagined audience.  _New media & society_, 13(1):114–133.
  * Meyer (2003) Ilan H Meyer. 2003.  Prejudice, social stress, and mental health in lesbian, gay, and bisexual populations: conceptual issues and research evidence.  _Psychological bulletin_ , 129(5):674.
  * Misra and Arora (2023) Rishabh Misra and Prahal Arora. 2023.  Sarcasm detection using news headlines dataset.  _AI Open_ , 4:13–18.
  * Pathak et al. (2021) Arjunil Pathak, Navid Madani, and Kenneth Joseph. 2021.  A method to analyze multiple social identities in twitter bios.  _Proceedings of the ACM on Human-Computer Interaction_ , 5(CSCW2):1–35.
  * Pavalanathan and De Choudhury (2015) Umashanthi Pavalanathan and Munmun De Choudhury. 2015.  Identity management and mental health discourse in social media.  In _Proceedings of the 24th international conference on world wide web_ , pages 315–321.
  * Pavlick and Tetreault (2016) Ellie Pavlick and Joel Tetreault. 2016.  An empirical analysis of formality in online communication.  _Transactions of the Association for Computational Linguistics_ , 4:61–74.
  * Pomerantz (2007) Anne Pomerantz. 2007.  Language and social identity.  _Journal of Linguistic Anthropology_ , 17(1):146–148.
  * Preoţiuc-Pietro and Ungar (2018) Daniel Preoţiuc-Pietro and Lyle Ungar. 2018.  User-level race and ethnicity predictors from Twitter text.  In _Proceedings of the 27th International Conference on Computational Linguistics_ , pages 1534–1545, Santa Fe, New Mexico, USA. Association for Computational Linguistics.
  * Priante et al. (2016) Anna Priante, Djoerd Hiemstra, Tijs Van Den Broek, Aaqib Saeed, Michel Ehrenhard, and Ariana Need. 2016.  # whoami in 160 characters? classifying social identities based on twitter profile descriptions.  In _Proceedings of the first workshop on NLP and computational social science_ , pages 55–65.
  * Rao and Tetreault (2018) Sudha Rao and Joel Tetreault. 2018.  Dear sir or madam, may I introduce the GYAFC dataset: Corpus, benchmarks and metrics for formality style transfer.  In _Proceedings of the 2018 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long Papers)_ , pages 129–140, New Orleans, Louisiana. Association for Computational Linguistics.
  * Sap et al. (2019) Maarten Sap, Dallas Card, Saadia Gabriel, Yejin Choi, and Noah A Smith. 2019.  The risk of racial bias in hate speech detection.  In _Proceedings of the 57th annual meeting of the association for computational linguistics_ , pages 1668–1678.
  * Schilling-Estes (2004) Natalie Schilling-Estes. 2004.  Constructing ethnicity in interaction.  _Journal of Sociolinguistics_ , 8(2):163–195.
  * Schlenker and Britt (1999) Barry R Schlenker and Thomas W Britt. 1999.  Beneficial impression management: Strategically controlling information to help friends.  _Journal of Personality and Social Psychology_ , 76(4):559.
  * Tucker and Jones (2023) Liam Tucker and Jason Jones. 2023.  Pronoun lists in profile bios display increased prevalence, systematic co-presence with other keywords and network tie clustering among us twitter users 2015-2022.  _Journal of Quantitative Description: Digital Media_ , 3.
  * van Dijck (2013) José van Dijck. 2013.  ‘you have one identity’: performing the self on facebook and linkedin.  _Media, Culture & Society_, 35(2):199–215.
  * Wang et al. (2019) Zijian Wang, Scott Hale, David Ifeoluwa Adelani, Przemyslaw Grabowicz, Timo Hartman, Fabian Flöck, and David Jurgens. 2019.  Demographic inference and representative population estimates from multilingual social media data.  In _The World Wide Web Conference_ , WWW ’19, page 2056–2067, New York, NY, USA. Association for Computing Machinery.
  * Wilson and Wun (2020) Lili-Michal Wilson and Christopher Wun. 2020.  Automatic classification of students on Twitter using simple profile information.  In _Proceedings of the 1st Conference of the Asia-Pacific Chapter of the Association for Computational Linguistics and the 10th International Joint Conference on Natural Language Processing: Student Research Workshop_ , pages 30–36, Suzhou, China. Association for Computational Linguistics.
  * Yan et al. (2022) Shen Yan, Kristen M. Altenburger, Yi-Chia Wang, and Justin Cheng. 2022.  What does perception bias on social networks tell us about friend count satisfaction?  In _Proceedings of the ACM Web Conference 2022_ , WWW ’22, page 2687–2695, New York, NY, USA. Association for Computing Machinery.
  * Yoder et al. (2020) Michael Miller Yoder, Qinlan Shen, Yansen Wang, Alex Coda, Yunseok Jang, Yale Song, Kapil Thadani, and Carolyn P. Rosé. 2020.  Phans, stans and cishets: Self-presentation effects on content propagation in tumblr.  In _12th ACM Conference on Web Science_ , WebSci ’20, page 39–48, New York, NY, USA. Association for Computing Machinery.
  * Yuan et al. (2023) Yunhao Yuan, Koustuv Saha, Barbara Keller, Erkki Tapio Isometsä, and Talayeh Aledavood. 2023.  Mental health coping stories on social media: A causal-inference study of papageno effect.  In _Proceedings of the ACM Web Conference 2023_ , WWW ’23, page 2677–2685, New York, NY, USA. Association for Computing Machinery.
  * Zivnuska et al. (2004) Suzanne Zivnuska, K. Michele Kacmar, L. A. Witt, Dawn S. Carlson, and Virginia K. Bratton. 2004.  Interactive effects of impression management and organizational politics on job performance.  _Journal of Organizational Behavior_ , 25(5):627–640.

Category | Subcategory | # users
---|---|---
Age | 13-17 | 871
| 18-24 | 8,872
| 25-34 | 2,449
| 35-49 | 381
| 50+ | 164
Education | Student | 23,201
Ethnicity | African | 575
| American | 5,397
| British | 1,487
| Canadian | 2,050
| German | 636
| Indian | 3,045
| Irish | 1,023
| Japanese | 349
| Korean | 259
| Mexican | 1,686
Gender pronouns | Men | 19,115
| Women | 36,708
| Non-binary | 4,070
Occupation | Administrative | 160
| Art | 28,746
| Business | 3,284
| Community | 635
| Computer | 3,031
| Education | 6,556
| Engineering | 4,765
| Healthcare | 4,109
| Legal | 1,117
| Management | 13,646
| Science | 2,645
Personal | Social Media | 39,310
| Sensitive | 1,797
Political | Conservative | 2,059
| Liberal | 2,347
| Activism | 22,203
Relationship | Partner | 6,966
| Parent | 12,233
| Sibling | 968
Religion | Catholic / Christian | 5,954
| Islam | 1,255
| Hinduism | 544
| Atheism | 387
| General | 3,029
Sexuality | LGBTQ+ | 3,772
Total |  | 283,793

Table 2: Count of users who added social identities to their Twitter profiles
once in our observation period for each subcategory-level identity.

##  Appendix A Details on Category- and Subcategory-level Identity
Categorization

We start from an initial set of social categories based on two relevant
studies. Priante et al. (2016) categorize social identities into five groups
based on the findings of Deaux et al. (1995): personal relationships,
vocations/avocations, political affiliations, ethnic/religious groups, and
stigmatized groups. Meanwhile, Yoder et al. (2020) constructed identity
categories based on Bucholtz and Hall (2005): age, ethnicity/nationality,
fandoms, gender, interests, location, personality type, pronouns, relationship
status, sexual orientation, and zodiac. Using this list of categories as a
starting point, one of the authors manually inspected each n-gram and assigned
it to a category when applicable. Furthermore, the n-grams within each
category were additionally grouped into subcategory levels. For instance, the
gender category consists of three subcategories: men, women, and nonbinary. A
total of 221 n-grams were assigned to a category and subcategory. A list of
the categories and subcategories can be found in Table 2. Descriptions of the
final categories are as follows:

  * •

Age This category contains the disclosed age of the user. We grouped age into
five bins to represent teenagers (13-17), college students (18-24), young
adults at early stages of their careers (24-35), adults at the age of
parenthood and advanced careers (35-49), and senior adults (50+). We
aknowledge different categorizations of age could be used in this study, such
as that of Wang et al. (2019).

  * •

Education We constructed a single-identity category Education to collect
instances of students disclosing their education status, such as degree name,
current university, or school year.

  * •

Ethnicity This category contains the self-declared ethnicity of the user. We
included words or phrases describing the user’s ethnicity as well as
nationality flag emojis which can be used to describe one’s nationality. Our
subcategories are limited to countries where there was at least one
corresponding n-gram.

  * •

Gender pronouns Following the work of Jiang et al. (2022), we use three
subcategories of gender pronouns: men, women, and nonbinary.

  * •

Occupation Occupation categories were obtained from the International Standard
Classifications of Occupations (ISCO-08) list, where we selected all sub-major
group categories which corresponded to any of the top n-grams we examined.

  * •

Political This category corresponds to the disclosed political leaning of the
user. Along with subcategories for conservative and liberal, we include
another category related to activism, which in this case corresponds to
phrases related to the Black Lives Matter movement.

  * •

Relationship Based on the frequent n-grams, we identify three types of family
relationship types mentioned in profiles: partner, parent, and sibling.

  * •

Religion We identify n-grams containing religious terms, and create
subcategories for each different religion that was mentioned. For Christianity
and Catholism we discover that it is difficult to split out the two and thus
combine them into a single category. Finally, n-grams genuinely mentioning
‘God’ are mapped to the General subcategory

  * •

Sexuality We identified n-grams corresponding to LGBTQ+ identities and map
them into a single subcategory. We remove phrases that signal only indirect
membership (e.g. LGBT-ally)

  * •

Personal We define a category for two additional types of self-disclosure. One
is the disclosure of additional social media accounts, and the other is that
of stigmatized identities such as joblessness, health issues, and trauma.

Category | F1 score
---|---
Age | 0.81
Education | 0.46
Ethnicity | 0.78
Gender pronouns | 0.98
Occupation | 0.76
Personal | 0.71
Political | 0.85
Relationship | 0.82
Religion | 0.86
Sexuality (LGBTQ+) | 0.82
Table 3: Performance on detecting an identity disclosure from profile changes, aggregated at category level. The performance of our pipeline is evaluated against the majority vote of the annotators. We achieve reasonable performance across all categories except for Education, which we remove from subsequent analyses. Category | Identity | Kripp. | F1 score
---|---|---|---
Age | 13-17 | 0.68 | 0.67
Age | 18-24 | 0.71 | 0.82
Age | 25-34 | 0.87 | 0.95
Age | 35-49 | 0.79 | 0.78
Age | 50+ | 0.85 | 0.82
Education | student | 0.17 | 0.46
Ethnicity | African | 1.0 | 0.57
Ethnicity | American | 0.57 | 0.75
Ethnicity | British | 0.81 | 1.0
Ethnicity | Canadian | 1.0 | 0.89
Ethnicity | German | 0.53 | 0.89
Ethnicity | Indian | 0.83 | 1.0
Ethnicity | Irish | 0.65 | 0.75
Ethnicity | Japanese | 0.36 | 0.57
Ethnicity | Korean | -0.02 | 0.0
Ethnicity | Mexican | 0.67 | 0.89
Gender | men | 0.93 | 1.0
Gender | nonbinary | 0.73 | 0.95
Gender | women | 0.87 | 1.0
Occupation | administrative | 0.73 | 0.89
Occupation | art | 0.41 | 0.31
Occupation | business | 0.66 | 0.75
Occupation | community | 0.55 | 0.82
Occupation | computer | 1.0 | 0.75
Occupation | education | 0.55 | 0.82
Occupation | engineering | 0.72 | 0.95
Occupation | healthcare | 0.71 | 0.82
Occupation | legal | 0.62 | 0.75
Occupation | management | 0.84 | 0.75
Occupation | science | 0.8 | 0.57
Personal | sensitive | 0.61 | 0.82
Personal | social media | 0.21 | 0.57
Political | activism | 0.51 | 0.95
Political | conservative | 0.93 | 0.82
Political | liberal | 0.58 | 0.75
Relationship | parent | 0.84 | 0.75
Relationship | partner | 0.93 | 0.95
Relationship | sibling | 0.78 | 0.75
Religion | atheism | 0.8 | 1.0
Religion | Catholic / Christian | 0.45 | 0.67
Religion | general | 0.8 | 0.95
Religion | Hinduism | 0.93 | 0.89
Religion | Islam | 0.85 | 0.75
Sexuality | LGBTQ+ | 0.78 | 0.82
Table 4: Performance on detecting an identity disclosure from profile changes
for each individual identity. The Krippendorff’s alpha agreement score is
computed from the results of the three annotators. The performance of our
pipeline is evaluated against the majority vote of the annotators. The three
identities with low performance are removed from subsequent analyses.

##  Appendix B Identifying Identity-specific Language on Twitter

Our analyses require models to quantify language that aligns with a particular
social identity. We aim to achieve this by formulating classification tasks to
distinguish the language patterns between two types of users.

###  B.1 Experiment setting

For each identity subcategory, we define AlwaysPositive users as those who (1)
did not make any changes to their profiles during our observation period, and
(2) contained phrases of a specific identity type in their profile. Similarly,
we define AlwaysNegative users as those who (1) did not make any changes, and
(2) did not include any identity-specific phrases in their profile. Here we
assume that the tweets posted by a user with an identity-specific phrase in
their profile are more likely to align with the listed identity, and so use
the labels of the user as proxies for the tweets. However, it would be
unrealistic to assume that all tweets contain such alignment. Therefore, for
each user, we assign positive/negative labels at corpus level instead of the
individual tweet-level, where each sample consists of a corpus of five
randomly sampled tweets posted by a user. We restrict our tweets to those that
have user-generated text other than URLs, which we replace with a [URL] token.
To distinguish the different texts, a </s> separation token is inserted
between each tweet.

For each identity subcategory, we sample up to 50K positive and 50K negative
users, which we split into train/test/validation sets on an 8:1:1 ratio with
balanced positive/negative samples. For identity classes with insufficient
positive samples, we allow each user to be represented in up to ten different
samples provided they have enough unique tweets. We allow for upsampling on
identities with small sample sizes on the training set. We finetune each
identity separately using a RoBERTa model pretrained on a Twitter corpus
(Barbieri et al., 2020) provided via the Hugging Face API. The training is
done on Pytorch 1.13 and Pytorch Lightning 1.8.6 on an NVidia A5000 machine.
We use a learning rate of 1e-6 after 100 initial warmup steps followed by
linear decay and run for a maximum of 10 epochs where we stop if the
validation performance measured in AUC does not increase after two consecutive
epochs.

###  B.2 Model performances

We evaluate the performances of all models using two metrics: AUC and F1
score. AUC scores are generally high, with all models exceeding a performance
of 0.7 (Figure 7). This indicates that the models are doing a good job at
assigning higher scores to tweets that contain more signals of identity and
vice versa. F1 scores are lower in general, with a few identities such as
age:35-49 and occupation:administrative performing worse than random 8. The
results from these two figures combined together indicate that while the model
sometimes struggles predicting the correct label (positive/negative) for some
identities, overall it does a decent job in producing continuous scores which
we can use for measuring strong and weak associations of certain identities
from texts. Therefore, we proceed with using all of the classifiers for
subsequent experiments.

###  B.3 Cross-identity similarities in language

We compare the pairwise similarities between the identity-specific languages
across different identities. We first sample a large corpus of one million
random tweets from the history of tweets by AlwaysNegative users, so that we
avoid biasing our tweets towards any particular identity. Next, we obtain the
identity scores for each identity by running every classifier on the same
corpus. We compute Spearman rank pairwise similarity between all identity
pairs. Figure 11 contains the pairwise scores for all pairs. We can observe
stronger similarity scores for within-category comparisons. This suggests that
the language of users who disclose identity have some level of similarity
regardless of identity type.

##  Appendix C Further details on propensity score matching

For each separate identity within the subcategory level, we use all covariates
to train a logistic regression model using scikit-learn, which we use for
assigning propensity scores to each sample. We stratify the scores into $N$
strata where $N$ equals the root number of positive samples. We use the Fisher
Jenks natural break algorithm (Jenks, 1967) to obtain the strata bins, which
we use for binning both IdentityAdded and NotAdded users according to
propensity scores. Within each strata, we assign matched pairs for each
IdentityAdded user from the pool of NotAdded users with the following steps.
We first limit to NotAdded users who changed their profiles in the same week
as the IdentityAdded user. Next, we computed the Euclidean distance between
the z-score normalized covariates to select up to 5 users with the shortest
distance to the IdentityAdded user.

Figure 7: AUC scores of identity-specific language classifiers on test set.
Almost all of our categories exceed 0.7, a reasonable cutoff for binary
classification. Figure 8: F1 scores of identity-specific language classifiers
on test set. While most tasks have a relatively high F1 score above 0.7, some
identities are harder to be predicted correctly in a binary setting. Figure 9:
Distribution of standardized mean differences for all covariates between
treated and control users (1) before and (2) after matching. The red line
indicates 0.1, which most of the covariates fall into after matching. This
indicates that the matching process significantly reduces potential
confounders due to unbalanced covariates. Figure 10: A heatmap comparing the
correlations of identity-specific language with different styles. Similar
categories exhibit similar styles. Figure 11: Pairwise comparison of the
identity classifiers. Each identity classifier was used to obtain the identity
scores from an identical dataset of 1 million randomly sample tweets.
Spearman’s rank was used to obtain the pairwise similarities between the score
distributrions of any two identities. Pairwise similarities are largest
between within-category comparisons, indicating that the language associated
with identity disclosure follows some categorical properties as well.

##  Appendix D Measuring topic and stylistic distances between IdentityAdded
and AlwaysPositive users

To measure topic distributions, for each identity we run zero-shot
contextualized topic models (Bianchi et al., 2021a, b) on the tweets of
AlwaysPositive users with 50 topics for 20 epochs, then obtain a
50-dimensional distribution which represents their topics $D^{T}_{AP}$. We
then infer the topic distributions of the pre- and post-treatment tweets from
IdentityAdded as $D^{T}_{pre}$ and $D^{T}_{post}$, which we use to measure the
Jensen-Shannon distances of each distribution to $D^{T}_{AP}$. For style, we
select five style variables from Kang and Hovy (2021) as well as classifier
models from the Hugging Face API trained on public datasets: offensiveness
(Barbieri et al., 2020), formality (Rao and Tetreault, 2018; Pavlick and
Tetreault, 2016), sarcasm (Misra and Arora, 2023), toxicity (cjadams et al.,
2017, 2019), and positive sentiment (Hartmann et al., 2023). For each
identity, we computed the binary style scores for every tweet of the
AlwaysPositive users to obtain a $N\times 5$ dimension matrix of style scores
with $N$ as the number of tweets. We fitted PCA on the matrix to obtain the
projection of its principal component, $D^{S}_{AP}$, which we use to represent
the stylistic distribution of AlwaysPositive users. Likewise, we obtained the
same matrices for tweets from pre- and post-treatment periods of IdentityAdded
users, and transformed these matrices into a single dimension using the
principal component from fitted PCA of AlwaysPositive, resulting in
$D^{S}_{pre}$ and $D^{S}_{post}$. We then used cohen’s d (Cohen, 2013) to
compute the difference between each of the style distributions to
$D^{S}_{AP}$.

Figure 12: Plot on effect sizes of total network in- and out-degree regardless
of identity type, where we see that the overall network does not increase as
much, confirming the existence of intentional rewiring towards those of the
same identity. Figure 13: Plot on effect sizes of total network in- and out-
degree when restricted to different identities in the same category. We
observe increased connectivity between users who disclose gender and
relationship status, especially parent and partner relationships. Figure 14:
Plot on effect sizes of in- and out-degree when restricted to the opposite
political ideology. Interestingly, we observe increased out-degree
connectivity from those who declare themselves as liberals towards
conservative users, but not from conservatives.