Burnout Assessment Tool

.title[
# Burnout Assessment Tool
]
.subtitle[
## Validity Evidence from Students and Workers of Singapore
]
.author[
### Jorge Sinval, Minglee Yong, & Wilmar B. Schaufeli
]
.date[
### 2024-03-20
]

---

# BAT Symposium 2024 Map

.white {
  color: #FFFFFF;
}

.red {
  color: #FF0000;
}

.green {
  color: #00FF00;
}

.kbd {
    display: inline-block;
    padding: .2em .5em;
    font-size: 0.75em;
    line-height: 1.75;
    color: #555;
    vertical-align: middle;
    background-color: #fcfcfc;
    border: solid 1px #ccc;
    border-bottom-color: #bbb;
    border-radius: 3px;
    box-shadow: inset 0 -1px 0 #bbb
}

</style>

---

---
class: inverse, center, middle

# .white[Introduction]  
<html><div style='float:left'></div><hr color='#EB811B' size=1px width=800px></html>

---

# Introduction: Burnout

.red[Burnout] is a state of chronic stress and exhaustion related to prolonged occupational activities (work or academic), resulting in decreased performance and disinterest in work/academic tasks.

Burnout impacts mental and physical health, performance, and can lead to higher turnover/dropout rates. Addressing this issue promotes overall well-being, enabling the development of balanced lifestyles and effective working/academic environments.

While burnout is traditionally a job context concept, several studies have explored its occurrence in academic settings (Schaufeli, Desart, and De
Witte, 2020).

---

# Introduction: BAT

Burnout Assessment Tool (BAT-12) is a 12-item self-report measure of burnout (Schaufeli Desart et al., 2020).

The BAT-12 has four first-order dimensions (_exhaustion_, _mental distance_, _cognitive impairment_, and _emotional impaiment_) nested under a second-order dimension, _burnout_ (core symptoms).

The BAT-12 has been adapted in several languages and countries, including Japan, China, Republic of Korea, the Netherlands, Portugal and Brazil (Schaufeli Desart et al., 2020).

---

# Introduction: Goal

Assess the psychometric properties of the BAT-12 with one sample of undergraduate students and one sample of workers in Singapore.

Explore how burnout is associated with the sociocultural variables as the fear of losing out and group conformity.

---

# .white[Method]  
<html><div style='float:left'></div><hr color='#EB811B' size=1px width=800px></html>

---

# Method

## Sampling

### Students

Full-time undergraduate students from a public university in Singapore were invited to participate in the study.

### Workers

Recent graduates from the same university, who are now employed, were also invited to participate.

## Procedure

Participants were invited via institutional emails to complete an online Qualtrics survey containing sociodemographic, academic questions, and psychometric instruments, and received a reimbursement of `$S$ \ 10$` (students) or `$S$ \ 15$` (workers), with data sourced from an ethically approved project (IRB-2022-591).

---

# Method

## Psychometric instruments

Burnout (BAT-12) (Maggiori, Rossier, and Savickas, 2017).  
Fear of Losing Out (FoLO-4) (Wee, Cheng, Choi, and Goh, 2022).  
Conformity Scale (Mehrabian and Stefl, 1995).  
Multidimensional Scale of Perceived Social Support — Revised (MSPSS) (Zimet, Dahlem, Zimet, and Farley, 1988).  
Life Orientation Test — Revised (LOT) (Scheier, Carver, and Bridges, 1994).

## Data Analysis

Software: _R_ and _RStudio_ (R Core Team, 2023; Posit Team, 2023)

Descriptive statistics  
CFA  
Reliability `$(\alpha; \omega; AVE)$`  
Measurement invariance (MGCFA)  
Multidimensional polytomous Rasch model (Briggs and Wilson, 2003) as a specific application of the multidimensional random coefficients multinomial logit model (MRCMLM) (Adams, Wilson, and Wang, 1997).  
Full SEM

---

# Burnout Assessment Tool - 12

<table>
<caption>BAT-12 Student Version</caption>
 <thead>
  <tr>
   <th style="text-align:left;"> Items </th>
   <th style="text-align:center;"> Core Symptoms </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> At school, I feel mentally exhausted. </td>
   <td style="text-align:center;"> Exhaustion </td>
  </tr>
  <tr>
   <td style="text-align:left;"> After a day at school, I find it hard to recover my energy. </td>
   <td style="text-align:center;"> Exhaustion </td>
  </tr>
  <tr>
   <td style="text-align:left;"> At school, I feel physically exhausted. </td>
   <td style="text-align:center;"> Exhaustion </td>
  </tr>
  <tr>
   <td style="text-align:left;"> I struggle to find any enthusiasm for school. </td>
   <td style="text-align:center;"> Mental Distance </td>
  </tr>
  <tr>
   <td style="text-align:left;"> I feel a strong aversion towards my school. </td>
   <td style="text-align:center;"> Mental Distance </td>
  </tr>
  <tr>
   <td style="text-align:left;"> I’m cynical about what my school means to others. </td>
   <td style="text-align:center;"> Mental Distance </td>
  </tr>
  <tr>
   <td style="text-align:left;"> At school, I feel unable to control my emotions. </td>
   <td style="text-align:center;"> Emotional Impairment </td>
  </tr>
  <tr>
   <td style="text-align:left;"> I do not recognize myself in the way I react emotionally at school. </td>
   <td style="text-align:center;"> Emotional Impairment </td>
  </tr>
  <tr>
   <td style="text-align:left;"> At school, I may overreact unintentionally. </td>
   <td style="text-align:center;"> Emotional Impairment </td>
  </tr>
  <tr>
   <td style="text-align:left;"> At school, I have trouble staying focused. </td>
   <td style="text-align:center;"> Cognitive Impairment </td>
  </tr>
  <tr>
   <td style="text-align:left;"> When I’m at school, I have trouble concentrating. </td>
   <td style="text-align:center;"> Cognitive Impairment </td>
  </tr>
  <tr>
   <td style="text-align:left;"> I make mistakes at school because I have my mind on other things. </td>
   <td style="text-align:center;"> Cognitive Impairment </td>
  </tr>
</tbody>
</table>

---

# Burnout Assessment Tool - 12

<table>
<caption>BAT-12 Work Version</caption>
 <thead>
  <tr>
   <th style="text-align:left;"> Items </th>
   <th style="text-align:center;"> Core Symptoms </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> At work, I feel mentally exhausted </td>
   <td style="text-align:center;"> Exhaustion </td>
  </tr>
  <tr>
   <td style="text-align:left;"> After a day at work, I find it hard to recover my energy. </td>
   <td style="text-align:center;"> Exhaustion </td>
  </tr>
  <tr>
   <td style="text-align:left;"> At work, I feel physically exhausted. </td>
   <td style="text-align:center;"> Exhaustion </td>
  </tr>
  <tr>
   <td style="text-align:left;"> I struggle to find any enthusiasm for my work. </td>
   <td style="text-align:center;"> Mental Distance </td>
  </tr>
  <tr>
   <td style="text-align:left;"> I feel a strong aversion towards my job. </td>
   <td style="text-align:center;"> Mental Distance </td>
  </tr>
  <tr>
   <td style="text-align:left;"> I’m cynical about what my work means to others. </td>
   <td style="text-align:center;"> Mental Distance </td>
  </tr>
  <tr>
   <td style="text-align:left;"> At work, I feel unable to control my emotions. </td>
   <td style="text-align:center;"> Emotional Impairment </td>
  </tr>
  <tr>
   <td style="text-align:left;"> I do not recognize myself in the way I react emotionally at work. </td>
   <td style="text-align:center;"> Emotional Impairment </td>
  </tr>
  <tr>
   <td style="text-align:left;"> At work, I may overreact unintentionally. </td>
   <td style="text-align:center;"> Emotional Impairment </td>
  </tr>
  <tr>
   <td style="text-align:left;"> At work, I have trouble staying focused. </td>
   <td style="text-align:center;"> Cognitive Impairment </td>
  </tr>
  <tr>
   <td style="text-align:left;"> When I’m working, I have trouble concentrating. </td>
   <td style="text-align:center;"> Cognitive Impairment </td>
  </tr>
  <tr>
   <td style="text-align:left;"> I make mistakes in my work because I have my mind on other things. </td>
   <td style="text-align:center;"> Cognitive Impairment </td>
  </tr>
</tbody>
</table>

---

# .white[Results]  
<html><div style='float:left'></div><hr color='#EB811B' size=1px width=800px></html>

---
class: inverse, center, middle

# .white[Sample Characterization]
<html><div style='float:left'></div><hr color='#EB811B' size=1px width=800px></html>

---
class: inverse, center, middle

# .white[Students]
<html><div style='float:left'></div><hr color='#EB811B' size=1px width=800px></html>

---

# Sample Characterization

<table>
 <thead>
  <tr>
   <th style="text-align:left;">  </th>
   <th style="text-align:center;"> Female </th>
   <th style="text-align:center;"> Male </th>
   <th style="text-align:center;"> Overall </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;">  </td>
   <td style="text-align:center;"> (N=784) </td>
   <td style="text-align:center;"> (N=561) </td>
   <td style="text-align:center;"> (N=1345) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Age (years) </td>
   <td style="text-align:center;">  </td>
   <td style="text-align:center;">  </td>
   <td style="text-align:center;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Mean (SD) </td>
   <td style="text-align:center;"> 21.9 (1.31) </td>
   <td style="text-align:center;"> 23.5 (1.72) </td>
   <td style="text-align:center;"> 22.5 (1.68) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Median [Min, Max] </td>
   <td style="text-align:center;"> 21.5 [19.3, 30.3] </td>
   <td style="text-align:center;"> 23.3 [19.3, 31.4] </td>
   <td style="text-align:center;"> 22.3 [19.3, 31.4] </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Missing </td>
   <td style="text-align:center;"> 5 (0.6%) </td>
   <td style="text-align:center;"> 2 (0.4%) </td>
   <td style="text-align:center;"> 7 (0.5%) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Ethnicity </td>
   <td style="text-align:center;">  </td>
   <td style="text-align:center;">  </td>
   <td style="text-align:center;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Chinese </td>
   <td style="text-align:center;"> 665 (84.8%) </td>
   <td style="text-align:center;"> 505 (90.0%) </td>
   <td style="text-align:center;"> 1170 (87.0%) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Indian </td>
   <td style="text-align:center;"> 55 (7.0%) </td>
   <td style="text-align:center;"> 29 (5.2%) </td>
   <td style="text-align:center;"> 84 (6.2%) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Malay </td>
   <td style="text-align:center;"> 23 (2.9%) </td>
   <td style="text-align:center;"> 8 (1.4%) </td>
   <td style="text-align:center;"> 31 (2.3%) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Others </td>
   <td style="text-align:center;"> 41 (5.2%) </td>
   <td style="text-align:center;"> 19 (3.4%) </td>
   <td style="text-align:center;"> 60 (4.5%) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Cumulative GPA </td>
   <td style="text-align:center;">  </td>
   <td style="text-align:center;">  </td>
   <td style="text-align:center;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Mean (SD) </td>
   <td style="text-align:center;"> 3.89 (0.665) </td>
   <td style="text-align:center;"> 4.06 (0.671) </td>
   <td style="text-align:center;"> 3.96 (0.673) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Median [Min, Max] </td>
   <td style="text-align:center;"> 3.99 [0, 5.00] </td>
   <td style="text-align:center;"> 4.20 [0, 5.00] </td>
   <td style="text-align:center;"> 4.06 [0, 5.00] </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Missing </td>
   <td style="text-align:center;"> 23 (2.9%) </td>
   <td style="text-align:center;"> 14 (2.5%) </td>
   <td style="text-align:center;"> 37 (2.8%) </td>
  </tr>
</tbody>
</table>

]

---

# .white[Workers]  
<html><div style='float:left'></div><hr color='#EB811B' size=1px width=800px></html>

---

# Sample Characterization

<table>
 <thead>
  <tr>
   <th style="text-align:left;">  </th>
   <th style="text-align:center;"> Female </th>
   <th style="text-align:center;"> Male </th>
   <th style="text-align:center;"> Overall </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;">  </td>
   <td style="text-align:center;"> (N=161) </td>
   <td style="text-align:center;"> (N=108) </td>
   <td style="text-align:center;"> (N=269) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Age (years) </td>
   <td style="text-align:center;">  </td>
   <td style="text-align:center;">  </td>
   <td style="text-align:center;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Mean (SD) </td>
   <td style="text-align:center;"> 23.7 (1.16) </td>
   <td style="text-align:center;"> 25.4 (1.52) </td>
   <td style="text-align:center;"> 24.4 (1.54) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Median [Min, Max] </td>
   <td style="text-align:center;"> 23.3 [21.3, 30.4] </td>
   <td style="text-align:center;"> 25.3 [21.3, 31.3] </td>
   <td style="text-align:center;"> 24.3 [21.3, 31.3] </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Ethnicity </td>
   <td style="text-align:center;">  </td>
   <td style="text-align:center;">  </td>
   <td style="text-align:center;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Chinese </td>
   <td style="text-align:center;"> 150 (93.2%) </td>
   <td style="text-align:center;"> 98 (90.7%) </td>
   <td style="text-align:center;"> 248 (92.2%) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Indian </td>
   <td style="text-align:center;"> 5 (3.1%) </td>
   <td style="text-align:center;"> 6 (5.6%) </td>
   <td style="text-align:center;"> 11 (4.1%) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Malay </td>
   <td style="text-align:center;"> 3 (1.9%) </td>
   <td style="text-align:center;"> 3 (2.8%) </td>
   <td style="text-align:center;"> 6 (2.2%) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Others </td>
   <td style="text-align:center;"> 3 (1.9%) </td>
   <td style="text-align:center;"> 1 (0.9%) </td>
   <td style="text-align:center;"> 4 (1.5%) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Course Final GPA </td>
   <td style="text-align:center;">  </td>
   <td style="text-align:center;">  </td>
   <td style="text-align:center;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Mean (SD) </td>
   <td style="text-align:center;"> 4.02 (0.472) </td>
   <td style="text-align:center;"> 4.16 (0.595) </td>
   <td style="text-align:center;"> 4.08 (0.528) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Median [Min, Max] </td>
   <td style="text-align:center;"> 4.06 [2.09, 4.92] </td>
   <td style="text-align:center;"> 4.26 [1.50, 5.00] </td>
   <td style="text-align:center;"> 4.15 [1.50, 5.00] </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Missing </td>
   <td style="text-align:center;"> 3 (1.9%) </td>
   <td style="text-align:center;"> 2 (1.9%) </td>
   <td style="text-align:center;"> 5 (1.9%) </td>
  </tr>
</tbody>
</table>

]

---

# .white[Validity Evidence Based on the Internal Structure]  
<html><div style='float:left'></div><hr color='#EB811B' size=1px width=800px></html>

---

# .white[Students]  
<html><div style='float:left'></div><hr color='#EB811B' size=1px width=800px></html>

---

# Items' distributional properties

The distributional properties of the model's indicators are presented in the following table. Various summary measures, a histogram, kurtosis `$(ku)$`, and skewness `$(sk)$` for each of items are presented. The psychometric sensitivity and distributional properties of the items were analyzed with this information. Values of `$|Ku|<7$` and `$|Sk|<3$` were indicative of absense of severe violations of the univariate normality that would recommend against the use of structural equation modeling (Finney and DiStefano, 2013).

---

# Items' distributional properties

<table class="table" style="color: black; margin-left: auto; margin-right: auto;">
<caption>Descriptives with histogram ($n=1350$)</caption>
 <thead>
  <tr>
   <th style="text-align:left;"> Item </th>
   <th style="text-align:right;"> $N_{missing}$ </th>
   <th style="text-align:right;"> $M$ </th>
   <th style="text-align:right;"> $SD$ </th>
   <th style="text-align:right;"> $Min$ </th>
   <th style="text-align:right;"> $P_{25}$ </th>
   <th style="text-align:right;"> $Mdn$ </th>
   <th style="text-align:right;"> $P_{75}$ </th>
   <th style="text-align:right;"> $Max$ </th>
   <th style="text-align:left;"> Histogram </th>
   <th style="text-align:right;"> $SEM$ </th>
   <th style="text-align:right;"> $CV$ </th>
   <th style="text-align:right;"> $Mode$ </th>
   <th style="text-align:right;"> $sk$ </th>
   <th style="text-align:right;"> $ku$ </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Item 1 </td>
   <td style="text-align:right;"> 61 </td>
   <td style="text-align:right;"> 3.47 </td>
   <td style="text-align:right;"> 0.94 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 4 </td>
   <td style="text-align:right;"> 5 </td>
   <td style="text-align:left;"> ▁▂▇▇▃ </td>
   <td style="text-align:right;"> 0.03 </td>
   <td style="text-align:right;"> 0.27 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> -0.20 </td>
   <td style="text-align:right;"> -0.25 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 2 </td>
   <td style="text-align:right;"> 61 </td>
   <td style="text-align:right;"> 3.35 </td>
   <td style="text-align:right;"> 1.02 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 4 </td>
   <td style="text-align:right;"> 5 </td>
   <td style="text-align:left;"> ▁▅▇▇▃ </td>
   <td style="text-align:right;"> 0.03 </td>
   <td style="text-align:right;"> 0.31 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> -0.09 </td>
   <td style="text-align:right;"> -0.66 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 3 </td>
   <td style="text-align:right;"> 61 </td>
   <td style="text-align:right;"> 3.25 </td>
   <td style="text-align:right;"> 1.05 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 4 </td>
   <td style="text-align:right;"> 5 </td>
   <td style="text-align:left;"> ▁▅▇▇▃ </td>
   <td style="text-align:right;"> 0.03 </td>
   <td style="text-align:right;"> 0.32 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> -0.08 </td>
   <td style="text-align:right;"> -0.64 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 4 </td>
   <td style="text-align:right;"> 61 </td>
   <td style="text-align:right;"> 3.04 </td>
   <td style="text-align:right;"> 1.04 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 4 </td>
   <td style="text-align:right;"> 5 </td>
   <td style="text-align:left;"> ▂▅▇▅▂ </td>
   <td style="text-align:right;"> 0.03 </td>
   <td style="text-align:right;"> 0.34 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 0.07 </td>
   <td style="text-align:right;"> -0.52 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 5 </td>
   <td style="text-align:right;"> 61 </td>
   <td style="text-align:right;"> 2.46 </td>
   <td style="text-align:right;"> 1.07 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 5 </td>
   <td style="text-align:left;"> ▅▇▇▂▁ </td>
   <td style="text-align:right;"> 0.03 </td>
   <td style="text-align:right;"> 0.43 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 0.48 </td>
   <td style="text-align:right;"> -0.29 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 6 </td>
   <td style="text-align:right;"> 61 </td>
   <td style="text-align:right;"> 2.40 </td>
   <td style="text-align:right;"> 1.12 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 5 </td>
   <td style="text-align:left;"> ▅▇▆▂▁ </td>
   <td style="text-align:right;"> 0.03 </td>
   <td style="text-align:right;"> 0.47 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 0.56 </td>
   <td style="text-align:right;"> -0.40 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 7 </td>
   <td style="text-align:right;"> 61 </td>
   <td style="text-align:right;"> 1.87 </td>
   <td style="text-align:right;"> 0.95 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 5 </td>
   <td style="text-align:left;"> ▇▇▃▁▁ </td>
   <td style="text-align:right;"> 0.03 </td>
   <td style="text-align:right;"> 0.51 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 1.13 </td>
   <td style="text-align:right;"> 1.05 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 8 </td>
   <td style="text-align:right;"> 61 </td>
   <td style="text-align:right;"> 1.82 </td>
   <td style="text-align:right;"> 0.99 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 5 </td>
   <td style="text-align:left;"> ▇▅▂▁▁ </td>
   <td style="text-align:right;"> 0.03 </td>
   <td style="text-align:right;"> 0.54 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 1.18 </td>
   <td style="text-align:right;"> 0.86 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 9 </td>
   <td style="text-align:right;"> 61 </td>
   <td style="text-align:right;"> 1.86 </td>
   <td style="text-align:right;"> 0.96 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 5 </td>
   <td style="text-align:left;"> ▇▆▃▁▁ </td>
   <td style="text-align:right;"> 0.03 </td>
   <td style="text-align:right;"> 0.51 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 1.01 </td>
   <td style="text-align:right;"> 0.52 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 10 </td>
   <td style="text-align:right;"> 61 </td>
   <td style="text-align:right;"> 2.89 </td>
   <td style="text-align:right;"> 1.04 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 4 </td>
   <td style="text-align:right;"> 5 </td>
   <td style="text-align:left;"> ▂▅▇▃▂ </td>
   <td style="text-align:right;"> 0.03 </td>
   <td style="text-align:right;"> 0.36 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 0.07 </td>
   <td style="text-align:right;"> -0.39 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 11 </td>
   <td style="text-align:right;"> 61 </td>
   <td style="text-align:right;"> 2.86 </td>
   <td style="text-align:right;"> 1.06 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 5 </td>
   <td style="text-align:left;"> ▂▅▇▃▂ </td>
   <td style="text-align:right;"> 0.03 </td>
   <td style="text-align:right;"> 0.37 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 0.14 </td>
   <td style="text-align:right;"> -0.42 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 12 </td>
   <td style="text-align:right;"> 61 </td>
   <td style="text-align:right;"> 2.55 </td>
   <td style="text-align:right;"> 1.04 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 5 </td>
   <td style="text-align:left;"> ▃▇▇▂▁ </td>
   <td style="text-align:right;"> 0.03 </td>
   <td style="text-align:right;"> 0.41 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 0.38 </td>
   <td style="text-align:right;"> -0.26 </td>
  </tr>
</tbody>
</table>

]

---

# Dimensionality

<div class="pre-name">analysis.Rmd</div>

```r
model_measurement <- "
Ex =~ CBATS1 + CBATS2 + CBATS3
MD =~ CBATS4 + CBATS5 + CBATS6
CI =~ CBATS10 + CBATS11 + CBATS12
EI =~ CBATS7 + CBATS8 + CBATS9

Burn =~ Ex + MD + CI + EI

CBATS10	~~	CBATS11
"

library(lavaan)
fit_model <- cfa(model = model_measurement,
                             data = ds,
                             ordered = bat_std_items,
                             estimator="wlsmv")
```

Modifications:

- residual correlation among items 10 and 11 (_cognitive impairment_ dimension)

---

# Lambdas `$(\hat\lambda)$`

<table class="table" style="color: black; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:left;">   </th>
   <th style="text-align:left;"> Exhaustion </th>
   <th style="text-align:left;"> Mental Distance </th>
   <th style="text-align:left;"> Cognitive Impairment </th>
   <th style="text-align:left;"> Emotional Impairment </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> CBATS1 </td>
   <td style="text-align:left;"> 0.864 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;"> CBATS2 </td>
   <td style="text-align:left;"> 0.875 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;"> CBATS3 </td>
   <td style="text-align:left;"> 0.829 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;"> CBATS4 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.848 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;"> CBATS5 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.838 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;"> CBATS6 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.750 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;"> CBATS10 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.819 </td>
   <td style="text-align:left;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;"> CBATS11 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.848 </td>
   <td style="text-align:left;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;"> CBATS12 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.832 </td>
   <td style="text-align:left;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;"> CBATS7 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.930 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> CBATS8 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.905 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> CBATS9 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.811 </td>
  </tr>
</tbody>
</table>

---

# Gamma (\$\hat\gamma\$)

The model's structural weights are presented in the following table.

<br>

<table class="table" style="color: black; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:left;">   </th>
   <th style="text-align:left;"> Burnout </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Exhaustion </td>
   <td style="text-align:left;"> 0.778 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Mental Distance </td>
   <td style="text-align:left;"> 0.913 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Cognitive Impairment </td>
   <td style="text-align:left;"> 0.836 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Emotional Impairment </td>
   <td style="text-align:left;"> 0.680 </td>
  </tr>
</tbody>
</table>

---

# Goodness-of-fit

The model presented the following goodness-of-fit indices `$(\chi^2_{scaled (49)}=849.99;p< .001; CFI_{robust}=0.943;$` `$TLI_{robust}=0.923;NFI_{scaled}=0.984; SRMR=0.060;RMSEA_{robust}=0.108;p_{(rmsea \leq 0.05)}< .001;$` `$90\%CI[0.099, 0.117])$`.

---

# Diagram

The diagram showing the standardized estimates.

<div class="grViz html-widget html-fill-item" id="htmlwidget-836a6a7d389a36f5c252" style="width:100%;height:432px;"></div>
<script type="application/json" data-for="htmlwidget-836a6a7d389a36f5c252">{"x":{"diagram":" digraph plot { \n graph [ layout = dot, rankdir = LR ] \n node [ shape = box, fontname = Helvetica ] \n node [shape = box] \n CBATS1; CBATS2; CBATS3; CBATS4; CBATS5; CBATS6; CBATS10; CBATS11; CBATS12; CBATS7; CBATS8; CBATS9 \n node [shape = oval] \n Ex; MD; CI; EI; Burn \n \n edge [ color = grey ] \n  Ex->CBATS1 [label = \"0.86***\"] Ex->CBATS2 [label = \"0.87***\"] Ex->CBATS3 [label = \"0.83***\"] MD->CBATS4 [label = \"0.85***\"] MD->CBATS5 [label = \"0.84***\"] MD->CBATS6 [label = \"0.75***\"] CI->CBATS10 [label = \"0.82***\"] CI->CBATS11 [label = \"0.85***\"] CI->CBATS12 [label = \"0.83***\"] EI->CBATS7 [label = \"0.93***\"] EI->CBATS8 [label = \"0.9***\"] EI->CBATS9 [label = \"0.81***\"] Burn->Ex [label = \"0.78***\"] Burn->MD [label = \"0.91***\"] Burn->CI [label = \"0.84***\"] Burn->EI [label = \"0.68***\"] CBATS11 -> CBATS10 [label = \"0.81***\", dir = \"both\"]\n}","config":{"engine":"dot","options":null}},"evals":[],"jsHooks":[]}</script>

---

# Item Fit

Note that there is much disagreement among measurement scholars about how to classify an infit our outfit statistic as “fitting” or "misfitting." However, you should be aware of commonly accepted rule-of-thumb values among Rasch researchers:
  
> Expected value is about 1.00 when data fit the model  
> Less than 1.00: Responses are too predictable; they resemble a Guttman-like (deterministic) pattern ("muted")  
> More than 1.00: Responses are too haphazard ("noisy"); there is too much variation to suggest that the estimate is a good representation of the response pattern

Some variation is expected, but noisy responses are usually more cause for concern than muted responses. Frequently used critical values for mean square fit statistics .

| *Type of Instrument* | *"Acceptable Range"* | 
| :---:        |    :----:   | 
| Multiple-choice test (high-stakes) | 0.80 – 1.20 | 
| Multiple-choice test (not high-stakes)| 0.70 – 1.30 | 
| .red[Rating scale] | .red[0.60 – 1.40] | 
| Clinical observation | 0.50 – 1.70 | 
| Judgment (when agreement is encouraged) | 0.40 – 1.20|

---

# Item Fit

<table class="table" style="color: black; margin-left: auto; margin-right: auto;">
<caption>Item Fit</caption>
 <thead>
  <tr>
   <th style="text-align:left;">   </th>
   <th style="text-align:right;"> $Outfit$ </th>
   <th style="text-align:right;"> $Infit$ </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> CBATS1 </td>
   <td style="text-align:right;"> 0.894 </td>
   <td style="text-align:right;"> 0.915 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> CBATS2 </td>
   <td style="text-align:right;"> 0.872 </td>
   <td style="text-align:right;"> 0.903 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> CBATS3 </td>
   <td style="text-align:right;"> 0.994 </td>
   <td style="text-align:right;"> 1.020 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> CBATS4 </td>
   <td style="text-align:right;"> 1.014 </td>
   <td style="text-align:right;"> 1.020 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> CBATS5 </td>
   <td style="text-align:right;"> 0.901 </td>
   <td style="text-align:right;"> 0.913 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> CBATS6 </td>
   <td style="text-align:right;"> 1.193 </td>
   <td style="text-align:right;"> 1.180 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> CBATS10 </td>
   <td style="text-align:right;"> 0.787 </td>
   <td style="text-align:right;"> 0.799 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> CBATS11 </td>
   <td style="text-align:right;"> 0.728 </td>
   <td style="text-align:right;"> 0.743 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> CBATS12 </td>
   <td style="text-align:right;"> 1.126 </td>
   <td style="text-align:right;"> 1.137 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> CBATS7 </td>
   <td style="text-align:right;"> 0.770 </td>
   <td style="text-align:right;"> 0.823 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> CBATS8 </td>
   <td style="text-align:right;"> 0.774 </td>
   <td style="text-align:right;"> 0.895 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> CBATS9 </td>
   <td style="text-align:right;"> 1.018 </td>
   <td style="text-align:right;"> 1.059 </td>
  </tr>
</tbody>
</table>

]

<table class="table" style="color: black; margin-left: auto; margin-right: auto;">
<caption>Item Fit</caption>
 <thead>
  <tr>
   <th style="text-align:left;"> Fit </th>
   <th style="text-align:right;"> $M$ </th>
   <th style="text-align:right;"> $SD$ </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Outfit </td>
   <td style="text-align:right;"> 0.923 </td>
   <td style="text-align:right;"> 0.149 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Infit </td>
   <td style="text-align:right;"> 0.951 </td>
   <td style="text-align:right;"> 0.135 </td>
  </tr>
</tbody>
</table>

]

---

# Wright Map

]

---

# Reliability: Internal consistency

**First-order**

The model's first-order internal consistency estimates are presented in the following table.

<table class="table" style="color: black; width: auto !important; margin-left: auto; margin-right: auto;">
<caption>Reliability estimates: First-order</caption>
 <thead>
  <tr>
   <th style="text-align:left;">   </th>
   <th style="text-align:right;"> Exhaustion </th>
   <th style="text-align:right;"> Mental Distance </th>
   <th style="text-align:right;"> Cognitive Impairment </th>
   <th style="text-align:right;"> Emotional Impairment </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> $\alpha_{ord}$ </td>
   <td style="text-align:right;"> 0.89 </td>
   <td style="text-align:right;"> 0.84 </td>
   <td style="text-align:right;"> 0.91 </td>
   <td style="text-align:right;"> 0.91 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> $\omega_{ord}$ </td>
   <td style="text-align:right;"> 0.86 </td>
   <td style="text-align:right;"> 0.82 </td>
   <td style="text-align:right;"> 0.78 </td>
   <td style="text-align:right;"> 0.87 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> $AVE$ </td>
   <td style="text-align:right;"> 0.73 </td>
   <td style="text-align:right;"> 0.66 </td>
   <td style="text-align:right;"> 0.69 </td>
   <td style="text-align:right;"> 0.78 </td>
  </tr>
</tbody>
</table>

---

# Reliability: Internal consistency

**Second-order**

The model's second-order internal consistency estimates are presented in the following table.

<table class="table" style="color: black; margin-left: auto; margin-right: auto;">
<caption>Reliability estimates: Second-order</caption>
 <thead>
  <tr>
   <th style="text-align:left;">   </th>
   <th style="text-align:right;"> $\omega_{L1}$ </th>
   <th style="text-align:right;"> $\omega_{L2}$ </th>
   <th style="text-align:right;"> $\omega_{Partial~L1}$ </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Burnout </td>
   <td style="text-align:right;"> 0.83 </td>
   <td style="text-align:right;"> 0.88 </td>
   <td style="text-align:right;"> 0.94 </td>
  </tr>
</tbody>
</table>

---

# .white[Workers]  
<html><div style='float:left'></div><hr color='#EB811B' size=1px width=800px></html>

---

# Items' distributional properties

---

# Items' distributional properties

<table class="table" style="color: black; margin-left: auto; margin-right: auto;">
<caption>Descriptives with histogram ($n=269$)</caption>
 <thead>
  <tr>
   <th style="text-align:left;"> Item </th>
   <th style="text-align:right;"> $N_{missing}$ </th>
   <th style="text-align:right;"> $M$ </th>
   <th style="text-align:right;"> $SD$ </th>
   <th style="text-align:right;"> $Min$ </th>
   <th style="text-align:right;"> $P_{25}$ </th>
   <th style="text-align:right;"> $Mdn$ </th>
   <th style="text-align:right;"> $P_{75}$ </th>
   <th style="text-align:right;"> $Max$ </th>
   <th style="text-align:left;"> Histogram </th>
   <th style="text-align:right;"> $SEM$ </th>
   <th style="text-align:right;"> $CV$ </th>
   <th style="text-align:right;"> $Mode$ </th>
   <th style="text-align:right;"> $sk$ </th>
   <th style="text-align:right;"> $ku$ </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Item 1 </td>
   <td style="text-align:right;"> 9 </td>
   <td style="text-align:right;"> 3.30 </td>
   <td style="text-align:right;"> 0.85 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 4 </td>
   <td style="text-align:right;"> 5 </td>
   <td style="text-align:left;"> ▁▂▇▆▁ </td>
   <td style="text-align:right;"> 0.05 </td>
   <td style="text-align:right;"> 0.26 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> -0.01 </td>
   <td style="text-align:right;"> -0.20 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 2 </td>
   <td style="text-align:right;"> 9 </td>
   <td style="text-align:right;"> 3.25 </td>
   <td style="text-align:right;"> 0.95 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 4 </td>
   <td style="text-align:right;"> 5 </td>
   <td style="text-align:left;"> ▁▃▇▅▂ </td>
   <td style="text-align:right;"> 0.06 </td>
   <td style="text-align:right;"> 0.29 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 0.16 </td>
   <td style="text-align:right;"> -0.38 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 3 </td>
   <td style="text-align:right;"> 9 </td>
   <td style="text-align:right;"> 3.18 </td>
   <td style="text-align:right;"> 0.95 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 4 </td>
   <td style="text-align:right;"> 5 </td>
   <td style="text-align:left;"> ▁▃▇▅▂ </td>
   <td style="text-align:right;"> 0.06 </td>
   <td style="text-align:right;"> 0.30 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 0.03 </td>
   <td style="text-align:right;"> -0.31 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 4 </td>
   <td style="text-align:right;"> 9 </td>
   <td style="text-align:right;"> 2.97 </td>
   <td style="text-align:right;"> 1.00 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 4 </td>
   <td style="text-align:right;"> 5 </td>
   <td style="text-align:left;"> ▁▇▇▅▂ </td>
   <td style="text-align:right;"> 0.06 </td>
   <td style="text-align:right;"> 0.34 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 0.30 </td>
   <td style="text-align:right;"> -0.48 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 5 </td>
   <td style="text-align:right;"> 9 </td>
   <td style="text-align:right;"> 2.56 </td>
   <td style="text-align:right;"> 0.99 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 5 </td>
   <td style="text-align:left;"> ▃▇▇▂▁ </td>
   <td style="text-align:right;"> 0.06 </td>
   <td style="text-align:right;"> 0.39 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 0.34 </td>
   <td style="text-align:right;"> -0.16 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 6 </td>
   <td style="text-align:right;"> 9 </td>
   <td style="text-align:right;"> 2.57 </td>
   <td style="text-align:right;"> 1.02 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 5 </td>
   <td style="text-align:left;"> ▃▇▇▂▁ </td>
   <td style="text-align:right;"> 0.06 </td>
   <td style="text-align:right;"> 0.40 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 0.37 </td>
   <td style="text-align:right;"> -0.15 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 7 </td>
   <td style="text-align:right;"> 9 </td>
   <td style="text-align:right;"> 2.03 </td>
   <td style="text-align:right;"> 0.90 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 5 </td>
   <td style="text-align:left;"> ▅▇▃▁▁ </td>
   <td style="text-align:right;"> 0.06 </td>
   <td style="text-align:right;"> 0.44 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 0.82 </td>
   <td style="text-align:right;"> 0.70 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 8 </td>
   <td style="text-align:right;"> 9 </td>
   <td style="text-align:right;"> 2.08 </td>
   <td style="text-align:right;"> 1.03 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 5 </td>
   <td style="text-align:left;"> ▆▇▃▁▁ </td>
   <td style="text-align:right;"> 0.06 </td>
   <td style="text-align:right;"> 0.49 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 0.96 </td>
   <td style="text-align:right;"> 0.58 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 9 </td>
   <td style="text-align:right;"> 9 </td>
   <td style="text-align:right;"> 2.11 </td>
   <td style="text-align:right;"> 0.98 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 5 </td>
   <td style="text-align:left;"> ▆▇▃▂▁ </td>
   <td style="text-align:right;"> 0.06 </td>
   <td style="text-align:right;"> 0.46 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 0.76 </td>
   <td style="text-align:right;"> 0.19 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 10 </td>
   <td style="text-align:right;"> 9 </td>
   <td style="text-align:right;"> 2.63 </td>
   <td style="text-align:right;"> 0.89 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 5 </td>
   <td style="text-align:left;"> ▂▇▇▂▁ </td>
   <td style="text-align:right;"> 0.06 </td>
   <td style="text-align:right;"> 0.34 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 0.49 </td>
   <td style="text-align:right;"> 0.39 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 11 </td>
   <td style="text-align:right;"> 9 </td>
   <td style="text-align:right;"> 2.60 </td>
   <td style="text-align:right;"> 0.89 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 5 </td>
   <td style="text-align:left;"> ▂▇▇▂▁ </td>
   <td style="text-align:right;"> 0.06 </td>
   <td style="text-align:right;"> 0.34 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 0.39 </td>
   <td style="text-align:right;"> 0.25 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 12 </td>
   <td style="text-align:right;"> 9 </td>
   <td style="text-align:right;"> 2.38 </td>
   <td style="text-align:right;"> 0.94 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 5 </td>
   <td style="text-align:left;"> ▃▇▆▂▁ </td>
   <td style="text-align:right;"> 0.06 </td>
   <td style="text-align:right;"> 0.39 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 0.55 </td>
   <td style="text-align:right;"> 0.22 </td>
  </tr>
</tbody>
</table>

]

---

# Dimensionality

<div class="pre-name">analysis.Rmd</div>

```r
model_measurement <- "
Ex =~ CBATS1 + CBATS2 + CBATS3
MD =~ CBATS4 + CBATS5 + CBATS6
CI =~ CBATS10 + CBATS11 + CBATS12
EI =~ CBATS7 + CBATS8 + CBATS9

Burn =~ Ex + MD + CI + EI

CBATS10	~~	CBATS11
"

Modifications:

- residual correlation among items 10 and 11 (_cognitive impairment_ dimension)

---

# Lambdas `$(\hat\lambda)$`

---

# Gamma (\$\hat\gamma\$)

The model's structural weights are presented in the following table.

<br>

---

# Goodness-of-fit

---

# Diagram

The diagram showing the standardized estimates.

<div class="grViz html-widget html-fill-item" id="htmlwidget-a54c19dc65905d860244" style="width:100%;height:432px;"></div>
<script type="application/json" data-for="htmlwidget-a54c19dc65905d860244">{"x":{"diagram":" digraph plot { \n graph [ layout = dot, rankdir = LR ] \n node [ shape = box, fontname = Helvetica ] \n node [shape = box] \n CBATS1; CBATS2; CBATS3; CBATS4; CBATS5; CBATS6; CBATS10; CBATS11; CBATS12; CBATS7; CBATS8; CBATS9 \n node [shape = oval] \n Ex; MD; CI; EI; Burn \n \n edge [ color = grey ] \n  Ex->CBATS1 [label = \"0.86***\"] Ex->CBATS2 [label = \"0.87***\"] Ex->CBATS3 [label = \"0.83***\"] MD->CBATS4 [label = \"0.85***\"] MD->CBATS5 [label = \"0.84***\"] MD->CBATS6 [label = \"0.75***\"] CI->CBATS10 [label = \"0.82***\"] CI->CBATS11 [label = \"0.85***\"] CI->CBATS12 [label = \"0.83***\"] EI->CBATS7 [label = \"0.93***\"] EI->CBATS8 [label = \"0.9***\"] EI->CBATS9 [label = \"0.81***\"] Burn->Ex [label = \"0.78***\"] Burn->MD [label = \"0.91***\"] Burn->CI [label = \"0.84***\"] Burn->EI [label = \"0.68***\"] CBATS11 -> CBATS10 [label = \"0.81***\", dir = \"both\"]\n}","config":{"engine":"dot","options":null}},"evals":[],"jsHooks":[]}</script>

---

# Item Fit

Some variation is expected, but noisy responses are usually more cause for concern than muted responses. Frequently used critical values for mean square fit statistics .

---

# Item Fit

]

]

---

# Wright Map

]

---

# Reliability: Internal consistency

**First-order**

The model's first-order internal consistency estimates are presented in the following table.

---

# Reliability: Internal consistency

**Second-order**

The model's second-order internal consistency estimates are presented in the following table.

---

# .white[Measurement Invariance]  
<html><div style='float:left'></div><hr color='#EB811B' size=1px width=800px></html>

---

# Students vs. Workers

Following Wu and Estabrook Wu and Estabrook (2016) recommendations.

**Configural model**: .orange[no constraints] across groups or repeated measures

```r
model_measurement <- "
Ex =~ bat1 + bat2 + bat3
MD =~ bat4 + bat5 + bat6
CI =~ bat10 + bat11 + bat12
EI =~ bat7 + bat8 + bat9

Burn =~ Ex + MD + CI + EI

bat10	~~	bat11
"

syntax.config <- measEq.syntax(configural.model = model_measurement,
                                         # NOTE: data provides info about numbers of
                                         #       groups and thresholds
                                         data = ds_mi,
                                         ordered = T,
                                         parameterization = "theta",
                                         ID.fac = "ul",
                                         ID.cat = "Wu.Estabrook.2016",
                                         group = "occupational_status")

## print lavaan syntax to the Console
fixMeans.c <- '
MD ~ c(0, 0)*1
CI ~ c(0, 0)*1
EI ~ c(0, 0)*1
Burn ~ c(0, 0)*1
'
syntax.config <- update(syntax.config,
                        change.syntax = fixMeans.c)
#cat(as.character(syntax.config))
## print a summary of model features
#lavaan::summary(syntax.config)

## Fit a model to the data either in a subsequent step (recommended):
mod.config <- as.character(syntax.config)

fit.config <- cfa(mod.config,
                  data = ds_mi,
                  group = "occupational_status",
                  ordered = T,
                  parameterization = "theta")
```
]

---

# Students vs. Workers

**Threshold invariance model**: equal .orange[thresholds] across groups or repeated measures

```r
## Threshold invariance:
syntax.thresh <- semTools::measEq.syntax(configural.model = model_measurement, 
                                         data = ds_mi,
                                         ordered = T,
                                         parameterization = "theta",
                                         ID.fac = "ul",
                                         ID.cat = "Wu.Estabrook.2016",
                                         group = "occupational_status",
                                         group.equal = c("thresholds"))

fixMeans.th <- '
MD ~ c(0, NA)*1
CI ~ c(0, NA)*1
EI ~ c(0, NA)*1
Burn ~ c(0, NA)*1
'

syntax.thresh <- update(syntax.thresh,
                        change.syntax = fixMeans.th)
#cat(as.character(syntax.thresh)) # save as text
mod.thresh <- as.character(syntax.thresh)

## fit model to data
fit.thresh <- cfa(model = mod.thresh,
                  data = ds_mi,
                  group = "occupational_status",
                  ordered = T,
                  parameterization = "theta")
```
]

---

# Students vs. Workers

**Metric (first-order) invariance model**: equal thresholds and .orange[loadings] across groups or repeated measures

```r
## test equivalence of loadings, given equivalence of thresholds
syntax.metric_1l <- measEq.syntax(configural.model = model_measurement,
                                  data = ds_mi,
                                  ordered = T,
                                  parameterization = "theta",
                                  ID.fac = "ul",
                                  ID.cat = "Wu.Estabrook.2016",
                                  group = "occupational_status",
                                  group.equal = c("thresholds","loadings"))

syntax.metric_1l <- update(syntax.metric_1l, change.syntax = fixMeans.th)

#summary(syntax.metric_1l)                    # summarize model features
#cat(as.character(syntax.metric_1l)) # print/view lavaan syntax

mod.metric_1l <- syntax.metric_1l |> as.character()

## fit model to data
fit.metric_1l <- cfa(model = mod.metric_1l,
                     data = ds_mi,
                     group = "occupational_status",
                     ordered = T,
                     parameterization = "theta")
```
]

---

# Students vs. Workers

**Metric (second-order) invariance model**: equal thresholds, loadings and .orange[structural weights] across groups or repeated measures

```r
##### Equal regressions (metric second-order)
syntax.metric_2l <- semTools::measEq.syntax(configural.model = model_measurement,
                                            data = ds_mi,
                                            ordered = T,
                                            parameterization = "theta",
                                            ID.fac = "ul",
                                            ID.cat = "Wu.Estabrook.2016",
                                            group = "occupational_status",
                                            group.equal = c("thresholds","loadings", "regressions"))

syntax.metric_2l <- update(object = syntax.metric_2l,
                           change.syntax = fixMeans.th)

#summary(syntax.metric_2l)                    # summarize model features
#cat(as.character(syntax.metric_2l)) # save as text

mod.metric_2l <- syntax.metric_2l |> as.character() # save as tex

## fit model to data
fit.metric_2l <- cfa(model = mod.metric_2l,
                     data = ds_mi,
                     group = "occupational_status",
                     ordered = T,
                     parameterization = "theta")
## test equivalence of loadings, given equivalence of thresholds
#anova(fit.config, fit.thresh, fit.metric_1l, fit.metric_2l)
```

]

---

# Students vs. Workers

**Scalar (second-order) invariance model**: equal thresholds, loadings, structural weights and .orange[intercepts (of first-order latent factors)] across groups or repeated measures

```r
## scalar invariance
syntax.scalar <- semTools::measEq.syntax(configural.model = model_measurement,
                                         data = ds_mi,
                                         ordered = T,
                                         parameterization = "theta",
                                         ID.fac = "ul",
                                         ID.cat = "Wu.Estabrook.2016",
                                         group = "occupational_status", 
                                         group.equal = c("thresholds","loadings",
                                                         "regressions","intercepts"))

syntax.scalar <- update(syntax.scalar,
                        change.syntax = fixMeans.th)

#summary(syntax.scalar)                    # summarize model features
#cat(as.character(syntax.scalar)) # save as text

mod.scalar <- syntax.scalar |> as.character()

mod.scalar <- "
## LOADINGS:

Ex =~ c(1, 1)*bat1 + c(lambda.1_1, lambda.1_1)*bat1
Ex =~ c(NA, NA)*bat2 + c(lambda.2_1, lambda.2_1)*bat2
Ex =~ c(NA, NA)*bat3 + c(lambda.3_1, lambda.3_1)*bat3
MD =~ c(1, 1)*bat4 + c(lambda.4_2, lambda.4_2)*bat4
MD =~ c(NA, NA)*bat5 + c(lambda.5_2, lambda.5_2)*bat5
MD =~ c(NA, NA)*bat6 + c(lambda.6_2, lambda.6_2)*bat6
CI =~ c(1, 1)*bat7 + c(lambda.7_3, lambda.7_3)*bat7
CI =~ c(NA, NA)*bat8 + c(lambda.8_3, lambda.8_3)*bat8
CI =~ c(NA, NA)*bat9 + c(lambda.9_3, lambda.9_3)*bat9
EI =~ c(1, 1)*bat10 + c(lambda.10_4, lambda.10_4)*bat10
EI =~ c(NA, NA)*bat11 + c(lambda.11_4, lambda.11_4)*bat11
EI =~ c(NA, NA)*bat12 + c(lambda.12_4, lambda.12_4)*bat12
Burn =~ c(1, 1)*Ex + c(beta.1_5, beta.1_5)*Ex
Burn =~ c(NA, NA)*MD + c(beta.2_5, beta.2_5)*MD
Burn =~ c(NA, NA)*CI + c(beta.3_5, beta.3_5)*CI
Burn =~ c(NA, NA)*EI + c(beta.4_5, beta.4_5)*EI

## THRESHOLDS:

bat1 | c(NA, NA)*t1 + c(bat1.thr1, bat1.thr1)*t1
bat1 | c(NA, NA)*t2 + c(bat1.thr2, bat1.thr2)*t2
bat1 | c(NA, NA)*t3 + c(bat1.thr3, bat1.thr3)*t3
bat1 | c(NA, NA)*t4 + c(bat1.thr4, bat1.thr4)*t4
bat2 | c(NA, NA)*t1 + c(bat2.thr1, bat2.thr1)*t1
bat2 | c(NA, NA)*t2 + c(bat2.thr2, bat2.thr2)*t2
bat2 | c(NA, NA)*t3 + c(bat2.thr3, bat2.thr3)*t3
bat2 | c(NA, NA)*t4 + c(bat2.thr4, bat2.thr4)*t4
bat3 | c(NA, NA)*t1 + c(bat3.thr1, bat3.thr1)*t1
bat3 | c(NA, NA)*t2 + c(bat3.thr2, bat3.thr2)*t2
bat3 | c(NA, NA)*t3 + c(bat3.thr3, bat3.thr3)*t3
bat3 | c(NA, NA)*t4 + c(bat3.thr4, bat3.thr4)*t4
bat4 | c(NA, NA)*t1 + c(bat4.thr1, bat4.thr1)*t1
bat4 | c(NA, NA)*t2 + c(bat4.thr2, bat4.thr2)*t2
bat4 | c(NA, NA)*t3 + c(bat4.thr3, bat4.thr3)*t3
bat4 | c(NA, NA)*t4 + c(bat4.thr4, bat4.thr4)*t4
bat5 | c(NA, NA)*t1 + c(bat5.thr1, bat5.thr1)*t1
bat5 | c(NA, NA)*t2 + c(bat5.thr2, bat5.thr2)*t2
bat5 | c(NA, NA)*t3 + c(bat5.thr3, bat5.thr3)*t3
bat5 | c(NA, NA)*t4 + c(bat5.thr4, bat5.thr4)*t4
bat6 | c(NA, NA)*t1 + c(bat6.thr1, bat6.thr1)*t1
bat6 | c(NA, NA)*t2 + c(bat6.thr2, bat6.thr2)*t2
bat6 | c(NA, NA)*t3 + c(bat6.thr3, bat6.thr3)*t3
bat6 | c(NA, NA)*t4 + c(bat6.thr4, bat6.thr4)*t4
bat7 | c(NA, NA)*t1 + c(bat7.thr1, bat7.thr1)*t1
bat7 | c(NA, NA)*t2 + c(bat7.thr2, bat7.thr2)*t2
bat7 | c(NA, NA)*t3 + c(bat7.thr3, bat7.thr3)*t3
bat7 | c(NA, NA)*t4 + c(bat7.thr4, bat7.thr4)*t4
bat8 | c(NA, NA)*t1 + c(bat8.thr1, bat8.thr1)*t1
bat8 | c(NA, NA)*t2 + c(bat8.thr2, bat8.thr2)*t2
bat8 | c(NA, NA)*t3 + c(bat8.thr3, bat8.thr3)*t3
bat8 | c(NA, NA)*t4 + c(bat8.thr4, bat8.thr4)*t4
bat9 | c(NA, NA)*t1 + c(bat9.thr1, bat9.thr1)*t1
bat9 | c(NA, NA)*t2 + c(bat9.thr2, bat9.thr2)*t2
bat9 | c(NA, NA)*t3 + c(bat9.thr3, bat9.thr3)*t3
bat9 | c(NA, NA)*t4 + c(bat9.thr4, bat9.thr4)*t4
bat10 | c(NA, NA)*t1 + c(bat10.thr1, bat10.thr1)*t1
bat10 | c(NA, NA)*t2 + c(bat10.thr2, bat10.thr2)*t2
bat10 | c(NA, NA)*t3 + c(bat10.thr3, bat10.thr3)*t3
bat10 | c(NA, NA)*t4 + c(bat10.thr4, bat10.thr4)*t4
bat11 | c(NA, NA)*t1 + c(bat11.thr1, bat11.thr1)*t1
bat11 | c(NA, NA)*t2 + c(bat11.thr2, bat11.thr2)*t2
bat11 | c(NA, NA)*t3 + c(bat11.thr3, bat11.thr3)*t3
bat11 | c(NA, NA)*t4 + c(bat11.thr4, bat11.thr4)*t4
bat12 | c(NA, NA)*t1 + c(bat12.thr1, bat12.thr1)*t1
bat12 | c(NA, NA)*t2 + c(bat12.thr2, bat12.thr2)*t2
bat12 | c(NA, NA)*t3 + c(bat12.thr3, bat12.thr3)*t3
bat12 | c(NA, NA)*t4 + c(bat12.thr4, bat12.thr4)*t4

## INTERCEPTS:

bat1 ~ c(0, 0)*1 + c(nu.1, nu.1)*1
bat2 ~ c(0, 0)*1 + c(nu.2, nu.2)*1
bat3 ~ c(0, 0)*1 + c(nu.3, nu.3)*1
bat4 ~ c(0, 0)*1 + c(nu.4, nu.4)*1
bat5 ~ c(0, 0)*1 + c(nu.5, nu.5)*1
bat6 ~ c(0, 0)*1 + c(nu.6, nu.6)*1
bat7 ~ c(0, 0)*1 + c(nu.7, nu.7)*1
bat8 ~ c(0, 0)*1 + c(nu.8, nu.8)*1
bat9 ~ c(0, 0)*1 + c(nu.9, nu.9)*1
bat10 ~ c(0, 0)*1 + c(nu.10, nu.10)*1
bat11 ~ c(0, 0)*1 + c(nu.11, nu.11)*1
bat12 ~ c(0, 0)*1 + c(nu.12, nu.12)*1

## UNIQUE-FACTOR VARIANCES:

bat1 ~~ c(1, NA)*bat1 + c(theta.1_1.g1, theta.1_1.g2)*bat1
bat2 ~~ c(1, NA)*bat2 + c(theta.2_2.g1, theta.2_2.g2)*bat2
bat3 ~~ c(1, NA)*bat3 + c(theta.3_3.g1, theta.3_3.g2)*bat3
bat4 ~~ c(1, NA)*bat4 + c(theta.4_4.g1, theta.4_4.g2)*bat4
bat5 ~~ c(1, NA)*bat5 + c(theta.5_5.g1, theta.5_5.g2)*bat5
bat6 ~~ c(1, NA)*bat6 + c(theta.6_6.g1, theta.6_6.g2)*bat6
bat7 ~~ c(1, NA)*bat7 + c(theta.7_7.g1, theta.7_7.g2)*bat7
bat8 ~~ c(1, NA)*bat8 + c(theta.8_8.g1, theta.8_8.g2)*bat8
bat9 ~~ c(1, NA)*bat9 + c(theta.9_9.g1, theta.9_9.g2)*bat9
bat10 ~~ c(1, NA)*bat10 + c(theta.10_10.g1, theta.10_10.g2)*bat10
bat11 ~~ c(1, NA)*bat11 + c(theta.11_11.g1, theta.11_11.g2)*bat11
bat12 ~~ c(1, NA)*bat12 + c(theta.12_12.g1, theta.12_12.g2)*bat12

## UNIQUE-FACTOR COVARIANCES:

bat10 ~~ c(NA, NA)*bat11 + c(theta.11_10.g1, theta.11_10.g2)*bat11

## LATENT MEANS/INTERCEPTS:

Ex ~ c(0, 0)*1 + c(alpha.1.g1, alpha.1.g2)*1
MD ~ c(0, NA)*1 + c(alpha.2.g1, alpha.2.g2)*1
CI ~ c(0, NA)*1 + c(alpha.3.g1, alpha.3.g2)*1
EI ~ c(0, NA)*1 + c(alpha.4.g1, alpha.4.g2)*1
Burn ~ c(0, NA)*1 + c(alpha.5.g1, alpha.5.g2)*1

## COMMON-FACTOR VARIANCES:

Ex ~~ c(NA, NA)*Ex + c(psi.1_1.g1, psi.1_1.g2)*Ex
MD ~~ c(NA, NA)*MD + c(psi.2_2.g1, psi.2_2.g2)*MD
CI ~~ c(NA, NA)*CI + c(psi.3_3.g1, psi.3_3.g2)*CI
EI ~~ c(NA, NA)*EI + c(psi.4_4.g1, psi.4_4.g2)*EI
Burn ~~ c(NA, NA)*Burn + c(psi.5_5.g1, psi.5_5.g2)*Burn

## COMMON-FACTOR COVARIANCES:

Ex ~~ c(0, 0)*MD + c(psi.2_1.g1, psi.2_1.g2)*MD
Ex ~~ c(0, 0)*CI + c(psi.3_1.g1, psi.3_1.g2)*CI
Ex ~~ c(0, 0)*EI + c(psi.4_1.g1, psi.4_1.g2)*EI
Ex ~~ c(0, 0)*Burn + c(psi.5_1.g1, psi.5_1.g2)*Burn
MD ~~ c(0, 0)*CI + c(psi.3_2.g1, psi.3_2.g2)*CI
MD ~~ c(0, 0)*EI + c(psi.4_2.g1, psi.4_2.g2)*EI
MD ~~ c(0, 0)*Burn + c(psi.5_2.g1, psi.5_2.g2)*Burn
CI ~~ c(0, 0)*EI + c(psi.4_3.g1, psi.4_3.g2)*EI
CI ~~ c(0, 0)*Burn + c(psi.5_3.g1, psi.5_3.g2)*Burn
EI ~~ c(0, 0)*Burn + c(psi.5_4.g1, psi.5_4.g2)*Burn
"

## fit model to data
fit.scalar <- cfa(model = mod.scalar,
                  data = ds_mi,
                  group = "occupational_status",
                  ordered = T,
                  parameterization = "theta")
## test equivalence of intercepts, given equal thresholds & loadings
#anova(fit.config, fit.thresh ,fit.metric_1l, fit.metric_2l, fit.scalar)
#summary(fit.scalar, std=T)
```

]

---

# Students vs. Workers

**Means invariance model**: equal thresholds, loadings, structural weights, intercepts (of first-order latent factors) and .orange[means] across groups or repeated measures

```r
syntax.means <- semTools::measEq.syntax(configural.model = model_measurement,
                                        data = ds_mi,
                                        ordered = T,
                                        parameterization = "theta",
                                        ID.fac = "ul",
                                        ID.cat = "Wu.Estabrook.2016",
                                        group = "occupational_status", 
                                        group.equal = c("thresholds","loadings",
                                                        "regressions","intercepts", "means"))

syntax.means <- update(syntax.means,
                        change.syntax = fixMeans.c)

#summary(syntax.means)                    # summarize model features
#cat(as.character(syntax.means)) # save as text
mod.means <- syntax.means  |> as.character()# save as text

## fit model to data
fit.means <- cfa(model = mod.means,
                 data = ds_mi,
                 group = "occupational_status",
                 ordered = T,
                 parameterization = "theta")
```

]

---

# Students vs. Workers

**Strict (second-order) invariance model**: equal thresholds, loadings, structural weights, intercepts (of first-order latent factors), means and .orange[disturbances] across groups or repeated measures

```r
## strict invariance
syntax.strict_2l <- measEq.syntax(configural.model = model_measurement,
                                  data = ds_mi,
                                  ordered = T,
                                  parameterization = "theta",
                                  ID.fac = "ul",
                                  ID.cat = "Wu.Estabrook.2016",
                                  group = "occupational_status", 
                                  group.equal = c("thresholds","loadings",
                                                  "regressions","intercepts"))

fixMeans.th <- '
MD ~ c(0, NA)*1
CI ~ c(0, NA)*1
EI ~ c(0, NA)*1
Burn ~ c(0, NA)*1
'

syntax.strict_2l <- update(object = syntax.strict_2l,
                           change.syntax = fixMeans.th)

fixDist <- '
Ex ~~ c(1, 1)*Ex + c(psi.1_1.g1, psi.1_1.g2)*Ex
MD ~~ c(1, 1)*MD + c(psi.2_2.g1, psi.2_2.g2)*MD
CI ~~ c(1, 1)*CI + c(psi.3_3.g1, psi.3_3.g2)*CI
EI ~~ c(1, 1)*EI + c(psi.4_4.g1, psi.4_4.g2)*EI
Burn ~~ c(NA, NA)*Burn + c(psi.5_5.g1, psi.5_5.g2)*Burn
'
syntax.strict_2l <- update(object = syntax.strict_2l,
                           change.syntax = fixDist)
#summary(syntax.strict_2l)                    # summarize model features
#cat(as.character(syntax.strict_2l)) # save as text
mod.strict_2l <- syntax.strict_2l |> as.character()# save as text

## fit model to data
fit.strict_2l <- cfa(model = mod.strict_2l, data = ds_mi, group = "occupational_status",
                     ordered = T, parameterization = "theta")
```

]

---

# Students vs. Workers

**Strict (first-order) invariance model**: equal thresholds, loadings, structural weights, intercepts (of first-order latent factors), means, disturbances and .orange[residuals] across groups or repeated measures

```r
## strict invariance
syntax.strict_1l <- semTools::measEq.syntax(configural.model = model_measurement,
                                  data = ds_mi,
                                  ordered = T,
                                  parameterization = "theta",
                                  ID.fac = "ul",
                                  ID.cat = "Wu.Estabrook.2016",
                                  group = "occupational_status", 
                                  group.equal = c("thresholds","loadings",
                                                  "regressions","intercepts",
                                                  "residuals"))

syntax.strict_1l <- update(object = syntax.strict_1l,
                           change.syntax = fixMeans.th)
syntax.strict_1l <- update(object = syntax.strict_1l,
                           change.syntax = fixDist)

#summary(syntax.strict_1l)                    # summarize model features
#cat(as.character(syntax.strict_1l)) # save as text
mod.strict_1l <- syntax.strict_1l |> as.character() # save as text

## fit model to data
fit.strict_1l <- cfa(model = mod.strict_1l, data = ds_mi, group = "occupational_status",
                     ordered = T, parameterization = "theta")
## test equivalence of intercepts, given equal thresholds & loadings
#anova(fit.config, fit.thresh ,fit.metric_1l, fit.metric_2l, fit.scalar, fit.means, fit.strict_2l, fit.strict_1l)
```

]

---

# Students vs. Workers

<table class="table" style="color: black; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:left;">   </th>
   <th style="text-align:left;"> $\chi^2_{scaled}$ </th>
   <th style="text-align:right;"> $df_{scaled}$ </th>
   <th style="text-align:left;"> $p_{\Delta\chi^2}$ </th>
   <th style="text-align:left;"> $CFI_{scaled}$ </th>
   <th style="text-align:left;"> $\Delta CFI_{scaled}$ </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Configural </td>
   <td style="text-align:left;"> 1,050.018 </td>
   <td style="text-align:right;"> 98 </td>
   <td style="text-align:left;"> - </td>
   <td style="text-align:left;"> 0.984 </td>
   <td style="text-align:left;"> - </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Thresholds </td>
   <td style="text-align:left;"> 1,045.546 </td>
   <td style="text-align:right;"> 118 </td>
   <td style="text-align:left;"> .034 </td>
   <td style="text-align:left;"> 0.984 </td>
   <td style="text-align:left;"> 0.000 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Factor loadings </td>
   <td style="text-align:left;"> 1,010.177 </td>
   <td style="text-align:right;"> 126 </td>
   <td style="text-align:left;"> .045 </td>
   <td style="text-align:left;"> 0.985 </td>
   <td style="text-align:left;"> 0.001 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Structural weights </td>
   <td style="text-align:left;"> 925.097 </td>
   <td style="text-align:right;"> 129 </td>
   <td style="text-align:left;"> .015 </td>
   <td style="text-align:left;"> 0.986 </td>
   <td style="text-align:left;"> 0.001 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Intercepts (first-order) </td>
   <td style="text-align:left;"> 967.161 </td>
   <td style="text-align:right;"> 141 </td>
   <td style="text-align:left;"> &lt; .001 </td>
   <td style="text-align:left;"> 0.986 </td>
   <td style="text-align:left;"> -0.001 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Latent means </td>
   <td style="text-align:left;"> 877.750 </td>
   <td style="text-align:right;"> 145 </td>
   <td style="text-align:left;"> &lt; .001 </td>
   <td style="text-align:left;"> 0.988 </td>
   <td style="text-align:left;"> 0.002 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Disturbances </td>
   <td style="text-align:left;"> 1,157.145 </td>
   <td style="text-align:right;"> 149 </td>
   <td style="text-align:left;"> &lt; .001 </td>
   <td style="text-align:left;"> 0.983 </td>
   <td style="text-align:left;"> -0.005 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Residuals </td>
   <td style="text-align:left;"> 1,063.605 </td>
   <td style="text-align:right;"> 161 </td>
   <td style="text-align:left;"> &lt; .001 </td>
   <td style="text-align:left;"> 0.985 </td>
   <td style="text-align:left;"> 0.002 </td>
  </tr>
</tbody>
<tfoot>
<tr>
<td style="padding: 0; border:0;" colspan="100%">
<sup>a</sup> The `\chi_{text{scaled}}^{2}` column contains the robust test. The `p_{Deltachi^2}` column contains the robust difference test which is a function of two standard (not robust) statistics.</td>
</tr>
</tfoot>
</table>

---

# Sex

<table class="table" style="color: black; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:left;">   </th>
   <th style="text-align:left;"> $\chi^2_{scaled}$ </th>
   <th style="text-align:right;"> $df_{scaled}$ </th>
   <th style="text-align:left;"> $p_{\Delta\chi^2}$ </th>
   <th style="text-align:left;"> $CFI_{scaled}$ </th>
   <th style="text-align:left;"> $\Delta CFI_{scaled}$ </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Configural </td>
   <td style="text-align:left;"> 957.010 </td>
   <td style="text-align:right;"> 98 </td>
   <td style="text-align:left;"> - </td>
   <td style="text-align:left;"> 0.985 </td>
   <td style="text-align:left;"> - </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Thresholds </td>
   <td style="text-align:left;"> 964.056 </td>
   <td style="text-align:right;"> 118 </td>
   <td style="text-align:left;"> .204 </td>
   <td style="text-align:left;"> 0.985 </td>
   <td style="text-align:left;"> 0.000 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Factor loadings </td>
   <td style="text-align:left;"> 942.516 </td>
   <td style="text-align:right;"> 126 </td>
   <td style="text-align:left;"> .832 </td>
   <td style="text-align:left;"> 0.985 </td>
   <td style="text-align:left;"> 0.001 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Structural weights </td>
   <td style="text-align:left;"> 811.051 </td>
   <td style="text-align:right;"> 129 </td>
   <td style="text-align:left;"> .618 </td>
   <td style="text-align:left;"> 0.988 </td>
   <td style="text-align:left;"> 0.002 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Intercepts (first-order) </td>
   <td style="text-align:left;"> 859.780 </td>
   <td style="text-align:right;"> 141 </td>
   <td style="text-align:left;"> &lt; .001 </td>
   <td style="text-align:left;"> 0.987 </td>
   <td style="text-align:left;"> -0.001 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Latent means </td>
   <td style="text-align:left;"> 739.950 </td>
   <td style="text-align:right;"> 145 </td>
   <td style="text-align:left;"> &lt; .001 </td>
   <td style="text-align:left;"> 0.989 </td>
   <td style="text-align:left;"> 0.002 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Disturbances </td>
   <td style="text-align:left;"> 983.354 </td>
   <td style="text-align:right;"> 149 </td>
   <td style="text-align:left;"> .003 </td>
   <td style="text-align:left;"> 0.985 </td>
   <td style="text-align:left;"> -0.004 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Residuals </td>
   <td style="text-align:left;"> 980.413 </td>
   <td style="text-align:right;"> 161 </td>
   <td style="text-align:left;"> &lt; .001 </td>
   <td style="text-align:left;"> 0.985 </td>
   <td style="text-align:left;"> 0.000 </td>
  </tr>
</tbody>
<tfoot>
<tr>
<td style="padding: 0; border:0;" colspan="100%">
<sup>a</sup> The `\chi_{text{scaled}}^{2}` column contains the robust test. The `p_{Deltachi^2}` column contains the robust difference test which is a function of two standard (not robust) statistics.</td>
</tr>
</tfoot>
</table>

---
class: inverse, center, middle

# .white[Validity Evidence based on the Relations to Other Variables]
<html><div style='float:left'></div><hr color='#EB811B' size=1px width=800px></html>

---
class: inverse, center, middle

# .white[Students]
<html><div style='float:left'></div><hr color='#EB811B' size=1px width=800px></html>

---

# Latent Correlations

The model presented the following goodness-of-fit indices `$(\chi^2_{scaled (751)}=3,012.52;p< .001; CFI_{scaled}=0.989;$` `$TLI_{scaled}=0.987;NFI_{scaled}=0.985; SRMR=0.052;RMSEA_{scaled}=0.048;p_{(rmsea \leq 0.05)}= .920;$` `$90\%CI[0.047, 0.050])$`.

<table class="table" style="color: black; margin-left: auto; margin-right: auto;">
<caption>Latent Correlations</caption>
 <thead>
  <tr>
   <th style="text-align:left;">  </th>
   <th style="text-align:right;"> 1 </th>
   <th style="text-align:right;"> 2 </th>
   <th style="text-align:right;"> 3 </th>
   <th style="text-align:right;"> 4 </th>
   <th style="text-align:right;"> 5 </th>
   <th style="text-align:right;"> 6 </th>
   <th style="text-align:left;"> 7 </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Burnout (1) </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;"> .15 </td>
   <td style="text-align:right;"> .13 </td>
   <td style="text-align:right;"> -.31 </td>
   <td style="text-align:right;"> .34 </td>
   <td style="text-align:right;"> -.19 </td>
   <td style="text-align:left;"> -.25 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Kiasuism (2) </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;"> .18 </td>
   <td style="text-align:right;"> -.07 </td>
   <td style="text-align:right;"> .23 </td>
   <td style="text-align:right;"> .04 </td>
   <td style="text-align:left;"> .08 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Conformism (3) </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;"> -.13 </td>
   <td style="text-align:right;"> .08 </td>
   <td style="text-align:right;"> .00 </td>
   <td style="text-align:left;"> -.04 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Optimism (4) </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;"> -.70 </td>
   <td style="text-align:right;"> .50 </td>
   <td style="text-align:left;"> .01 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Pessimism (5) </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;"> -.30 </td>
   <td style="text-align:left;"> -.11 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Support (6) </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:left;"> .06 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Cumulative GPA (7) </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:left;">  </td>
  </tr>
</tbody>
</table>

---

# Reliabillity

## First-order

The model's first-order internal consistency estimates are presented in the following table.

<table class="table" style="color: black; margin-left: auto; margin-right: auto;">
<caption>Reliability estimates: First-order</caption>
 <thead>
  <tr>
   <th style="text-align:left;">   </th>
   <th style="text-align:right;"> Ex </th>
   <th style="text-align:right;"> Md </th>
   <th style="text-align:right;"> Ci </th>
   <th style="text-align:right;"> Ei </th>
   <th style="text-align:right;"> Kiasuism </th>
   <th style="text-align:right;"> Conformism </th>
   <th style="text-align:right;"> Opt </th>
   <th style="text-align:right;"> Pess </th>
   <th style="text-align:right;"> Sup_fam </th>
   <th style="text-align:right;"> Sup_frd </th>
   <th style="text-align:right;"> Sup_oth </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> $\omega_{ord}$ </td>
   <td style="text-align:right;"> 0.86 </td>
   <td style="text-align:right;"> 0.82 </td>
   <td style="text-align:right;"> 0.79 </td>
   <td style="text-align:right;"> 0.87 </td>
   <td style="text-align:right;"> 0.88 </td>
   <td style="text-align:right;"> 0.76 </td>
   <td style="text-align:right;"> 0.68 </td>
   <td style="text-align:right;"> 0.72 </td>
   <td style="text-align:right;"> 0.91 </td>
   <td style="text-align:right;"> 0.92 </td>
   <td style="text-align:right;"> 0.97 </td>
  </tr>
</tbody>
</table>

## Second-order

The model's second-order internal consistency estimates are presented in the following table.

---

# .white[Workers]
<html><div style='float:left'></div><hr color='#EB811B' size=1px width=800px></html>

---

# Latent Correlations

The model presented the following goodness-of-fit indices `$(\chi^2_{scaled (751)}=1,047.85;p< .001; CFI_{scaled}=0.993;$` `$TLI_{scaled}=0.992;NFI_{scaled}=0.976; SRMR=0.062;RMSEA_{scaled}=0.039; p_{(rmsea \leq 0.05)}> .999;$` `$90\%CI[0.033, 0.045])$`.

<table class="table" style="color: black; margin-left: auto; margin-right: auto;">
<caption>Latent Correlations</caption>
 <thead>
  <tr>
   <th style="text-align:left;">  </th>
   <th style="text-align:right;"> 1 </th>
   <th style="text-align:right;"> 2 </th>
   <th style="text-align:right;"> 3 </th>
   <th style="text-align:right;"> 4 </th>
   <th style="text-align:right;"> 5 </th>
   <th style="text-align:right;"> 6 </th>
   <th style="text-align:left;"> 7 </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Burnout (1) </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:left;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Kiasuism (2) </td>
   <td style="text-align:right;"> .18 </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:left;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Conformism (3) </td>
   <td style="text-align:right;"> .14 </td>
   <td style="text-align:right;"> .10 </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:left;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Optimism (4) </td>
   <td style="text-align:right;"> -.20 </td>
   <td style="text-align:right;"> -.01 </td>
   <td style="text-align:right;"> -.17 </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:left;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Pessimism (5) </td>
   <td style="text-align:right;"> .35 </td>
   <td style="text-align:right;"> .14 </td>
   <td style="text-align:right;"> .11 </td>
   <td style="text-align:right;"> -.62 </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:left;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Support (6) </td>
   <td style="text-align:right;"> -.15 </td>
   <td style="text-align:right;"> .18 </td>
   <td style="text-align:right;"> .07 </td>
   <td style="text-align:right;"> .42 </td>
   <td style="text-align:right;"> -.22 </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:left;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Final course GPA (7) </td>
   <td style="text-align:right;"> -.03 </td>
   <td style="text-align:right;"> .01 </td>
   <td style="text-align:right;"> -.01 </td>
   <td style="text-align:right;"> .10 </td>
   <td style="text-align:right;"> -.28 </td>
   <td style="text-align:right;"> .12 </td>
   <td style="text-align:left;">  </td>
  </tr>
</tbody>
</table>

---

# Reliability

## First-order

The model's first-order internal consistency estimates are presented in the following table.

<table class="table" style="color: black; margin-left: auto; margin-right: auto;">
<caption>Reliability estimates: First-order</caption>
 <thead>
  <tr>
   <th style="text-align:left;">   </th>
   <th style="text-align:right;"> Ex </th>
   <th style="text-align:right;"> Md </th>
   <th style="text-align:right;"> Ci </th>
   <th style="text-align:right;"> Ei </th>
   <th style="text-align:right;"> Kiasuism </th>
   <th style="text-align:right;"> Conformism </th>
   <th style="text-align:right;"> Opt </th>
   <th style="text-align:right;"> Pess </th>
   <th style="text-align:right;"> Sup_fam </th>
   <th style="text-align:right;"> Sup_frd </th>
   <th style="text-align:right;"> Sup_oth </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> $\omega_{ord}$ </td>
   <td style="text-align:right;"> 0.81 </td>
   <td style="text-align:right;"> 0.8 </td>
   <td style="text-align:right;"> 0.65 </td>
   <td style="text-align:right;"> 0.86 </td>
   <td style="text-align:right;"> 0.89 </td>
   <td style="text-align:right;"> 0.75 </td>
   <td style="text-align:right;"> 0.64 </td>
   <td style="text-align:right;"> 0.74 </td>
   <td style="text-align:right;"> 0.9 </td>
   <td style="text-align:right;"> 0.92 </td>
   <td style="text-align:right;"> 0.98 </td>
  </tr>
</tbody>
</table>

## Second-order

The model's second-order internal consistency estimates are presented in the following table.

<table class="table" style="color: black; margin-left: auto; margin-right: auto;">
<caption>Reliability estimates: Second-order</caption>
 <thead>
  <tr>
   <th style="text-align:left;">   </th>
   <th style="text-align:right;"> $\omega_{L1}$ </th>
   <th style="text-align:right;"> $\omega_{L2}$ </th>
   <th style="text-align:right;"> $\omega_{Partial~L1}$ </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Burnout </td>
   <td style="text-align:right;"> 0.84 </td>
   <td style="text-align:right;"> 0.90 </td>
   <td style="text-align:right;"> 0.93 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Social Support </td>
   <td style="text-align:right;"> 0.69 </td>
   <td style="text-align:right;"> 0.71 </td>
   <td style="text-align:right;"> 0.96 </td>
  </tr>
</tbody>
</table>

---

# Discussion

BAT-12 demonstrated strong validity evidence, aligning with the expected dimensions of burnout core symptoms, including Exhaustion, Mental Distance, Cognitive Impairment and Emotional Impairment.

Good reliability (in terms of internal consistency) was observed for all factors.

Measurement invariance was found for occupational status and sex.

---

# Discussion

Convergent validity was supported through negative correlations with optimism, and social support, as well as positive correlations with pessimism,fear of losing out and conformism (for both groups).

Cumulative GPA was negatively correlated with burnout (only for students).

Cultural aspects (vertical conformity and kiasuism).

---

# Conclusion

The BAT-12 was found to have good psychometric properties for assessing burnout among Singaporean undergraduate students and workers.

The study highlighted the importance of considering sociocultural context variables when examining occupational health constructs and offered valuable insights into the applicability of the BAT-12 in populations of undergraduates and of workers.

---

# References

Adams, R. J., M. Wilson, et al. (1997). "The multidimensional random
coefficients multinomial logit model". In: _Applied Psychological
Measurement_ 21.1, pp. 1-23. ISSN: 0146-6216. DOI:
[10.1177/0146621697211001](https://doi.org/10.1177%2F0146621697211001).
eprint: 0803973233.

Briggs, D. C. and M. Wilson (2003). "An introduction to
multidimensional measurement using Rasch models.". In: _Journal of
Applied Measurement_ 4.1, pp. 87-100. ISSN: 1529-7713.

Finney, S. J. and C. DiStefano (2013). "Non-normal and categorical data
in structural equation modeling". In: _Structural equation modeling: A
second course_. Ed. by G. R. Hancock and R. O. Mueller. 2nd ed.
Charlotte, NC: Information Age Publishing. Chap. 11, pp. 439-492.

Maggiori, C., J. Rossier, et al. (2017). "Career Adapt-Abilities
Scale–Short Form (CAAS-SF): Construction and validation". In: _Journal
of Career Assessment_ 25.2, pp. 312-325. ISSN: 1069-0727. DOI:
[10.1177/1069072714565856](https://doi.org/10.1177%2F1069072714565856).

Mehrabian, A. and C. A. Stefl (1995). "Basic temperament components of
loneliness, shyness, and conformity". In: _Social Behavior and
Personality: an international journal_ 23.3, pp. 253-263. ISSN:
0301-2212. DOI:
[10.2224/sbp.1995.23.3.253](https://doi.org/10.2224%2Fsbp.1995.23.3.253).

---

# References

Posit Team (2023). _RStudio: Integrated development for R (version
2023.3.0.386) [Computer software]_. Boston, MA. URL:
[http://www.posit.co/](http://www.posit.co/).

---

# Next Steps, Questions and Comments

1. **The burnout-depression conundrum**
   - The relationship between burnout and depression.

2. **Longitudinal Analysis**
   - Importance of tracking burnout, depression, and anxiety over time.

3. **Singapore's Context**
   - Relevance of BAT for Singapore's students and workers.

.can-edit.key-measurement[
- ...
]