Burnout Assessment Tool

.title[
# Burnout Assessment Tool
]
.subtitle[
## Validity evidence for the workers secondary symptoms version and for the student short version
]
.author[
### Jorge Sinval, Wilmar B. Schaufeli, & Sílvia Silva
]
.date[
### 2024-04-04
]

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# BAT Symposium 2024 Map

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# .white[Introduction]  
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# Introduction: Burnout

The Burnout Assessment Tool (BAT) is a recognized psychometric tool for measuring burnout. It introduces a novel approach to burnout as a multidimensional construct, consisting of two second-order dimensions &mdash; core and secondary symptoms.

Previous studies have examined the psychometric properties of the BAT-23 and BAT-12 in Portugal.

However, no research has yet explored the validity of the BAT-S (secondary symptoms version) in Portugal or the psychometric properties of the BAT-12 in Portuguese university students.

---

# Introduction: Goal

Assess the psychometric characteristics of the Portuguese versions of BAT-S in working professionals and BAT-12 in university students.

More specifically, the study aims to: investigate the validity evidence based on the internal structure (dimensionality, reliability, and measurement invariance) as well as the validity evidence based on the relations to other variables.

---

# .white[Method]  
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# Method

## Sampling

### Students

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

### Workers

Workers of a Public Administration Organization and workers of various occupations (several companies).

---

# Method

## Procedure

### Students

Participants were invited via institutional emails to complete an online LimeSurvey containing sociodemographic, and academic questions.

### Workers

Participants were invited completed an online LimeSurvey containing sociodemographic, and professional questions.

---

# Method

## Psychometric instruments

### Students

Burnout (BAT-12) (Schaufeli, Desart, and De
Witte, 2020).  
DASS-21 (Lovibond and Lovibond, 1995).  
Compound Psychological Capital (CPC-12R) (Lorenz, Hagitte, and Prasath, 2022).  
University Student Engagement Inventory (USEI) (Marôco, Marôco, Campos, and Fredricks, 2016).  
FSozUK-6 (Kliem, Mö{ß}le, Rehbein, Hellmann, Zenger, and Brähler, 2015).  
Dropout Intention (Casanova, Gomes, Bernardo, Nú{n}ez, and Almeida, 2021).  
Satisfaction with Education (Casanova Gomes et al., 2021).

### Workers

Burnout Assessment Tool &mdash; Secondary Symptoms (BAT-S) (Schaufeli Desart et al., 2020).  
Colleagues’ incivility (Matthews and Ritter, 2019).  
Clients’ incivility (Matthews and Ritter, 2019).  
Negative change from the Job Demands-Resources Questionnaire (Schaufeli, 2015).  
Bureaucracy (Red Tape) from the Job Demands-Resources Questionnaire (Schaufeli, 2015).

## Data Analysis

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

CFA  
Reliability `\((\alpha; \omega; AVE)\)`  
Measurement invariance (MGCFA)  
Multidimensional polytomous Rasch model  as a specific application of the multidimensional random coefficients multinomial logit model (MRCMLM) .  
Full SEM

---

# .white[Results]  
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# .white[Sample Characterization]
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# .white[Students]
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# Sample Characterization

<table class="table" style="color: black; width: auto !important; margin-left: auto; margin-right: auto;">
<caption>Medical Undergraduate Students</caption>
 <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=263) </td>
   <td style="text-align:center;"> (N=87) </td>
   <td style="text-align:center;"> (N=350) </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;"> 20.2 (4.17) </td>
   <td style="text-align:center;"> 20.3 (3.43) </td>
   <td style="text-align:center;"> 20.2 (3.99) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Median [Min, Max] </td>
   <td style="text-align:center;"> 19.0 [17.0, 49.0] </td>
   <td style="text-align:center;"> 19.0 [17.0, 34.0] </td>
   <td style="text-align:center;"> 19.0 [17.0, 49.0] </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Moved from the city of origin </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;"> N </td>
   <td style="text-align:center;"> 155 (58.9%) </td>
   <td style="text-align:center;"> 53 (60.9%) </td>
   <td style="text-align:center;"> 208 (59.4%) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Y </td>
   <td style="text-align:center;"> 108 (41.1%) </td>
   <td style="text-align:center;"> 34 (39.1%) </td>
   <td style="text-align:center;"> 142 (40.6%) </td>
  </tr>
</tbody>
</table>
]

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# .white[Workers]  
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# Sample Characterization

## Workers of a Public Administration Organization

<table class="table" style="color: black; width: auto !important; margin-left: auto; margin-right: auto;">
<caption>Workers of Public Administration Organization</caption>
 <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=263) </td>
   <td style="text-align:center;"> (N=104) </td>
   <td style="text-align:center;"> (N=367) </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;"> [20; 24] </td>
   <td style="text-align:center;"> 0 (0%) </td>
   <td style="text-align:center;"> 0 (0%) </td>
   <td style="text-align:center;"> 0 (0%) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> [25; 29] </td>
   <td style="text-align:center;"> 4 (1.5%) </td>
   <td style="text-align:center;"> 1 (1.0%) </td>
   <td style="text-align:center;"> 5 (1.4%) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> [30; 34] </td>
   <td style="text-align:center;"> 2 (0.8%) </td>
   <td style="text-align:center;"> 1 (1.0%) </td>
   <td style="text-align:center;"> 3 (0.8%) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> [35; 39] </td>
   <td style="text-align:center;"> 18 (6.8%) </td>
   <td style="text-align:center;"> 10 (9.6%) </td>
   <td style="text-align:center;"> 28 (7.6%) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> [40; 44] </td>
   <td style="text-align:center;"> 54 (20.5%) </td>
   <td style="text-align:center;"> 22 (21.2%) </td>
   <td style="text-align:center;"> 76 (20.7%) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> [45; 49] </td>
   <td style="text-align:center;"> 80 (30.4%) </td>
   <td style="text-align:center;"> 31 (29.8%) </td>
   <td style="text-align:center;"> 111 (30.2%) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> [50; 54] </td>
   <td style="text-align:center;"> 53 (20.2%) </td>
   <td style="text-align:center;"> 17 (16.3%) </td>
   <td style="text-align:center;"> 70 (19.1%) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> [55; 59] </td>
   <td style="text-align:center;"> 30 (11.4%) </td>
   <td style="text-align:center;"> 9 (8.7%) </td>
   <td style="text-align:center;"> 39 (10.6%) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> [60; 65] </td>
   <td style="text-align:center;"> 22 (8.4%) </td>
   <td style="text-align:center;"> 13 (12.5%) </td>
   <td style="text-align:center;"> 35 (9.5%) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Academic level </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;"> High school, vocational education or lower </td>
   <td style="text-align:center;"> 103 (39.2%) </td>
   <td style="text-align:center;"> 36 (34.6%) </td>
   <td style="text-align:center;"> 139 (37.9%) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Graduation </td>
   <td style="text-align:center;"> 41 (15.6%) </td>
   <td style="text-align:center;"> 12 (11.5%) </td>
   <td style="text-align:center;"> 53 (14.4%) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Post-graduation </td>
   <td style="text-align:center;"> 119 (45.2%) </td>
   <td style="text-align:center;"> 56 (53.8%) </td>
   <td style="text-align:center;"> 175 (47.7%) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Occupational group (ISCO-08) </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;"> Clerical Support Workers </td>
   <td style="text-align:center;"> 43 (16.3%) </td>
   <td style="text-align:center;"> 9 (8.7%) </td>
   <td style="text-align:center;"> 52 (14.2%) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Managers </td>
   <td style="text-align:center;"> 12 (4.6%) </td>
   <td style="text-align:center;"> 8 (7.7%) </td>
   <td style="text-align:center;"> 20 (5.4%) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Professionals </td>
   <td style="text-align:center;"> 206 (78.3%) </td>
   <td style="text-align:center;"> 84 (80.8%) </td>
   <td style="text-align:center;"> 290 (79.0%) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Technicians and Associate Professionals </td>
   <td style="text-align:center;"> 2 (0.8%) </td>
   <td style="text-align:center;"> 3 (2.9%) </td>
   <td style="text-align:center;"> 5 (1.4%) </td>
  </tr>
</tbody>
</table>

]

---

# Sample Characterization

## Multi-Occupational Sample of Workers

<table class="table" style="color: black; width: auto !important; margin-left: auto; margin-right: auto;">
<caption>Other Samples</caption>
 <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=206) </td>
   <td style="text-align:center;"> (N=70) </td>
   <td style="text-align:center;"> (N=276) </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;"> 39.4 (10.9) </td>
   <td style="text-align:center;"> 37.0 (13.3) </td>
   <td style="text-align:center;"> 38.8 (11.6) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Median [Min, Max] </td>
   <td style="text-align:center;"> 41.0 [18.0, 63.0] </td>
   <td style="text-align:center;"> 37.5 [18.0, 68.0] </td>
   <td style="text-align:center;"> 40.0 [18.0, 68.0] </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Academic level </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;"> High school, vocational education or lower </td>
   <td style="text-align:center;"> 60 (29.1%) </td>
   <td style="text-align:center;"> 18 (25.7%) </td>
   <td style="text-align:center;"> 78 (28.3%) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Graduation </td>
   <td style="text-align:center;"> 91 (44.2%) </td>
   <td style="text-align:center;"> 38 (54.3%) </td>
   <td style="text-align:center;"> 129 (46.7%) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Post-graduation </td>
   <td style="text-align:center;"> 55 (26.7%) </td>
   <td style="text-align:center;"> 14 (20.0%) </td>
   <td style="text-align:center;"> 69 (25.0%) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Occupational group (ISCO-08) </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;"> Clerical Support Workers </td>
   <td style="text-align:center;"> 64 (31.1%) </td>
   <td style="text-align:center;"> 11 (15.7%) </td>
   <td style="text-align:center;"> 75 (27.2%) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Craft and Related Trades Workers </td>
   <td style="text-align:center;"> 2 (1.0%) </td>
   <td style="text-align:center;"> 3 (4.3%) </td>
   <td style="text-align:center;"> 5 (1.8%) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Elementary Occupations </td>
   <td style="text-align:center;"> 1 (0.5%) </td>
   <td style="text-align:center;"> 3 (4.3%) </td>
   <td style="text-align:center;"> 4 (1.4%) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Managers </td>
   <td style="text-align:center;"> 23 (11.2%) </td>
   <td style="text-align:center;"> 19 (27.1%) </td>
   <td style="text-align:center;"> 42 (15.2%) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Plant and Machine Operators and Assemblers </td>
   <td style="text-align:center;"> 5 (2.4%) </td>
   <td style="text-align:center;"> 2 (2.9%) </td>
   <td style="text-align:center;"> 7 (2.5%) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Services and Sales Workers </td>
   <td style="text-align:center;"> 62 (30.1%) </td>
   <td style="text-align:center;"> 21 (30.0%) </td>
   <td style="text-align:center;"> 83 (30.1%) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Technicians and Associate Professionals </td>
   <td style="text-align:center;"> 49 (23.8%) </td>
   <td style="text-align:center;"> 11 (15.7%) </td>
   <td style="text-align:center;"> 60 (21.7%) </td>
  </tr>
</tbody>
</table>

]

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# .white[Validity Evidence Based on the Internal Structure]  
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# .white[Students]  
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# 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 (\(n=484\))</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;"> 115 </td>
   <td style="text-align:right;"> 3.37 </td>
   <td style="text-align:right;"> 0.80 </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;"> 0.04 </td>
   <td style="text-align:right;"> 0.24 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> -0.09 </td>
   <td style="text-align:right;"> 0.05 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 2 </td>
   <td style="text-align:right;"> 115 </td>
   <td style="text-align:right;"> 3.31 </td>
   <td style="text-align:right;"> 0.93 </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;"> 0.28 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> -0.34 </td>
   <td style="text-align:right;"> 0.11 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 3 </td>
   <td style="text-align:right;"> 115 </td>
   <td style="text-align:right;"> 2.80 </td>
   <td style="text-align:right;"> 0.98 </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;"> 0.05 </td>
   <td style="text-align:right;"> 0.35 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 0.16 </td>
   <td style="text-align:right;"> -0.50 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 4 </td>
   <td style="text-align:right;"> 115 </td>
   <td style="text-align:right;"> 2.47 </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;"> 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;"> 0.05 </td>
   <td style="text-align:right;"> 0.40 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 0.33 </td>
   <td style="text-align:right;"> -0.31 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 5 </td>
   <td style="text-align:right;"> 115 </td>
   <td style="text-align:right;"> 1.77 </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;"> 1 </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;"> 0.05 </td>
   <td style="text-align:right;"> 0.58 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 1.47 </td>
   <td style="text-align:right;"> 1.67 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 6 </td>
   <td style="text-align:right;"> 115 </td>
   <td style="text-align:right;"> 1.93 </td>
   <td style="text-align:right;"> 1.11 </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;"> 0.57 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 1.10 </td>
   <td style="text-align:right;"> 0.44 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 7 </td>
   <td style="text-align:right;"> 115 </td>
   <td style="text-align:right;"> 2.05 </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;"> 3 </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;"> 0.47 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 0.81 </td>
   <td style="text-align:right;"> 0.17 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 8 </td>
   <td style="text-align:right;"> 115 </td>
   <td style="text-align:right;"> 1.85 </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;"> 0.05 </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;"> 1.00 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 9 </td>
   <td style="text-align:right;"> 115 </td>
   <td style="text-align:right;"> 1.97 </td>
   <td style="text-align:right;"> 0.94 </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;"> 0.05 </td>
   <td style="text-align:right;"> 0.47 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 0.68 </td>
   <td style="text-align:right;"> -0.18 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 10 </td>
   <td style="text-align:right;"> 115 </td>
   <td style="text-align:right;"> 2.80 </td>
   <td style="text-align:right;"> 0.93 </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;"> 0.05 </td>
   <td style="text-align:right;"> 0.33 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 0.12 </td>
   <td style="text-align:right;"> -0.13 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 11 </td>
   <td style="text-align:right;"> 115 </td>
   <td style="text-align:right;"> 2.79 </td>
   <td style="text-align:right;"> 0.93 </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;"> 0.05 </td>
   <td style="text-align:right;"> 0.33 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 0.18 </td>
   <td style="text-align:right;"> -0.16 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 12 </td>
   <td style="text-align:right;"> 115 </td>
   <td style="text-align:right;"> 2.77 </td>
   <td style="text-align:right;"> 1.01 </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;"> 0.05 </td>
   <td style="text-align:right;"> 0.36 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 0.17 </td>
   <td style="text-align:right;"> -0.44 </td>
  </tr>
</tbody>
</table>

]

---

# Dimensionality

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

```r
model_measurement <- "
Ex =~ bat12.1._i + bat12.2._i + bat12.3._i
MD =~ bat12.4._i + bat12.5._i + bat12.6._i
CI =~ bat12.7._i + bat12.8._i + bat12.9._i
EI =~ bat12.10._i + bat12.11._i + bat12.12._i

Burn =~ Ex + MD + CI + EI
"

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

---

# 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;"> bat12.1._i </td>
   <td style="text-align:left;"> 0.819 </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;"> bat12.2._i </td>
   <td style="text-align:left;"> 0.718 </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;"> bat12.3._i </td>
   <td style="text-align:left;"> 0.841 </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;"> bat12.4._i </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.923 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;"> bat12.5._i </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.834 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;"> bat12.6._i </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.625 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;"> bat12.7._i </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.828 </td>
   <td style="text-align:left;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;"> bat12.8._i </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.890 </td>
   <td style="text-align:left;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;"> bat12.9._i </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.733 </td>
   <td style="text-align:left;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;"> bat12.10._i </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.965 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> bat12.11._i </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.938 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> bat12.12._i </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.768 </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;"> 0.868 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Mental Distance </td>
   <td style="text-align:left;"> 0.825 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Cognitive Impairment </td>
   <td style="text-align:left;"> 0.728 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Emotional Impairment </td>
   <td style="text-align:left;"> 0.751 </td>
  </tr>
</tbody>
</table>

---

# Goodness-of-fit

```r
gof <- c("df.scaled",
         "chisq.scaled",
         "pvalue.scaled",
         "cfi.scaled",
         "nfi.scaled",
         "tli.scaled",
         "srmr",
         "rmsea.scaled",
         "rmsea.ci.lower.scaled",
         "rmsea.ci.upper.scaled",
         "rmsea.pvalue.scaled")
gofs_model <- fitmeasures(object = fit_model,
                          fit.measures = gof) %>%
  round(digits = 3)
```

The model presented the following goodness-of-fit indices `\((\chi^2_{scaled (50)}=196.24;p< .001;CFI_{scaled}=0.98;TLI_{scaled}=0.98;NFI_{scaled}=0.98;SRMR=0.05;RMSEA_{scaled}=0.09;p_{(rmsea \leq 0.05)}< .001; 90\%CI[0.08, 0.10])\)`.

---

# Diagram

The diagram showing the standardized estimates.

<div class="grViz html-widget html-fill-item" id="htmlwidget-90bd5c7e4f05c88f90c5" style="width:100%;height:432px;"></div>
<script type="application/json" data-for="htmlwidget-90bd5c7e4f05c88f90c5">{"x":{"diagram":" digraph plot { \n graph [ layout = dot, rankdir = LR ] \n node [ shape = box, fontname = Helvetica ] \n node [shape = box] \n bat121_i; bat122_i; bat123_i; bat124_i; bat125_i; bat126_i; bat127_i; bat128_i; bat129_i; bat1210_i; bat1211_i; bat1212_i \n node [shape = oval] \n Ex; MD; CI; EI; Burn \n \n edge [ color = grey ] \n  Ex->bat121_i [label = \"0.82***\"] Ex->bat122_i [label = \"0.72***\"] Ex->bat123_i [label = \"0.84***\"] MD->bat124_i [label = \"0.92***\"] MD->bat125_i [label = \"0.83***\"] MD->bat126_i [label = \"0.62***\"] CI->bat127_i [label = \"0.83***\"] CI->bat128_i [label = \"0.89***\"] CI->bat129_i [label = \"0.73***\"] EI->bat1210_i [label = \"0.97***\"] EI->bat1211_i [label = \"0.94***\"] EI->bat1212_i [label = \"0.77***\"] Burn->Ex [label = \"0.87***\"] Burn->MD [label = \"0.82***\"] Burn->CI [label = \"0.73***\"] Burn->EI [label = \"0.75***\"] \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;"> 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;"> 0.977 </td>
   <td style="text-align:right;"> 0.169 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Infit </td>
   <td style="text-align:right;"> 0.987 </td>
   <td style="text-align:right;"> 0.143 </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;"> 0.83 </td>
   <td style="text-align:right;"> 0.83 </td>
   <td style="text-align:right;"> 0.86 </td>
   <td style="text-align:right;"> 0.88 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> \(\omega_{ord}\) </td>
   <td style="text-align:right;"> 0.79 </td>
   <td style="text-align:right;"> 0.78 </td>
   <td style="text-align:right;"> 0.82 </td>
   <td style="text-align:right;"> 0.88 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> \(AVE\) </td>
   <td style="text-align:right;"> 0.63 </td>
   <td style="text-align:right;"> 0.65 </td>
   <td style="text-align:right;"> 0.67 </td>
   <td style="text-align:right;"> 0.80 </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;"> 0.87 </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 (\(n=857\))</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;"> 0 </td>
   <td style="text-align:right;"> 3.22 </td>
   <td style="text-align:right;"> 0.86 </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;"> -0.07 </td>
   <td style="text-align:right;"> 0.16 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 2 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 3.20 </td>
   <td style="text-align:right;"> 0.87 </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;"> -0.03 </td>
   <td style="text-align:right;"> 0.05 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 3 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 3.09 </td>
   <td style="text-align:right;"> 0.93 </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;"> 0.30 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> -0.01 </td>
   <td style="text-align:right;"> -0.27 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 4 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 2.84 </td>
   <td style="text-align:right;"> 0.92 </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;"> 0.32 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 0.17 </td>
   <td style="text-align:right;"> -0.27 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 5 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 2.82 </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;"> 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;"> 0.35 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 0.25 </td>
   <td style="text-align:right;"> -0.30 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 6 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 2.47 </td>
   <td style="text-align:right;"> 0.91 </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;"> 0.37 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 0.47 </td>
   <td style="text-align:right;"> 0.04 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 7 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 2.50 </td>
   <td style="text-align:right;"> 0.90 </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;"> 0.36 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 0.41 </td>
   <td style="text-align:right;"> -0.03 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 8 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 3.12 </td>
   <td style="text-align:right;"> 0.93 </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;"> 0.30 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 0.01 </td>
   <td style="text-align:right;"> -0.16 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 9 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 2.75 </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;"> 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;"> 0.36 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 0.24 </td>
   <td style="text-align:right;"> -0.27 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 10 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 2.30 </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;"> 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;"> 0.53 </td>
   <td style="text-align:right;"> -0.25 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 11 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 2.04 </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;"> 0.04 </td>
   <td style="text-align:right;"> 0.51 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 0.79 </td>
   <td style="text-align:right;"> 0.00 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 12 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 1.86 </td>
   <td style="text-align:right;"> 0.97 </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;"> 0.52 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 1.04 </td>
   <td style="text-align:right;"> 0.59 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 13 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 1.75 </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;"> 1 </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;"> 1.19 </td>
   <td style="text-align:right;"> 0.80 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 14 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 2.44 </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;"> 0.03 </td>
   <td style="text-align:right;"> 0.38 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 0.39 </td>
   <td style="text-align:right;"> -0.08 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 15 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 2.75 </td>
   <td style="text-align:right;"> 1.11 </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;"> 0.04 </td>
   <td style="text-align:right;"> 0.40 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 0.32 </td>
   <td style="text-align:right;"> -0.62 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 16 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 2.17 </td>
   <td style="text-align:right;"> 0.84 </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;"> 0.39 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 0.55 </td>
   <td style="text-align:right;"> 0.24 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 17 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 2.45 </td>
   <td style="text-align:right;"> 0.88 </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;"> 0.36 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 0.42 </td>
   <td style="text-align:right;"> 0.25 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 18 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 2.24 </td>
   <td style="text-align:right;"> 0.82 </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;"> 0.37 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 0.59 </td>
   <td style="text-align:right;"> 0.56 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 19 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 2.09 </td>
   <td style="text-align:right;"> 0.82 </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;"> 0.39 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 0.72 </td>
   <td style="text-align:right;"> 1.00 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 20 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 1.88 </td>
   <td style="text-align:right;"> 0.88 </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;"> 0.47 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 0.96 </td>
   <td style="text-align:right;"> 0.80 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 21 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 2.35 </td>
   <td style="text-align:right;"> 0.90 </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;"> 0.38 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 0.34 </td>
   <td style="text-align:right;"> -0.19 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 22 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 2.00 </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;"> 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;"> 0.77 </td>
   <td style="text-align:right;"> 0.10 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 23 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 2.08 </td>
   <td style="text-align:right;"> 0.81 </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;"> 0.39 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 0.52 </td>
   <td style="text-align:right;"> 0.25 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 24 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 2.85 </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;"> 4 </td>
   <td style="text-align:right;"> 5 </td>
   <td style="text-align:left;"> ▂▇▇▆▂ </td>
   <td style="text-align:right;"> 0.04 </td>
   <td style="text-align:right;"> 0.37 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 0.08 </td>
   <td style="text-align:right;"> -0.65 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 25 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 3.47 </td>
   <td style="text-align:right;"> 0.90 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 4 </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;"> 0.26 </td>
   <td style="text-align:right;"> 4 </td>
   <td style="text-align:right;"> -0.31 </td>
   <td style="text-align:right;"> 0.00 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 26 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 3.32 </td>
   <td style="text-align:right;"> 0.90 </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;"> -0.13 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 27 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 2.29 </td>
   <td style="text-align:right;"> 1.07 </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;"> 0.04 </td>
   <td style="text-align:right;"> 0.47 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 0.44 </td>
   <td style="text-align:right;"> -0.62 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 28 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 2.58 </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;"> 0.04 </td>
   <td style="text-align:right;"> 0.41 </td>
   <td style="text-align:right;"> 2 </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 29 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 1.93 </td>
   <td style="text-align:right;"> 0.97 </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;"> 0.03 </td>
   <td style="text-align:right;"> 0.50 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 0.83 </td>
   <td style="text-align:right;"> -0.04 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 30 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 2.25 </td>
   <td style="text-align:right;"> 1.12 </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;"> 0.04 </td>
   <td style="text-align:right;"> 0.50 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 0.54 </td>
   <td style="text-align:right;"> -0.67 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 31 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 2.62 </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;"> 3 </td>
   <td style="text-align:right;"> 5 </td>
   <td style="text-align:left;"> ▃▇▇▅▁ </td>
   <td style="text-align:right;"> 0.04 </td>
   <td style="text-align:right;"> 0.40 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 0.20 </td>
   <td style="text-align:right;"> -0.65 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 32 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 3.13 </td>
   <td style="text-align:right;"> 1.10 </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;"> 0.04 </td>
   <td style="text-align:right;"> 0.35 </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> -0.15 </td>
   <td style="text-align:right;"> -0.71 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Item 33 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 2.04 </td>
   <td style="text-align:right;"> 0.72 </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;"> 2 </td>
   <td style="text-align:right;"> 5 </td>
   <td style="text-align:left;"> ▂▇▂▁▁ </td>
   <td style="text-align:right;"> 0.02 </td>
   <td style="text-align:right;"> 0.35 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 0.80 </td>
   <td style="text-align:right;"> 1.66 </td>
  </tr>
</tbody>
</table>

]

---

# Dimensionality

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

```r
model_measurement <- "
Ex =~ W_EX1+W_EX2+W_EX3+W_EX4+W_EX5+W_EX6+W_EX7+W_EX8
MD =~ W_MD1+W_MD2+W_MD3+W_MD4+W_MD5
CI =~ W_CC1+W_CC2+W_CC3+W_CC4+W_CC5
EI =~ W_EC1+W_EC2+W_EC3+W_EC4+W_EC5
PD =~ W_PD2+W_PD3+W_PD4+W_PD5+W_PD6
PC =~ W_PC1+W_PC2+W_PC3+W_PC4+W_PC5

Core =~ Ex+ MD + CI + EI
Sec =~ PD+ PC
"

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

---

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

.scroll-box-26[
<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>
   <th style="text-align:left;"> Psychological Distress </th>
   <th style="text-align:left;"> Psychosomatic Complaints </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> W_EX1 </td>
   <td style="text-align:left;"> 0.825 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </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;"> W_EX2 </td>
   <td style="text-align:left;"> 0.632 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </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;"> W_EX3 </td>
   <td style="text-align:left;"> 0.842 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </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;"> W_EX4 </td>
   <td style="text-align:left;"> 0.817 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </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;"> W_EX5 </td>
   <td style="text-align:left;"> 0.854 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </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;"> W_EX6 </td>
   <td style="text-align:left;"> 0.859 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </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;"> W_EX7 </td>
   <td style="text-align:left;"> 0.866 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </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;"> W_EX8 </td>
   <td style="text-align:left;"> 0.852 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </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;"> W_MD1 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.882 </td>
   <td style="text-align:left;">  </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;"> W_MD2 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.741 </td>
   <td style="text-align:left;">  </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;"> W_MD3 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.880 </td>
   <td style="text-align:left;">  </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;"> W_MD4 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.846 </td>
   <td style="text-align:left;">  </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;"> W_MD5 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.706 </td>
   <td style="text-align:left;">  </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;"> W_CC1 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.894 </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;"> W_CC2 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.649 </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;"> W_CC3 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.737 </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;"> W_CC4 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.883 </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;"> W_CC5 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.787 </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;"> W_EC1 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.733 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_EC2 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.877 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_EC3 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.731 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_EC4 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.933 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_EC5 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.742 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_PD2 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.658 </td>
   <td style="text-align:left;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_PD3 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.774 </td>
   <td style="text-align:left;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_PD4 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.937 </td>
   <td style="text-align:left;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_PD5 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.813 </td>
   <td style="text-align:left;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_PD6 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.636 </td>
   <td style="text-align:left;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_PC1 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.801 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_PC2 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.684 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_PC3 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.666 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_PC4 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.687 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_PC5 </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.661 </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;"> Core </th>
   <th style="text-align:left;"> Secondary </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Exhaustion </td>
   <td style="text-align:left;"> 0.866 </td>
   <td style="text-align:left;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Mental Distance </td>
   <td style="text-align:left;"> 0.866 </td>
   <td style="text-align:left;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Cognitive Impairment </td>
   <td style="text-align:left;"> 0.795 </td>
   <td style="text-align:left;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Emotional Impairment </td>
   <td style="text-align:left;"> 0.807 </td>
   <td style="text-align:left;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Psychological Distress </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.983 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Psychosomatic Complaints </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> 0.867 </td>
  </tr>
</tbody>
</table>

---

# Goodness-of-fit

The model presented the following goodness-of-fit indices `\((\chi^2_{scaled (488)}=3,233.96;p< .001;CFI_{scaled}=0.92;TLI_{scaled}=0.92;NFI_{scaled}=0.91;SRMR=0.06;RMSEA_{scaled}=0.08;p_{(rmsea \leq 0.05)}< .001; 90\%CI[0.08, 0.08])\)`

---

# Diagram

The diagram showing the standardized estimates.

<div class="grViz html-widget html-fill-item" id="htmlwidget-d47ec233273445ec3022" style="width:100%;height:432px;"></div>
<script type="application/json" data-for="htmlwidget-d47ec233273445ec3022">{"x":{"diagram":" digraph plot { \n graph [ layout = dot, rankdir = LR ] \n node [ shape = box, fontname = Helvetica ] \n node [shape = box] \n W_EX1; W_EX2; W_EX3; W_EX4; W_EX5; W_EX6; W_EX7; W_EX8; W_MD1; W_MD2; W_MD3; W_MD4; W_MD5; W_CC1; W_CC2; W_CC3; W_CC4; W_CC5; W_EC1; W_EC2; W_EC3; W_EC4; W_EC5; W_PD2; W_PD3; W_PD4; W_PD5; W_PD6; W_PC1; W_PC2; W_PC3; W_PC4; W_PC5 \n node [shape = oval] \n Ex; MD; CI; EI; PD; PC; Core; Sec \n \n edge [ color = grey ] \n  Ex->W_EX1 [label = \"0.82***\"] Ex->W_EX2 [label = \"0.63***\"] Ex->W_EX3 [label = \"0.84***\"] Ex->W_EX4 [label = \"0.82***\"] Ex->W_EX5 [label = \"0.85***\"] Ex->W_EX6 [label = \"0.86***\"] Ex->W_EX7 [label = \"0.87***\"] Ex->W_EX8 [label = \"0.85***\"] MD->W_MD1 [label = \"0.88***\"] MD->W_MD2 [label = \"0.74***\"] MD->W_MD3 [label = \"0.88***\"] MD->W_MD4 [label = \"0.85***\"] MD->W_MD5 [label = \"0.71***\"] CI->W_CC1 [label = \"0.89***\"] CI->W_CC2 [label = \"0.65***\"] CI->W_CC3 [label = \"0.74***\"] CI->W_CC4 [label = \"0.88***\"] CI->W_CC5 [label = \"0.79***\"] EI->W_EC1 [label = \"0.73***\"] EI->W_EC2 [label = \"0.88***\"] EI->W_EC3 [label = \"0.73***\"] EI->W_EC4 [label = \"0.93***\"] EI->W_EC5 [label = \"0.74***\"] PD->W_PD2 [label = \"0.66***\"] PD->W_PD3 [label = \"0.77***\"] PD->W_PD4 [label = \"0.94***\"] PD->W_PD5 [label = \"0.81***\"] PD->W_PD6 [label = \"0.64***\"] PC->W_PC1 [label = \"0.8***\"] PC->W_PC2 [label = \"0.68***\"] PC->W_PC3 [label = \"0.67***\"] PC->W_PC4 [label = \"0.69***\"] PC->W_PC5 [label = \"0.66***\"] Core->Ex [label = \"0.87***\"] Core->MD [label = \"0.87***\"] Core->CI [label = \"0.79***\"] Core->EI [label = \"0.81***\"] Sec->PD [label = \"0.98***\"] Sec->PC [label = \"0.87***\"] Sec -> Core [label = \"0.76***\", 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

<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;"> W_EX1 </td>
   <td style="text-align:right;"> 0.924 </td>
   <td style="text-align:right;"> 0.922 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_EX2 </td>
   <td style="text-align:right;"> 1.339 </td>
   <td style="text-align:right;"> 1.330 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_EX3 </td>
   <td style="text-align:right;"> 0.871 </td>
   <td style="text-align:right;"> 0.866 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_EX4 </td>
   <td style="text-align:right;"> 0.901 </td>
   <td style="text-align:right;"> 0.907 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_EX5 </td>
   <td style="text-align:right;"> 0.982 </td>
   <td style="text-align:right;"> 0.942 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_EX6 </td>
   <td style="text-align:right;"> 0.972 </td>
   <td style="text-align:right;"> 0.964 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_EX7 </td>
   <td style="text-align:right;"> 0.847 </td>
   <td style="text-align:right;"> 0.855 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_EX8 </td>
   <td style="text-align:right;"> 0.865 </td>
   <td style="text-align:right;"> 0.872 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_MD1 </td>
   <td style="text-align:right;"> 1.023 </td>
   <td style="text-align:right;"> 1.001 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_MD2 </td>
   <td style="text-align:right;"> 1.166 </td>
   <td style="text-align:right;"> 1.169 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_MD3 </td>
   <td style="text-align:right;"> 1.004 </td>
   <td style="text-align:right;"> 0.860 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_MD4 </td>
   <td style="text-align:right;"> 0.769 </td>
   <td style="text-align:right;"> 0.874 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_MD5 </td>
   <td style="text-align:right;"> 1.289 </td>
   <td style="text-align:right;"> 1.225 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_CC1 </td>
   <td style="text-align:right;"> 0.807 </td>
   <td style="text-align:right;"> 0.810 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_CC2 </td>
   <td style="text-align:right;"> 1.392 </td>
   <td style="text-align:right;"> 1.339 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_CC3 </td>
   <td style="text-align:right;"> 0.962 </td>
   <td style="text-align:right;"> 0.967 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_CC4 </td>
   <td style="text-align:right;"> 0.768 </td>
   <td style="text-align:right;"> 0.768 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_CC5 </td>
   <td style="text-align:right;"> 0.924 </td>
   <td style="text-align:right;"> 0.940 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_EC1 </td>
   <td style="text-align:right;"> 1.144 </td>
   <td style="text-align:right;"> 1.114 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_EC2 </td>
   <td style="text-align:right;"> 0.829 </td>
   <td style="text-align:right;"> 0.847 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_EC3 </td>
   <td style="text-align:right;"> 1.061 </td>
   <td style="text-align:right;"> 1.055 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_EC4 </td>
   <td style="text-align:right;"> 0.846 </td>
   <td style="text-align:right;"> 0.881 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_EC5 </td>
   <td style="text-align:right;"> 0.989 </td>
   <td style="text-align:right;"> 0.972 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_PD2 </td>
   <td style="text-align:right;"> 1.154 </td>
   <td style="text-align:right;"> 1.148 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_PD3 </td>
   <td style="text-align:right;"> 0.905 </td>
   <td style="text-align:right;"> 0.908 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_PD4 </td>
   <td style="text-align:right;"> 0.713 </td>
   <td style="text-align:right;"> 0.715 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_PD5 </td>
   <td style="text-align:right;"> 0.850 </td>
   <td style="text-align:right;"> 0.874 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_PD6 </td>
   <td style="text-align:right;"> 1.280 </td>
   <td style="text-align:right;"> 1.221 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_PC1 </td>
   <td style="text-align:right;"> 0.880 </td>
   <td style="text-align:right;"> 0.907 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_PC2 </td>
   <td style="text-align:right;"> 1.262 </td>
   <td style="text-align:right;"> 1.114 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_PC3 </td>
   <td style="text-align:right;"> 1.049 </td>
   <td style="text-align:right;"> 1.051 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_PC4 </td>
   <td style="text-align:right;"> 1.065 </td>
   <td style="text-align:right;"> 1.063 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> W_PC5 </td>
   <td style="text-align:right;"> 0.990 </td>
   <td style="text-align:right;"> 1.017 </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;"> 0.995 </td>
   <td style="text-align:right;"> 0.176 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Infit </td>
   <td style="text-align:right;"> 0.985 </td>
   <td style="text-align:right;"> 0.154 </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>
   <th style="text-align:right;"> Psychological Distress </th>
   <th style="text-align:right;"> Psychosomatic Complaints </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> \(\alpha_{ord}\) </td>
   <td style="text-align:right;"> 0.94 </td>
   <td style="text-align:right;"> 0.90 </td>
   <td style="text-align:right;"> 0.89 </td>
   <td style="text-align:right;"> 0.90 </td>
   <td style="text-align:right;"> 0.86 </td>
   <td style="text-align:right;"> 0.83 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> \(\omega_{ord}\) </td>
   <td style="text-align:right;"> 0.92 </td>
   <td style="text-align:right;"> 0.88 </td>
   <td style="text-align:right;"> 0.86 </td>
   <td style="text-align:right;"> 0.87 </td>
   <td style="text-align:right;"> 0.84 </td>
   <td style="text-align:right;"> 0.79 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> \(AVE\) </td>
   <td style="text-align:right;"> 0.68 </td>
   <td style="text-align:right;"> 0.66 </td>
   <td style="text-align:right;"> 0.63 </td>
   <td style="text-align:right;"> 0.65 </td>
   <td style="text-align:right;"> 0.60 </td>
   <td style="text-align:right;"> 0.49 </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;"> Core </td>
   <td style="text-align:right;"> 0.88 </td>
   <td style="text-align:right;"> 0.9 </td>
   <td style="text-align:right;"> 0.97 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Secondary </td>
   <td style="text-align:right;"> 0.88 </td>
   <td style="text-align:right;"> 0.9 </td>
   <td style="text-align:right;"> 0.97 </td>
  </tr>
</tbody>
</table>

---

# .white[Measurement Invariance]  
<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>

---

# Longitudinal Measurement Invariance

<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;"> 272.758 </td>
   <td style="text-align:right;"> 100 </td>
   <td style="text-align:left;"> - </td>
   <td style="text-align:left;"> 0.982 </td>
   <td style="text-align:left;"> - </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Thresholds </td>
   <td style="text-align:left;"> 283.431 </td>
   <td style="text-align:right;"> 121 </td>
   <td style="text-align:left;"> .751 </td>
   <td style="text-align:left;"> 0.983 </td>
   <td style="text-align:left;"> 0.001 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Factor loadings </td>
   <td style="text-align:left;"> 275.451 </td>
   <td style="text-align:right;"> 129 </td>
   <td style="text-align:left;"> .920 </td>
   <td style="text-align:left;"> 0.985 </td>
   <td style="text-align:left;"> 0.002 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Structural weights </td>
   <td style="text-align:left;"> 257.646 </td>
   <td style="text-align:right;"> 132 </td>
   <td style="text-align:left;"> .811 </td>
   <td style="text-align:left;"> 0.987 </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;"> 272.873 </td>
   <td style="text-align:right;"> 144 </td>
   <td style="text-align:left;"> .108 </td>
   <td style="text-align:left;"> 0.986 </td>
   <td style="text-align:left;"> 0.000 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Latent means </td>
   <td style="text-align:left;"> 247.223 </td>
   <td style="text-align:right;"> 148 </td>
   <td style="text-align:left;"> .403 </td>
   <td style="text-align:left;"> 0.990 </td>
   <td style="text-align:left;"> 0.003 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Disturbances </td>
   <td style="text-align:left;"> 331.068 </td>
   <td style="text-align:right;"> 153 </td>
   <td style="text-align:left;"> &lt; .001 </td>
   <td style="text-align:left;"> 0.981 </td>
   <td style="text-align:left;"> -0.008 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Residuals </td>
   <td style="text-align:left;"> 369.780 </td>
   <td style="text-align:right;"> 163 </td>
   <td style="text-align:left;"> &lt; .001 </td>
   <td style="text-align:left;"> 0.978 </td>
   <td style="text-align:left;"> -0.003 </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 (wave 1) Measurement Invariance

<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;"> 243.121 </td>
   <td style="text-align:right;"> 100 </td>
   <td style="text-align:left;"> - </td>
   <td style="text-align:left;"> 0.982 </td>
   <td style="text-align:left;"> - </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Thresholds </td>
   <td style="text-align:left;"> 268.723 </td>
   <td style="text-align:right;"> 120 </td>
   <td style="text-align:left;"> .049 </td>
   <td style="text-align:left;"> 0.981 </td>
   <td style="text-align:left;"> -0.001 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Factor loadings </td>
   <td style="text-align:left;"> 272.621 </td>
   <td style="text-align:right;"> 128 </td>
   <td style="text-align:left;"> .282 </td>
   <td style="text-align:left;"> 0.981 </td>
   <td style="text-align:left;"> 0.001 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Structural weights </td>
   <td style="text-align:left;"> 258.889 </td>
   <td style="text-align:right;"> 131 </td>
   <td style="text-align:left;"> .612 </td>
   <td style="text-align:left;"> 0.984 </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;"> 276.824 </td>
   <td style="text-align:right;"> 143 </td>
   <td style="text-align:left;"> .026 </td>
   <td style="text-align:left;"> 0.983 </td>
   <td style="text-align:left;"> -0.001 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Latent means </td>
   <td style="text-align:left;"> 269.352 </td>
   <td style="text-align:right;"> 147 </td>
   <td style="text-align:left;"> .042 </td>
   <td style="text-align:left;"> 0.984 </td>
   <td style="text-align:left;"> 0.001 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Disturbances </td>
   <td style="text-align:left;"> 372.188 </td>
   <td style="text-align:right;"> 151 </td>
   <td style="text-align:left;"> &lt; .001 </td>
   <td style="text-align:left;"> 0.972 </td>
   <td style="text-align:left;"> -0.013 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Residuals </td>
   <td style="text-align:left;"> 372.949 </td>
   <td style="text-align:right;"> 163 </td>
   <td style="text-align:left;"> .036 </td>
   <td style="text-align:left;"> 0.973 </td>
   <td style="text-align:left;"> 0.001 </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>

---

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

---

# Sex Measurement Invariance

<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;"> 3,042.528 </td>
   <td style="text-align:right;"> 977 </td>
   <td style="text-align:left;"> - </td>
   <td style="text-align:left;"> 0.938 </td>
   <td style="text-align:left;"> - </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Thresholds </td>
   <td style="text-align:left;"> 3,063.867 </td>
   <td style="text-align:right;"> 1037 </td>
   <td style="text-align:left;"> .174 </td>
   <td style="text-align:left;"> 0.940 </td>
   <td style="text-align:left;"> 0.001 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Factor loadings </td>
   <td style="text-align:left;"> 2,991.656 </td>
   <td style="text-align:right;"> 1064 </td>
   <td style="text-align:left;"> .715 </td>
   <td style="text-align:left;"> 0.943 </td>
   <td style="text-align:left;"> 0.003 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Structural weights </td>
   <td style="text-align:left;"> 2,936.027 </td>
   <td style="text-align:right;"> 1068 </td>
   <td style="text-align:left;"> .080 </td>
   <td style="text-align:left;"> 0.944 </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;"> 2,990.975 </td>
   <td style="text-align:right;"> 1101 </td>
   <td style="text-align:left;"> &lt; .001 </td>
   <td style="text-align:left;"> 0.944 </td>
   <td style="text-align:left;"> -0.001 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Latent means </td>
   <td style="text-align:left;"> 2,887.937 </td>
   <td style="text-align:right;"> 1107 </td>
   <td style="text-align:left;"> &lt; .001 </td>
   <td style="text-align:left;"> 0.947 </td>
   <td style="text-align:left;"> 0.003 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Disturbances </td>
   <td style="text-align:left;"> 3,363.290 </td>
   <td style="text-align:right;"> 1112 </td>
   <td style="text-align:left;"> &lt; .001 </td>
   <td style="text-align:left;"> 0.933 </td>
   <td style="text-align:left;"> -0.014 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Residuals </td>
   <td style="text-align:left;"> 2,931.484 </td>
   <td style="text-align:right;"> 1145 </td>
   <td style="text-align:left;"> &lt; .001 </td>
   <td style="text-align:left;"> 0.947 </td>
   <td style="text-align:left;"> 0.014 </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 `\((\chi^2_{scaled (2592)}=4,290.12;p< .001; CFI_{scaled}=0.925;\)` `\(TLI_{scaled}=0.922;NFI_{scaled}=0.831; SRMR=0.074;RMSEA_{scaled}=0.045;p_{(rmsea \leq 0.05)}> .999;\)` `\(90\%CI[0.043, 0.048])\)`.

<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;"> -.77 </td>
   <td style="text-align:right;"> -.71 </td>
   <td style="text-align:right;"> -.77 </td>
   <td style="text-align:right;"> .86 </td>
   <td style="text-align:right;"> -.57 </td>
   <td style="text-align:left;"> .68 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Academic Engagement (2) </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;"> .69 </td>
   <td style="text-align:right;"> .62 </td>
   <td style="text-align:right;"> -.43 </td>
   <td style="text-align:right;"> .53 </td>
   <td style="text-align:left;"> -.55 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Satisfaction with Education (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;"> .65 </td>
   <td style="text-align:right;"> -.41 </td>
   <td style="text-align:right;"> .45 </td>
   <td style="text-align:left;"> -.61 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Psychological Capital (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;"> -.72 </td>
   <td style="text-align:right;"> .48 </td>
   <td style="text-align:left;"> -.62 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> General Distress (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;"> -.52 </td>
   <td style="text-align:left;"> .51 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Social 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;"> -.39 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Dropout Intention (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;"> B </th>
   <th style="text-align:right;"> E </th>
   <th style="text-align:right;"> C </th>
   <th style="text-align:right;"> Satedu </th>
   <th style="text-align:right;"> H </th>
   <th style="text-align:right;"> R </th>
   <th style="text-align:right;"> O </th>
   <th style="text-align:right;"> D </th>
   <th style="text-align:right;"> A </th>
   <th style="text-align:right;"> S </th>
   <th style="text-align:right;"> Socsup </th>
   <th style="text-align:right;"> Dropint </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> \(\omega_{ord}\) </td>
   <td style="text-align:right;"> 0.78 </td>
   <td style="text-align:right;"> 0.79 </td>
   <td style="text-align:right;"> 0.81 </td>
   <td style="text-align:right;"> 0.9 </td>
   <td style="text-align:right;"> 0.73 </td>
   <td style="text-align:right;"> 0.8 </td>
   <td style="text-align:right;"> 0.78 </td>
   <td style="text-align:right;"> 0.79 </td>
   <td style="text-align:right;"> 0.77 </td>
   <td style="text-align:right;"> 0.77 </td>
   <td style="text-align:right;"> 0.83 </td>
   <td style="text-align:right;"> 0.9 </td>
   <td style="text-align:right;"> 0.88 </td>
   <td style="text-align:right;"> 0.88 </td>
   <td style="text-align:right;"> 0.85 </td>
   <td style="text-align:right;"> 0.91 </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;"> 0.82 </td>
   <td style="text-align:right;"> 0.87 </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>

---

# Latent Correlations

The model presented the following goodness-of-fit indices `\((\chi^2_{scaled (1059)}=2,383.17;p< .001; CFI_{scaled}=0.954;\)` `\(TLI_{scaled}=0.951;NFI_{scaled}=0.920; SRMR=0.064;RMSEA_{scaled}=0.061; p_{(rmsea \leq 0.05)}< .001;\)` `\(90\%CI[0.058, 0.064])\)`.

<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>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Core (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>
  </tr>
  <tr>
   <td style="text-align:left;"> Secondary (2) </td>
   <td style="text-align:right;"> .80 </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>
  </tr>
  <tr>
   <td style="text-align:left;"> Colleagues Incivility (3) </td>
   <td style="text-align:right;"> .47 </td>
   <td style="text-align:right;"> .32 </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>
  </tr>
  <tr>
   <td style="text-align:left;"> Clients Incivility (4) </td>
   <td style="text-align:right;"> .47 </td>
   <td style="text-align:right;"> .41 </td>
   <td style="text-align:right;"> .35 </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Negative Change (5) </td>
   <td style="text-align:right;"> -.52 </td>
   <td style="text-align:right;"> -.34 </td>
   <td style="text-align:right;"> -.39 </td>
   <td style="text-align:right;"> -.32 </td>
   <td style="text-align:right;">  </td>
   <td style="text-align:right;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Bureaucracy (6) </td>
   <td style="text-align:right;"> .58 </td>
   <td style="text-align:right;"> .39 </td>
   <td style="text-align:right;"> .39 </td>
   <td style="text-align:right;"> .34 </td>
   <td style="text-align:right;"> -.59 </td>
   <td style="text-align:right;">  </td>
  </tr>
</tbody>
</table>

---

# Reliability

## First-order

The model's first-order internal consistency estimates are presented in the following 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;"> Core </td>
   <td style="text-align:right;"> 0.90 </td>
   <td style="text-align:right;"> 0.93 </td>
   <td style="text-align:right;"> 0.98 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Secondary </td>
   <td style="text-align:right;"> 0.89 </td>
   <td style="text-align:right;"> 0.94 </td>
   <td style="text-align:right;"> 0.94 </td>
  </tr>
</tbody>
</table>

---

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

---

# Discussion

## BAT-12 Student's Version

Original dimensionality ✅  
Internal consistency `\((\omega_i \geq .78)\)` ✅  
Measurement invariance across sex and longitudinal measurements ✅

Strong negative latent correlations with academic engagement, satisfaction with education, psychological capital, and social support while revealing strong positive latent correlations with psychological distress and dropout intention. ✅

---

# Discussion

## BAT-S Workers's Version

Original dimensionality ✅  
Items' mean square fit statistics `\((M_{infit} = 0.99; SD_{infit} = 0.18; M_{outfit} = 0.98; SD_{outfit} = 0.15)\)` ✅  
Internal consistency `\((\omega_i \geq .79)\)` ✅  
Measurement invariance across sex ✅

Core symptoms exhibited moderate/strong correlations with colleagues’ incivility, clients’ incivility, negative change, and bureaucracy, while the secondary symptoms presented weaker correlations with the same variables. ✅

---

# Conclusion

Once again BAT presents good psychometric properties.

The samples are not representative of either the Portuguese population of workers or university students.

---

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---

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---

# Questions/comments

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