class: center, middle, inverse, title-slide .title[ # Career Adaptability in the Singaporean Sociocultural Context ] .subtitle[ ## Validity Evidence from a Longitudinal Sample of University Students ] .author[ ### Jorge Sinval, & Minglee Yong ] .date[ ### 2023-11-22 ] --- class: inverse, center, middle # Introduction <html><div style='float:left'></div><hr color='#EB811B' size=1px width=800px></html> <style> .orange { color: #EB811B; } .green { color: #00FF00; } .kbd { display: inline-block; padding: .2em .5em; font-size: 0.75em; line-height: 1.75; color: #555; vertical-align: middle; background-color: #fcfcfc; border: solid 1px #ccc; border-bottom-color: #bbb; border-radius: 3px; box-shadow: inset 0 -1px 0 #bbb } </style> <style>.xe__progress-bar__container { bottom:0; opacity: 1; position:absolute; right:0; left: 0; } .xe__progress-bar { height: 0.25em; background-color: green; width: calc(var(--slide-current) / var(--slide-total) * 100%); } .remark-visible .xe__progress-bar { animation: xe__progress-bar__wipe 200ms forwards; animation-timing-function: cubic-bezier(.86,0,.07,1); } @keyframes xe__progress-bar__wipe { 0% { width: calc(var(--slide-previous) / var(--slide-total) * 100%); } 100% { width: calc(var(--slide-current) / var(--slide-total) * 100%); } }</style><div> <style type="text/css">.xaringan-extra-logo { width: 225px; height: 128px; z-index: 0; background-image: url(assets/img/nie-logo.png); background-size: contain; background-repeat: no-repeat; position: absolute; top:0.1em;right:0.1em; } </style> <script>(function () { let tries = 0 function addLogo () { if (typeof slideshow === 'undefined') { tries += 1 if (tries < 10) { setTimeout(addLogo, 100) } } else { document.querySelectorAll('.remark-slide-content:not(.title-slide):not(.inverse):not(.hide_logo)') .forEach(function (slide) { const logo = document.createElement('div') logo.classList = 'xaringan-extra-logo' logo.href = null slide.appendChild(logo) }) } } document.addEventListener('DOMContentLoaded', addLogo) })()</script> </div><style>.panelset{--panel-tab-active-foreground: #1A292C;--panel-tab-hover-foreground: #d22;}</style><style> .search { --search-icon-fill: black; --search-input-background: rgb(204, 204, 204); --search-input-foreground: black; --search-input-border: 1px solid rgb(249, 38, 114); --search-match-background: blue; --search-match-foreground: black; --search-match-current-background: green; --search-match-current-foreground: black; }</style> --- # Introduction: Career Adaptability Career adaptability (CA) is a key construct in the life design paradigm. -- Career adaptability is defined as the ability to cope with diverse job requirements, and to change jobs in line with the individual’s constraints and needs. --- # Introduction: CAAS-SF Career Adapt-Abilities Scale — Short-Form (CAAS-SF) is a 12-item self-report measure of career adaptability (Maggiori, Rossier, and Savickas, 2017). -- The CAAS-SF has four first-order dimensions (_concern_, _control_, _curiosity_, and _confidence_) nested under a second-order dimension, _career adaptability_. --- # Introduction: Goal Assess the psychometric properties of the CAAS-SF with a longitudinal sample of Singaporean undergraduate students. -- Explore how career adaptability could be associated with the sociocultural variables of the fear of losing out and group conformity. --- # Method ## Sampling Undergraduate students aged 17 to 29 years and enrolled full-time at a Singaporean public university across 17 faculties/institutes were invited to participate in the study. ## Procedure Participants were invited via institutional emails to complete an online Qualtrics survey containing sociodemographic, academic questions, and psychometric instruments, and received a reimbursement of S$10, with data sourced from an ethically approved project (IRB-2022-591). --- # Method ## Psychometric instruments Career adaptability (CAAS-SF) (Maggiori Rossier et al., 2017). Fear of Losing Out (FoLO-4) (Wee, Cheng, Choi, and Goh, 2022). Conformity Scale (Mehrabian and Stefl, 1995). Multidimensional Scale of Perceived Social Support — Revised (MSPSS) (Zimet, Dahlem, Zimet, and Farley, 1988). Life Orientation Test — Revised (LOT) (Scheier, Carver, and Bridges, 1994). ## Data Analysis Software: _R_ and _RStudio_ (R Core Team, 2023; Posit Team, 2023) Descriptive statistics CFA Reliability `\((\alpha; \omega; AVE)\)` Measurement invariance (MGCFA) Multidimensional polytomous Rasch model (Briggs and Wilson, 2003) as a specific application of the multidimensional random coefficients multinomial logit model (MRCMLM) (Adams, Wilson, and Wang, 1997). Full SEM --- # Results: Sample Characterization <table> <thead> <tr> <th style="text-align:left;"> </th> <th style="text-align:center;"> Female </th> <th style="text-align:center;"> Male </th> <th style="text-align:center;"> Overall </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;"> </td> <td style="text-align:center;"> (N=1330) </td> <td style="text-align:center;"> (N=1021) </td> <td style="text-align:center;"> (N=2351) </td> </tr> <tr> <td style="text-align:left;"> Age (years) </td> <td style="text-align:center;"> </td> <td style="text-align:center;"> </td> <td style="text-align:center;"> </td> </tr> <tr> <td style="text-align:left;"> Mean (SD) </td> <td style="text-align:center;"> 21.3 (1.51) </td> <td style="text-align:center;"> 22.8 (1.86) </td> <td style="text-align:center;"> 22.0 (1.82) </td> </tr> <tr> <td style="text-align:left;"> Median [Min, Max] </td> <td style="text-align:center;"> 21.3 [18.3, 29.3] </td> <td style="text-align:center;"> 22.4 [18.3, 30.3] </td> <td style="text-align:center;"> 22.3 [18.3, 30.3] </td> </tr> <tr> <td style="text-align:left;"> Missing </td> <td style="text-align:center;"> 1 (0.1%) </td> <td style="text-align:center;"> 0 (0%) </td> <td style="text-align:center;"> 1 (0.0%) </td> </tr> <tr> <td style="text-align:left;"> Ethnicity </td> <td style="text-align:center;"> </td> <td style="text-align:center;"> </td> <td style="text-align:center;"> </td> </tr> <tr> <td style="text-align:left;"> Chinese </td> <td style="text-align:center;"> 1132 (85.1%) </td> <td style="text-align:center;"> 888 (87.0%) </td> <td style="text-align:center;"> 2020 (85.9%) </td> </tr> <tr> <td style="text-align:left;"> Indian </td> <td style="text-align:center;"> 97 (7.3%) </td> <td style="text-align:center;"> 69 (6.8%) </td> <td style="text-align:center;"> 166 (7.1%) </td> </tr> <tr> <td style="text-align:left;"> Malay </td> <td style="text-align:center;"> 44 (3.3%) </td> <td style="text-align:center;"> 24 (2.4%) </td> <td style="text-align:center;"> 68 (2.9%) </td> </tr> <tr> <td style="text-align:left;"> Others </td> <td style="text-align:center;"> 57 (4.3%) </td> <td style="text-align:center;"> 40 (3.9%) </td> <td style="text-align:center;"> 97 (4.1%) </td> </tr> </tbody> </table> --- # Results: Sample Characterization <table> <thead> <tr> <th style="text-align:left;"> </th> <th style="text-align:center;"> Female </th> <th style="text-align:center;"> Male </th> <th style="text-align:center;"> Overall </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;"> </td> <td style="text-align:center;"> (N=1330) </td> <td style="text-align:center;"> (N=1021) </td> <td style="text-align:center;"> (N=2351) </td> </tr> <tr> <td style="text-align:left;"> Year/level of study </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;"> Year 1 </td> <td style="text-align:center;"> 331 (24.9%) </td> <td style="text-align:center;"> 249 (24.4%) </td> <td style="text-align:center;"> 580 (24.7%) </td> </tr> <tr> <td style="text-align:left;"> Year 2 </td> <td style="text-align:center;"> 370 (27.8%) </td> <td style="text-align:center;"> 312 (30.6%) </td> <td style="text-align:center;"> 682 (29.0%) </td> </tr> <tr> <td style="text-align:left;"> Year 3 </td> <td style="text-align:center;"> 350 (26.3%) </td> <td style="text-align:center;"> 235 (23.0%) </td> <td style="text-align:center;"> 585 (24.9%) </td> </tr> <tr> <td style="text-align:left;"> Year 4 </td> <td style="text-align:center;"> 279 (21.0%) </td> <td style="text-align:center;"> 225 (22.0%) </td> <td style="text-align:center;"> 504 (21.4%) </td> </tr> <tr> <td style="text-align:left;"> Household income </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;"> $10,000 & above per month </td> <td style="text-align:center;"> 337 (25.3%) </td> <td style="text-align:center;"> 188 (18.4%) </td> <td style="text-align:center;"> 525 (22.3%) </td> </tr> <tr> <td style="text-align:left;"> $2,000 to $3,999 per month </td> <td style="text-align:center;"> 246 (18.5%) </td> <td style="text-align:center;"> 218 (21.4%) </td> <td style="text-align:center;"> 464 (19.7%) </td> </tr> <tr> <td style="text-align:left;"> $4,000 to $5,999 per month </td> <td style="text-align:center;"> 244 (18.3%) </td> <td style="text-align:center;"> 213 (20.9%) </td> <td style="text-align:center;"> 457 (19.4%) </td> </tr> <tr> <td style="text-align:left;"> $6,000 to $7,999 per month </td> <td style="text-align:center;"> 221 (16.6%) </td> <td style="text-align:center;"> 145 (14.2%) </td> <td style="text-align:center;"> 366 (15.6%) </td> </tr> <tr> <td style="text-align:left;"> $8,000 to $9,999 per month </td> <td style="text-align:center;"> 171 (12.9%) </td> <td style="text-align:center;"> 109 (10.7%) </td> <td style="text-align:center;"> 280 (11.9%) </td> </tr> <tr> <td style="text-align:left;"> Below $2,000 per month </td> <td style="text-align:center;"> 111 (8.3%) </td> <td style="text-align:center;"> 148 (14.5%) </td> <td style="text-align:center;"> 259 (11.0%) </td> </tr> </tbody> </table> --- # Results: Sample Characterization <table> <thead> <tr> <th style="text-align:left;"> </th> <th style="text-align:center;"> Female </th> <th style="text-align:center;"> Male </th> <th style="text-align:center;"> Overall </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;"> </td> <td style="text-align:center;"> (N=1330) </td> <td style="text-align:center;"> (N=1021) </td> <td style="text-align:center;"> (N=2351) </td> </tr> <tr> <td style="text-align:left;"> GPA last semester </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;"> 1.0 to 1.49 </td> <td style="text-align:center;"> 1 (0.1%) </td> <td style="text-align:center;"> 0 (0%) </td> <td style="text-align:center;"> 1 (0.0%) </td> </tr> <tr> <td style="text-align:left;"> 1.5 to 1.99 </td> <td style="text-align:center;"> 2 (0.2%) </td> <td style="text-align:center;"> 3 (0.3%) </td> <td style="text-align:center;"> 5 (0.2%) </td> </tr> <tr> <td style="text-align:left;"> 2.0 to 2.49 </td> <td style="text-align:center;"> 15 (1.1%) </td> <td style="text-align:center;"> 23 (2.3%) </td> <td style="text-align:center;"> 38 (1.6%) </td> </tr> <tr> <td style="text-align:left;"> 2.5 to 2.99 </td> <td style="text-align:center;"> 50 (3.8%) </td> <td style="text-align:center;"> 35 (3.4%) </td> <td style="text-align:center;"> 85 (3.6%) </td> </tr> <tr> <td style="text-align:left;"> 3.0 to 3.49 </td> <td style="text-align:center;"> 120 (9.0%) </td> <td style="text-align:center;"> 68 (6.7%) </td> <td style="text-align:center;"> 188 (8.0%) </td> </tr> <tr> <td style="text-align:left;"> 3.5 to 3.99 </td> <td style="text-align:center;"> 254 (19.1%) </td> <td style="text-align:center;"> 134 (13.1%) </td> <td style="text-align:center;"> 388 (16.5%) </td> </tr> <tr> <td style="text-align:left;"> 4.0 to 4.49 </td> <td style="text-align:center;"> 348 (26.2%) </td> <td style="text-align:center;"> 199 (19.5%) </td> <td style="text-align:center;"> 547 (23.3%) </td> </tr> <tr> <td style="text-align:left;"> 4.5 to 5.00 </td> <td style="text-align:center;"> 160 (12.0%) </td> <td style="text-align:center;"> 231 (22.6%) </td> <td style="text-align:center;"> 391 (16.6%) </td> </tr> <tr> <td style="text-align:left;"> Not Applicable (First year students) </td> <td style="text-align:center;"> 380 (28.6%) </td> <td style="text-align:center;"> 327 (32.0%) </td> <td style="text-align:center;"> 707 (30.1%) </td> </tr> <tr> <td style="text-align:left;"> 0.0 to 0.49 </td> <td style="text-align:center;"> 0 (0%) </td> <td style="text-align:center;"> 1 (0.1%) </td> <td style="text-align:center;"> 1 (0.0%) </td> </tr> </tbody> </table> --- # Results: Sample Characterization <table> <thead> <tr> <th style="text-align:left;"> </th> <th style="text-align:center;"> Female </th> <th style="text-align:center;"> Male </th> <th style="text-align:center;"> Overall </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;"> </td> <td style="text-align:center;"> (N=1330) </td> <td style="text-align:center;"> (N=1021) </td> <td style="text-align:center;"> (N=2351) </td> </tr> <tr> <td style="text-align:left;"> Cumulative GPA </td> <td style="text-align:center;"> </td> <td style="text-align:center;"> </td> <td style="text-align:center;"> </td> </tr> <tr> <td style="text-align:left;"> 1.5 to 1.99 </td> <td style="text-align:center;"> 2 (0.2%) </td> <td style="text-align:center;"> 1 (0.1%) </td> <td style="text-align:center;"> 3 (0.1%) </td> </tr> <tr> <td style="text-align:left;"> 2.0 to 2.49 </td> <td style="text-align:center;"> 16 (1.2%) </td> <td style="text-align:center;"> 11 (1.1%) </td> <td style="text-align:center;"> 27 (1.1%) </td> </tr> <tr> <td style="text-align:left;"> 2.5 to 2.99 </td> <td style="text-align:center;"> 38 (2.9%) </td> <td style="text-align:center;"> 31 (3.0%) </td> <td style="text-align:center;"> 69 (2.9%) </td> </tr> <tr> <td style="text-align:left;"> 3.0 to 3.49 </td> <td style="text-align:center;"> 143 (10.8%) </td> <td style="text-align:center;"> 80 (7.8%) </td> <td style="text-align:center;"> 223 (9.5%) </td> </tr> <tr> <td style="text-align:left;"> 3.5 to 3.99 </td> <td style="text-align:center;"> 290 (21.8%) </td> <td style="text-align:center;"> 134 (13.1%) </td> <td style="text-align:center;"> 424 (18.0%) </td> </tr> <tr> <td style="text-align:left;"> 4.0 to 4.49 </td> <td style="text-align:center;"> 350 (26.3%) </td> <td style="text-align:center;"> 234 (22.9%) </td> <td style="text-align:center;"> 584 (24.8%) </td> </tr> <tr> <td style="text-align:left;"> 4.5 to 5.00 </td> <td style="text-align:center;"> 112 (8.4%) </td> <td style="text-align:center;"> 202 (19.8%) </td> <td style="text-align:center;"> 314 (13.4%) </td> </tr> <tr> <td style="text-align:left;"> Not Applicable (First year students) </td> <td style="text-align:center;"> 379 (28.5%) </td> <td style="text-align:center;"> 326 (31.9%) </td> <td style="text-align:center;"> 705 (30.0%) </td> </tr> <tr> <td style="text-align:left;"> 0.0 to 0.49 </td> <td style="text-align:center;"> 0 (0%) </td> <td style="text-align:center;"> 2 (0.2%) </td> <td style="text-align:center;"> 2 (0.1%) </td> </tr> </tbody> </table> --- class: inverse, center, middle # Valdity Evidence <html><div style='float:left'></div><hr color='#EB811B' size=1px width=800px></html> --- name: validitysources1 # Evidence Sources ## Five major sources of test validity: Evidence based on Messick and AERA, APA & NCME **Content** — relationship between test content and the construct of interest; theory; hypothesis about content; independent assessment of match between content sampled and domain of interest; solid, scientific, quantitative evidence. **Response Process** — analysis of individual responses to stimuli; debriefing of examinees; process studies aimed at understanding what is measured and the soundness of intended score interpretations; quality assurance and quality control of assessment data. **Internal Structure** — data internal to assessments such as: reliability or reproducibility of scores; inter-item correlations; statistical characteristics of items; statistical analysis of item option function; factor studies of dimensionality; Differential Item Functioning (DIF) studies. --- name: validitysources2 # Evidence Sources ## Five major sources of test validity: Evidence based on Messick and AERA, APA & NCME **Relations to Other Variables** — data external to assessments such as: correlations of assessment variable(s) to external, independent measures; hypothesis and theory driven investigations; correlational research based on previous studies, literature: a. Convergent and discriminant evidence: relationships between similar and different measures b. Test-criterion evidence: relationships between test and criterion measure(s) c. Validity generalization: can the validity evidence be generalized? Evidence that the validity studies may generalize to other settings. **Evidence Based on Consequences of Testing** — intended and unintended consequences of test use; differential consequences of test use; impact of assessment on participants, organizations, society. --- class: inverse, center, middle # Validity Evidence Based on the Internal Structure <html><div style='float:left'></div><hr color='#EB811B' size=1px width=800px></html> --- # Items' distributional properties The distributional properties of the model's indicators are presented in the following table. Various summary measures, a histogram, kurtosis `\((ku)\)`, and skewness `\((sk)\)` for each of items are presented. The psychometric sensitivity and distributional properties of the items were analyzed with this information. Values of `\(|Ku|<7\)` and `\(|Sk|<3\)` were indicative of absense of severe violations of the univariate normality that would recommend against the use of structural equation modeling (Finney and DiStefano, 2013). --- # Items' distributional properties .font80[ <table class="table" style="margin-left: auto; margin-right: auto;"> <caption>Descriptives with histogram (\(n_{wave~1}=2364\))</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;"> 13 </td> <td style="text-align:right;"> 2.78 </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;"> 0.02 </td> <td style="text-align:right;"> 0.40 </td> <td style="text-align:right;"> 2 </td> <td style="text-align:right;"> 0.24 </td> <td style="text-align:right;"> -0.68 </td> </tr> <tr> <td style="text-align:left;"> Item 2 </td> <td style="text-align:right;"> 13 </td> <td style="text-align:right;"> 2.50 </td> <td style="text-align:right;"> 1.05 </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;"> 0.02 </td> <td style="text-align:right;"> 0.42 </td> <td style="text-align:right;"> 2 </td> <td style="text-align:right;"> 0.45 </td> <td style="text-align:right;"> -0.45 </td> </tr> <tr> <td style="text-align:left;"> Item 3 </td> <td style="text-align:right;"> 13 </td> <td style="text-align:right;"> 2.94 </td> <td style="text-align:right;"> 1.05 </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;"> 0.02 </td> <td style="text-align:right;"> 0.36 </td> <td style="text-align:right;"> 3 </td> <td style="text-align:right;"> 0.07 </td> <td style="text-align:right;"> -0.65 </td> </tr> <tr> <td style="text-align:left;"> Item 4 </td> <td style="text-align:right;"> 13 </td> <td style="text-align:right;"> 3.19 </td> <td style="text-align:right;"> 1.07 </td> <td style="text-align:right;"> 1 </td> <td style="text-align:right;"> 2 </td> <td style="text-align:right;"> 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;"> 0.02 </td> <td style="text-align:right;"> 0.33 </td> <td style="text-align:right;"> 3 </td> <td style="text-align:right;"> -0.01 </td> <td style="text-align:right;"> -0.68 </td> </tr> <tr> <td style="text-align:left;"> Item 5 </td> <td style="text-align:right;"> 13 </td> <td style="text-align:right;"> 3.52 </td> <td style="text-align:right;"> 0.96 </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;"> 0.02 </td> <td style="text-align:right;"> 0.27 </td> <td style="text-align:right;"> 4 </td> <td style="text-align:right;"> -0.16 </td> <td style="text-align:right;"> -0.56 </td> </tr> <tr> <td style="text-align:left;"> Item 6 </td> <td style="text-align:right;"> 13 </td> <td style="text-align:right;"> 3.46 </td> <td style="text-align:right;"> 1.07 </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;"> 0.02 </td> <td style="text-align:right;"> 0.31 </td> <td style="text-align:right;"> 4 </td> <td style="text-align:right;"> -0.29 </td> <td style="text-align:right;"> -0.57 </td> </tr> <tr> <td style="text-align:left;"> Item 7 </td> <td style="text-align:right;"> 13 </td> <td style="text-align:right;"> 3.18 </td> <td style="text-align:right;"> 1.09 </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;"> 0.02 </td> <td style="text-align:right;"> 0.34 </td> <td style="text-align:right;"> 3 </td> <td style="text-align:right;"> -0.02 </td> <td style="text-align:right;"> -0.79 </td> </tr> <tr> <td style="text-align:left;"> Item 8 </td> <td style="text-align:right;"> 13 </td> <td style="text-align:right;"> 3.31 </td> <td style="text-align:right;"> 1.01 </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;"> 0.02 </td> <td style="text-align:right;"> 0.31 </td> <td style="text-align:right;"> 3 </td> <td style="text-align:right;"> -0.15 </td> <td style="text-align:right;"> -0.56 </td> </tr> <tr> <td style="text-align:left;"> Item 9 </td> <td style="text-align:right;"> 13 </td> <td style="text-align:right;"> 3.28 </td> <td style="text-align:right;"> 0.99 </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;"> 0.02 </td> <td style="text-align:right;"> 0.30 </td> <td style="text-align:right;"> 3 </td> <td style="text-align:right;"> -0.04 </td> <td style="text-align:right;"> -0.59 </td> </tr> <tr> <td style="text-align:left;"> Item 10 </td> <td style="text-align:right;"> 13 </td> <td style="text-align:right;"> 3.32 </td> <td style="text-align:right;"> 0.98 </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;"> 0.02 </td> <td style="text-align:right;"> 0.29 </td> <td style="text-align:right;"> 3 </td> <td style="text-align:right;"> -0.13 </td> <td style="text-align:right;"> -0.54 </td> </tr> <tr> <td style="text-align:left;"> Item 11 </td> <td style="text-align:right;"> 13 </td> <td style="text-align:right;"> 3.10 </td> <td style="text-align:right;"> 1.03 </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;"> 0.02 </td> <td style="text-align:right;"> 0.33 </td> <td style="text-align:right;"> 3 </td> <td style="text-align:right;"> 0.06 </td> <td style="text-align:right;"> -0.63 </td> </tr> <tr> <td style="text-align:left;"> Item 12 </td> <td style="text-align:right;"> 13 </td> <td style="text-align:right;"> 3.10 </td> <td style="text-align:right;"> 1.03 </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;"> 0.02 </td> <td style="text-align:right;"> 0.33 </td> <td style="text-align:right;"> 3 </td> <td style="text-align:right;"> 0.02 </td> <td style="text-align:right;"> -0.59 </td> </tr> </tbody> </table> ] --- # Items' distributional properties .font80[ <table class="table" style="margin-left: auto; margin-right: auto;"> <caption>Descriptives with histogram (\(n_{wave~2}=1943\))</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;"> 64 </td> <td style="text-align:right;"> 2.88 </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;"> 0.03 </td> <td style="text-align:right;"> 0.38 </td> <td style="text-align:right;"> 2 </td> <td style="text-align:right;"> 0.16 </td> <td style="text-align:right;"> -0.78 </td> </tr> <tr> <td style="text-align:left;"> Item 2 </td> <td style="text-align:right;"> 64 </td> <td style="text-align:right;"> 2.63 </td> <td style="text-align:right;"> 1.07 </td> <td style="text-align:right;"> 1 </td> <td style="text-align:right;"> 2 </td> <td style="text-align:right;"> 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;"> 0.02 </td> <td style="text-align:right;"> 0.41 </td> <td style="text-align:right;"> 2 </td> <td style="text-align:right;"> 0.29 </td> <td style="text-align:right;"> -0.63 </td> </tr> <tr> <td style="text-align:left;"> Item 3 </td> <td style="text-align:right;"> 64 </td> <td style="text-align:right;"> 2.97 </td> <td style="text-align:right;"> 1.07 </td> <td style="text-align:right;"> 1 </td> <td style="text-align:right;"> 2 </td> <td style="text-align:right;"> 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;"> 0.02 </td> <td style="text-align:right;"> 0.36 </td> <td style="text-align:right;"> 3 </td> <td style="text-align:right;"> -0.01 </td> <td style="text-align:right;"> -0.68 </td> </tr> <tr> <td style="text-align:left;"> Item 4 </td> <td style="text-align:right;"> 64 </td> <td style="text-align:right;"> 3.21 </td> <td style="text-align:right;"> 1.04 </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;"> 0.02 </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;"> -0.55 </td> </tr> <tr> <td style="text-align:left;"> Item 5 </td> <td style="text-align:right;"> 64 </td> <td style="text-align:right;"> 3.49 </td> <td style="text-align:right;"> 0.98 </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;"> 0.02 </td> <td style="text-align:right;"> 0.28 </td> <td style="text-align:right;"> 4 </td> <td style="text-align:right;"> -0.29 </td> <td style="text-align:right;"> -0.39 </td> </tr> <tr> <td style="text-align:left;"> Item 6 </td> <td style="text-align:right;"> 64 </td> <td style="text-align:right;"> 3.44 </td> <td style="text-align:right;"> 1.07 </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;"> 0.02 </td> <td style="text-align:right;"> 0.31 </td> <td style="text-align:right;"> 4 </td> <td style="text-align:right;"> -0.29 </td> <td style="text-align:right;"> -0.57 </td> </tr> <tr> <td style="text-align:left;"> Item 7 </td> <td style="text-align:right;"> 64 </td> <td style="text-align:right;"> 3.15 </td> <td style="text-align:right;"> 1.09 </td> <td style="text-align:right;"> 1 </td> <td style="text-align:right;"> 2 </td> <td style="text-align:right;"> 3 </td> <td style="text-align:right;"> 4 </td> <td style="text-align:right;"> 5 </td> <td style="text-align:left;"> ▂▆▇▇▃ </td> <td style="text-align:right;"> 0.03 </td> <td style="text-align:right;"> 0.34 </td> <td style="text-align:right;"> 3 </td> <td style="text-align:right;"> -0.07 </td> <td style="text-align:right;"> -0.71 </td> </tr> <tr> <td style="text-align:left;"> Item 8 </td> <td style="text-align:right;"> 64 </td> <td style="text-align:right;"> 3.36 </td> <td style="text-align:right;"> 1.00 </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;"> 0.02 </td> <td style="text-align:right;"> 0.30 </td> <td style="text-align:right;"> 3 </td> <td style="text-align:right;"> -0.16 </td> <td style="text-align:right;"> -0.52 </td> </tr> <tr> <td style="text-align:left;"> Item 9 </td> <td style="text-align:right;"> 64 </td> <td style="text-align:right;"> 3.27 </td> <td style="text-align:right;"> 0.99 </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;"> 0.02 </td> <td style="text-align:right;"> 0.30 </td> <td style="text-align:right;"> 3 </td> <td style="text-align:right;"> -0.10 </td> <td style="text-align:right;"> -0.56 </td> </tr> <tr> <td style="text-align:left;"> Item 10 </td> <td style="text-align:right;"> 64 </td> <td style="text-align:right;"> 3.32 </td> <td style="text-align:right;"> 1.00 </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;"> 0.02 </td> <td style="text-align:right;"> 0.30 </td> <td style="text-align:right;"> 3 </td> <td style="text-align:right;"> -0.16 </td> <td style="text-align:right;"> -0.49 </td> </tr> <tr> <td style="text-align:left;"> Item 11 </td> <td style="text-align:right;"> 64 </td> <td style="text-align:right;"> 3.09 </td> <td style="text-align:right;"> 1.03 </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;"> 0.02 </td> <td style="text-align:right;"> 0.33 </td> <td style="text-align:right;"> 3 </td> <td style="text-align:right;"> 0.03 </td> <td style="text-align:right;"> -0.61 </td> </tr> <tr> <td style="text-align:left;"> Item 12 </td> <td style="text-align:right;"> 64 </td> <td style="text-align:right;"> 3.12 </td> <td style="text-align:right;"> 1.00 </td> <td style="text-align:right;"> 1 </td> <td style="text-align:right;"> 2 </td> <td style="text-align:right;"> 3 </td> <td style="text-align:right;"> 4 </td> <td style="text-align:right;"> 5 </td> <td style="text-align:left;"> ▁▅▇▆▂ </td> <td style="text-align:right;"> 0.02 </td> <td style="text-align:right;"> 0.32 </td> <td style="text-align:right;"> 3 </td> <td style="text-align:right;"> 0.00 </td> <td style="text-align:right;"> -0.53 </td> </tr> </tbody> </table> ] --- # Dimensionality <div class="pre-name">analysis_caas-sf.R</div> ```r model_measurement_w1 <- " ## wave 1 concern concern =~ ACAAS1 + ACAAS2 + ACAAS3 ## wave 1 control control =~ ACAAS4 + ACAAS5 + ACAAS6 ## wave 1 curiosity curiosity =~ ACAAS7 + ACAAS8 + ACAAS9 ## wave 1 confidence confidence =~ ACAAS10 + ACAAS11 + ACAAS12 #career adaptability caradapt =~ concern + control + curiosity + confidence #second-order latent factor *ACAAS1 ~~ ACAAS2 #after analyzing the modification indices *ACAAS7 ~~ ACAAS9 #after analyzing the modification indices " fit_model <- cfa(m = model_measurement_w1,d = ds_w1,ord = T, estimator="wlsmv") summary(fit_model, std=T) ``` --- # Dimensionality .scroll-box-20[ ``` ## lavaan 0.6.16 ended normally after 43 iterations ## ## Estimator DWLS ## Optimization method NLMINB ## Number of model parameters 66 ## ## Used Total ## Number of observations 2351 2364 ## ## Model Test User Model: ## Standard Scaled ## Test Statistic 690.664 1307.588 ## Degrees of freedom 48 48 ## P-value (Chi-square) 0.000 0.000 ## Scaling correction factor 0.533 ## Shift parameter 10.809 ## simple second-order correction ## ## Parameter Estimates: ## ## Standard errors Robust.sem ## Information Expected ## Information saturated (h1) model Unstructured ## ## Latent Variables: ## Estimate Std.Err z-value P(>|z|) Std.lv Std.all ## concern =~ ## ACAAS1 1.000 0.730 0.730 ## ACAAS2 1.129 0.017 64.816 0.000 0.824 0.824 ## ACAAS3 1.187 0.025 47.404 0.000 0.867 0.867 ## control =~ ## ACAAS4 1.000 0.820 0.820 ## ACAAS5 1.065 0.013 78.875 0.000 0.873 0.873 ## ACAAS6 0.990 0.014 70.438 0.000 0.812 0.812 ## curiosity =~ ## ACAAS7 1.000 0.830 0.830 ## ACAAS8 0.918 0.014 64.151 0.000 0.762 0.762 ## ACAAS9 0.937 0.014 65.543 0.000 0.778 0.778 ## confidence =~ ## ACAAS10 1.000 0.800 0.800 ## ACAAS11 0.996 0.014 71.781 0.000 0.797 0.797 ## ACAAS12 1.075 0.014 76.866 0.000 0.860 0.860 ## caradapt =~ ## concern 1.000 0.783 0.783 ## control 1.228 0.030 40.666 0.000 0.856 0.856 ## curiosity 1.368 0.033 40.854 0.000 0.942 0.942 ## confidence 1.228 0.031 39.905 0.000 0.877 0.877 ## ## Covariances: ## Estimate Std.Err z-value P(>|z|) Std.lv Std.all ## .ACAAS1 ~~ ## .ACAAS2 0.153 0.013 11.425 0.000 0.153 0.395 ## .ACAAS7 ~~ ## .ACAAS9 -0.131 0.012 -11.058 0.000 -0.131 -0.375 ## ## Intercepts: ## Estimate Std.Err z-value P(>|z|) Std.lv Std.all ## .ACAAS1 0.000 0.000 0.000 ## .ACAAS2 0.000 0.000 0.000 ## .ACAAS3 0.000 0.000 0.000 ## .ACAAS4 0.000 0.000 0.000 ## .ACAAS5 0.000 0.000 0.000 ## .ACAAS6 0.000 0.000 0.000 ## .ACAAS7 0.000 0.000 0.000 ## .ACAAS8 0.000 0.000 0.000 ## .ACAAS9 0.000 0.000 0.000 ## .ACAAS10 0.000 0.000 0.000 ## .ACAAS11 0.000 0.000 0.000 ## .ACAAS12 0.000 0.000 0.000 ## .concern 0.000 0.000 0.000 ## .control 0.000 0.000 0.000 ## .curiosity 0.000 0.000 0.000 ## .confidence 0.000 0.000 0.000 ## caradapt 0.000 0.000 0.000 ## ## Thresholds: ## Estimate Std.Err z-value P(>|z|) Std.lv Std.all ## ACAAS1|t1 -1.203 0.034 -35.443 0.000 -1.203 -1.203 ## ACAAS1|t2 -0.154 0.026 -5.916 0.000 -0.154 -0.154 ## ACAAS1|t3 0.624 0.028 22.475 0.000 0.624 0.624 ## ACAAS1|t4 1.474 0.039 37.643 0.000 1.474 1.474 ## ACAAS2|t1 -0.969 0.031 -31.471 0.000 -0.969 -0.969 ## ACAAS2|t2 0.148 0.026 5.710 0.000 0.148 0.148 ## ACAAS2|t3 0.892 0.030 29.761 0.000 0.892 0.892 ## ACAAS2|t4 1.761 0.047 37.264 0.000 1.761 1.761 ## ACAAS3|t1 -1.420 0.038 -37.407 0.000 -1.420 -1.420 ## ACAAS3|t2 -0.365 0.026 -13.763 0.000 -0.365 -0.365 ## ACAAS3|t3 0.497 0.027 18.369 0.000 0.497 0.497 ## ACAAS3|t4 1.471 0.039 37.632 0.000 1.471 1.471 ## ACAAS4|t1 -1.660 0.044 -37.696 0.000 -1.660 -1.660 ## ACAAS4|t2 -0.602 0.028 -21.796 0.000 -0.602 -0.602 ## ACAAS4|t3 0.289 0.026 11.016 0.000 0.289 0.289 ## ACAAS4|t4 1.167 0.033 34.948 0.000 1.167 1.167 ## ACAAS5|t1 -2.221 0.069 -31.982 0.000 -2.221 -2.221 ## ACAAS5|t2 -1.054 0.032 -33.133 0.000 -1.054 -1.054 ## ACAAS5|t3 -0.028 0.026 -1.093 0.274 -0.028 -0.028 ## ACAAS5|t4 0.983 0.031 31.754 0.000 0.983 0.983 ## ACAAS6|t1 -1.771 0.048 -37.203 0.000 -1.771 -1.771 ## ACAAS6|t2 -0.882 0.030 -29.538 0.000 -0.882 -0.882 ## ACAAS6|t3 -0.012 0.026 -0.474 0.635 -0.012 -0.012 ## ACAAS6|t4 0.924 0.030 30.497 0.000 0.924 0.924 ## ACAAS7|t1 -1.631 0.043 -37.762 0.000 -1.631 -1.631 ## ACAAS7|t2 -0.548 0.027 -20.067 0.000 -0.548 -0.548 ## ACAAS7|t3 0.259 0.026 9.907 0.000 0.259 0.259 ## ACAAS7|t4 1.142 0.033 34.584 0.000 1.142 1.142 ## ACAAS8|t1 -1.836 0.050 -36.748 0.000 -1.836 -1.836 ## ACAAS8|t2 -0.777 0.029 -26.881 0.000 -0.777 -0.777 ## ACAAS8|t3 0.149 0.026 5.751 0.000 0.149 0.149 ## ACAAS8|t4 1.182 0.034 35.155 0.000 1.182 1.182 ## ACAAS9|t1 -1.944 0.054 -35.741 0.000 -1.944 -1.944 ## ACAAS9|t2 -0.761 0.029 -26.455 0.000 -0.761 -0.761 ## ACAAS9|t3 0.214 0.026 8.221 0.000 0.214 0.214 ## ACAAS9|t4 1.210 0.034 35.528 0.000 1.210 1.210 ## ACAAS10|t1 -1.958 0.055 -35.586 0.000 -1.958 -1.958 ## ACAAS10|t2 -0.815 0.029 -27.879 0.000 -0.815 -0.815 ## ACAAS10|t3 0.144 0.026 5.545 0.000 0.144 0.144 ## ACAAS10|t4 1.221 0.034 35.667 0.000 1.221 1.221 ## ACAAS11|t1 -1.699 0.045 -37.565 0.000 -1.699 -1.699 ## ACAAS11|t2 -0.530 0.027 -19.462 0.000 -0.530 -0.530 ## ACAAS11|t3 0.379 0.027 14.295 0.000 0.379 0.379 ## ACAAS11|t4 1.327 0.036 36.765 0.000 1.327 1.327 ## ACAAS12|t1 -1.639 0.043 -37.746 0.000 -1.639 -1.639 ## ACAAS12|t2 -0.551 0.027 -20.148 0.000 -0.551 -0.551 ## ACAAS12|t3 0.378 0.027 14.254 0.000 0.378 0.378 ## ACAAS12|t4 1.327 0.036 36.765 0.000 1.327 1.327 ## ## Variances: ## Estimate Std.Err z-value P(>|z|) Std.lv Std.all ## .ACAAS1 0.467 0.467 0.467 ## .ACAAS2 0.320 0.320 0.320 ## .ACAAS3 0.249 0.249 0.249 ## .ACAAS4 0.327 0.327 0.327 ## .ACAAS5 0.237 0.237 0.237 ## .ACAAS6 0.341 0.341 0.341 ## .ACAAS7 0.311 0.311 0.311 ## .ACAAS8 0.420 0.420 0.420 ## .ACAAS9 0.394 0.394 0.394 ## .ACAAS10 0.360 0.360 0.360 ## .ACAAS11 0.365 0.365 0.365 ## .ACAAS12 0.260 0.260 0.260 ## .concern 0.207 0.011 19.616 0.000 0.387 0.387 ## .control 0.180 0.010 18.321 0.000 0.268 0.268 ## .curiosity 0.078 0.010 7.485 0.000 0.113 0.113 ## .confidence 0.148 0.009 15.654 0.000 0.230 0.230 ## caradapt 0.327 0.015 21.156 0.000 1.000 1.000 ## ## Scales y*: ## Estimate Std.Err z-value P(>|z|) Std.lv Std.all ## ACAAS1 1.000 1.000 1.000 ## ACAAS2 1.000 1.000 1.000 ## ACAAS3 1.000 1.000 1.000 ## ACAAS4 1.000 1.000 1.000 ## ACAAS5 1.000 1.000 1.000 ## ACAAS6 1.000 1.000 1.000 ## ACAAS7 1.000 1.000 1.000 ## ACAAS8 1.000 1.000 1.000 ## ACAAS9 1.000 1.000 1.000 ## ACAAS10 1.000 1.000 1.000 ## ACAAS11 1.000 1.000 1.000 ## ACAAS12 1.000 1.000 1.000 ``` ] Modifications: - residual correlation among items 1 and 2 (_concern_ dimension); and, - residual correlation among items 7 and 9 (_curiosity_ dimension). --- # Lambdas `\((\lambda)\)` .font60[ <table class="table" style="margin-left: auto; margin-right: auto;"> <caption>Standardized Factor Loadings</caption> <thead> <tr> <th style="text-align:left;"> </th> <th style="text-align:left;"> concern </th> <th style="text-align:left;"> control </th> <th style="text-align:left;"> curiosity </th> <th style="text-align:left;"> confidence </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;"> ACAAS1 </td> <td style="text-align:left;"> 0.730 </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;"> ACAAS2 </td> <td style="text-align:left;"> 0.824 </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;"> ACAAS3 </td> <td style="text-align:left;"> 0.867 </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;"> ACAAS4 </td> <td style="text-align:left;"> </td> <td style="text-align:left;"> 0.820 </td> <td style="text-align:left;"> </td> <td style="text-align:left;"> </td> </tr> <tr> <td style="text-align:left;"> ACAAS5 </td> <td style="text-align:left;"> </td> <td style="text-align:left;"> 0.873 </td> <td style="text-align:left;"> </td> <td style="text-align:left;"> </td> </tr> <tr> <td style="text-align:left;"> ACAAS6 </td> <td style="text-align:left;"> </td> <td style="text-align:left;"> 0.812 </td> <td style="text-align:left;"> </td> <td style="text-align:left;"> </td> </tr> <tr> <td style="text-align:left;"> ACAAS7 </td> <td style="text-align:left;"> </td> <td style="text-align:left;"> </td> <td style="text-align:left;"> 0.830 </td> <td style="text-align:left;"> </td> </tr> <tr> <td style="text-align:left;"> ACAAS8 </td> <td style="text-align:left;"> </td> <td style="text-align:left;"> </td> <td style="text-align:left;"> 0.762 </td> <td style="text-align:left;"> </td> </tr> <tr> <td style="text-align:left;"> ACAAS9 </td> <td style="text-align:left;"> </td> <td style="text-align:left;"> </td> <td style="text-align:left;"> 0.778 </td> <td style="text-align:left;"> </td> </tr> <tr> <td style="text-align:left;"> ACAAS10 </td> <td style="text-align:left;"> </td> <td style="text-align:left;"> </td> <td style="text-align:left;"> </td> <td style="text-align:left;"> 0.800 </td> </tr> <tr> <td style="text-align:left;"> ACAAS11 </td> <td style="text-align:left;"> </td> <td style="text-align:left;"> </td> <td style="text-align:left;"> </td> <td style="text-align:left;"> 0.797 </td> </tr> <tr> <td style="text-align:left;"> ACAAS12 </td> <td style="text-align:left;"> </td> <td style="text-align:left;"> </td> <td style="text-align:left;"> </td> <td style="text-align:left;"> 0.860 </td> </tr> </tbody> </table> ] --- # Gammas `\((\gamma)\)` .font80[ <table class="table" style="margin-left: auto; margin-right: auto;"> <caption>Standardized Structural Weights</caption> <thead> <tr> <th style="text-align:left;"> </th> <th style="text-align:right;"> Career Adaptability </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;"> Concern </td> <td style="text-align:right;"> 0.783 </td> </tr> <tr> <td style="text-align:left;"> Control </td> <td style="text-align:right;"> 0.856 </td> </tr> <tr> <td style="text-align:left;"> Curiosity </td> <td style="text-align:right;"> 0.942 </td> </tr> <tr> <td style="text-align:left;"> Confidence </td> <td style="text-align:right;"> 0.877 </td> </tr> </tbody> </table> ] --- # Goodness-of-fit The model presented a satisfactory fit `\((\chi^2_{scaled (48)}=1,307.59;p< .001;CFI_{robust}=0.95;TLI_{robust}=0.93;\)` `\(NFI_{scaled}=0.97;SRMR=0.04; RMSEA_{robust}=0.09;p_{(rmsea \leq 0.05)}< .001; 90\%CI[0.09, 0.10])\)` accordingly with the usual cutoff standards(Hu and Bentler, 1999). --- # Diagram The diagram showing the standardized estimates. <div class="grViz html-widget html-fill-item" id="htmlwidget-fee70293e1f4fc35dc93" style="width:100%;height:432px;"></div> <script type="application/json" data-for="htmlwidget-fee70293e1f4fc35dc93">{"x":{"diagram":" digraph plot { \n graph [ layout = dot, rankdir = LR ] \n node [ shape = box, fontname = Helvetica ] \n node [shape = box] \n ACAAS1; ACAAS2; ACAAS3; ACAAS4; ACAAS5; ACAAS6; ACAAS7; ACAAS8; ACAAS9; ACAAS10; ACAAS11; ACAAS12 \n node [shape = oval] \n concern; control; curiosity; confidence; caradapt \n \n edge [ color = grey ] \n concern->ACAAS1 [label = \"0.73***\"] concern->ACAAS2 [label = \"0.82***\"] concern->ACAAS3 [label = \"0.87***\"] control->ACAAS4 [label = \"0.82***\"] control->ACAAS5 [label = \"0.87***\"] control->ACAAS6 [label = \"0.81***\"] curiosity->ACAAS7 [label = \"0.83***\"] curiosity->ACAAS8 [label = \"0.76***\"] curiosity->ACAAS9 [label = \"0.78***\"] confidence->ACAAS10 [label = \"0.8***\"] confidence->ACAAS11 [label = \"0.8***\"] confidence->ACAAS12 [label = \"0.86***\"] caradapt->concern [label = \"0.78***\"] caradapt->control [label = \"0.86***\"] caradapt->curiosity [label = \"0.94***\"] caradapt->confidence [label = \"0.88***\"] ACAAS2 -> ACAAS1 [label = \"0.4***\", dir = \"both\"] ACAAS9 -> ACAAS7 [label = \"-0.38***\", dir = \"both\"]\n}","config":{"engine":"dot","options":null}},"evals":[],"jsHooks":[]}</script> --- # Item Fit Note that there is much disagreement among measurement scholars about how to classify an infit our outfit statistic as “fitting” or "misfitting." However, you should be aware of commonly accepted rule-of-thumb values among Rasch researchers: > Expected value is about 1.00 when data fit the model > Less than 1.00: Responses are too predictable; they resemble a Guttman-like (deterministic) pattern ("muted") > More than 1.00: Responses are too haphazard ("noisy"); there is too much variation to suggest that the estimate is a good representation of the response pattern Some variation is expected, but noisy responses are usually more cause for concern than muted responses. Frequently used critical values for mean square fit statistics . | *Type of Instrument* | *"Acceptable Range"* | | :---: | :----: | | Multiple-choice test (high-stakes) | 0.80 – 1.20 | | Multiple-choice test (not high-stakes)| 0.70 – 1.30 | | Rating scale | 0.60 – 1.40 | | Clinical observation | 0.50 – 1.70 | | Judgment (when agreement is encouraged) | 0.40 – 1.20| --- # Item Fit .font80[ <table class="table" style="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;"> ACAAS1 </td> <td style="text-align:right;"> 1.018 </td> <td style="text-align:right;"> 1.023 </td> </tr> <tr> <td style="text-align:left;"> ACAAS2 </td> <td style="text-align:right;"> 0.872 </td> <td style="text-align:right;"> 0.892 </td> </tr> <tr> <td style="text-align:left;"> ACAAS3 </td> <td style="text-align:right;"> 0.972 </td> <td style="text-align:right;"> 0.981 </td> </tr> <tr> <td style="text-align:left;"> ACAAS4 </td> <td style="text-align:right;"> 1.029 </td> <td style="text-align:right;"> 1.028 </td> </tr> <tr> <td style="text-align:left;"> ACAAS5 </td> <td style="text-align:right;"> 0.869 </td> <td style="text-align:right;"> 0.883 </td> </tr> <tr> <td style="text-align:left;"> ACAAS6 </td> <td style="text-align:right;"> 1.014 </td> <td style="text-align:right;"> 1.027 </td> </tr> <tr> <td style="text-align:left;"> ACAAS7 </td> <td style="text-align:right;"> 0.992 </td> <td style="text-align:right;"> 1.011 </td> </tr> <tr> <td style="text-align:left;"> ACAAS8 </td> <td style="text-align:right;"> 1.013 </td> <td style="text-align:right;"> 1.024 </td> </tr> <tr> <td style="text-align:left;"> ACAAS9 </td> <td style="text-align:right;"> 1.045 </td> <td style="text-align:right;"> 1.060 </td> </tr> <tr> <td style="text-align:left;"> ACAAS10 </td> <td style="text-align:right;"> 1.007 </td> <td style="text-align:right;"> 1.022 </td> </tr> <tr> <td style="text-align:left;"> ACAAS11 </td> <td style="text-align:right;"> 1.006 </td> <td style="text-align:right;"> 1.015 </td> </tr> <tr> <td style="text-align:left;"> ACAAS12 </td> <td style="text-align:right;"> 0.883 </td> <td style="text-align:right;"> 0.897 </td> </tr> </tbody> </table> ] --- # Item Fit <table class="table" style="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;"> 0.064 </td> </tr> <tr> <td style="text-align:left;"> Infit </td> <td style="text-align:right;"> 0.989 </td> <td style="text-align:right;"> 0.062 </td> </tr> </tbody> </table> --- # Wright Map .center[ <img src="data:image/png;base64,#presentation_files/figure-html/unnamed-chunk-18-1.png" width="80%" /> ] --- # Internal Structure ## Reliability: Internal consistency **First-order** The model's first-order internal consistency estimates are presented in the following table. <table class="table" style="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;"> Concern </th> <th style="text-align:right;"> Control </th> <th style="text-align:right;"> Curiosity </th> <th style="text-align:right;"> Confidence </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;"> \( \alpha_{ord} \) </td> <td style="text-align:right;"> 0.876 </td> <td style="text-align:right;"> 0.870 </td> <td style="text-align:right;"> 0.806 </td> <td style="text-align:right;"> 0.853 </td> </tr> <tr> <td style="text-align:left;"> \( \omega_{ord} \) </td> <td style="text-align:right;"> 0.781 </td> <td style="text-align:right;"> 0.839 </td> <td style="text-align:right;"> 0.833 </td> <td style="text-align:right;"> 0.827 </td> </tr> <tr> <td style="text-align:left;"> \( AVE \) </td> <td style="text-align:right;"> 0.655 </td> <td style="text-align:right;"> 0.698 </td> <td style="text-align:right;"> 0.625 </td> <td style="text-align:right;"> 0.672 </td> </tr> </tbody> </table> --- # Internal Structure ## Reliability: Internal consistency **Second-order** The model's second-order internal consistency estimates are presented in the following table. <table class="table" style="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;"> Career Adaptability </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;"> \( \omega_{L1} \) </td> <td style="text-align:right;"> 0.876 </td> </tr> <tr> <td style="text-align:left;"> \( \omega_{L2} \) </td> <td style="text-align:right;"> 0.925 </td> </tr> <tr> <td style="text-align:left;"> \( \omega_{Partial~L1} \) </td> <td style="text-align:right;"> 0.946 </td> </tr> </tbody> </table> --- # Dimensionality <div class="pre-name">analysis_caas-sf.R</div> ```r model_measurement_w2 <- " ## wave 1 concern concern =~ BCAAS1 + BCAAS2 + BCAAS3 ## wave 1 control control =~ BCAAS4 + BCAAS5 + BCAAS6 ## wave 1 curiosity curiosity =~ BCAAS7 + BCAAS8 + BCAAS9 ## wave 1 confidence confidence =~ BCAAS10 + BCAAS11 + BCAAS12 #career adaptability caradapt =~ concern + control + curiosity + confidence BCAAS1 ~~ BCAAS2 #<< modification indices added BCAAS7 ~~ BCAAS9 #<< modification indices added " fit_model <- cfa(m = model_measurement_w2,d = ds_w2,ord = T, estimator="wlsmv") summary(fit_model, std=T) ``` --- # Dimensionality .scroll-box-20[ ``` ## lavaan 0.6.16 ended normally after 43 iterations ## ## Estimator DWLS ## Optimization method NLMINB ## Number of model parameters 66 ## ## Used Total ## Number of observations 1879 1943 ## ## Model Test User Model: ## Standard Scaled ## Test Statistic 657.981 1421.130 ## Degrees of freedom 48 48 ## P-value (Chi-square) 0.000 0.000 ## Scaling correction factor 0.466 ## Shift parameter 9.972 ## simple second-order correction ## ## Parameter Estimates: ## ## Standard errors Robust.sem ## Information Expected ## Information saturated (h1) model Unstructured ## ## Latent Variables: ## Estimate Std.Err z-value P(>|z|) Std.lv Std.all ## concern =~ ## BCAAS1 1.000 0.762 0.762 ## BCAAS2 1.112 0.016 69.041 0.000 0.847 0.847 ## BCAAS3 1.152 0.021 56.144 0.000 0.878 0.878 ## control =~ ## BCAAS4 1.000 0.851 0.851 ## BCAAS5 1.024 0.012 88.086 0.000 0.871 0.871 ## BCAAS6 0.976 0.012 83.816 0.000 0.831 0.831 ## curiosity =~ ## BCAAS7 1.000 0.818 0.818 ## BCAAS8 0.942 0.014 69.389 0.000 0.771 0.771 ## BCAAS9 0.989 0.014 73.046 0.000 0.809 0.809 ## confidence =~ ## BCAAS10 1.000 0.835 0.835 ## BCAAS11 1.000 0.011 89.547 0.000 0.835 0.835 ## BCAAS12 1.032 0.011 90.702 0.000 0.862 0.862 ## caradapt =~ ## concern 1.000 0.804 0.804 ## control 1.234 0.027 45.477 0.000 0.888 0.888 ## curiosity 1.304 0.029 45.077 0.000 0.976 0.976 ## confidence 1.254 0.028 44.584 0.000 0.920 0.920 ## ## Covariances: ## Estimate Std.Err z-value P(>|z|) Std.lv Std.all ## .BCAAS1 ~~ ## .BCAAS2 0.135 0.012 11.437 0.000 0.135 0.391 ## .BCAAS7 ~~ ## .BCAAS9 -0.098 0.011 -9.062 0.000 -0.098 -0.290 ## ## Intercepts: ## Estimate Std.Err z-value P(>|z|) Std.lv Std.all ## .BCAAS1 0.000 0.000 0.000 ## .BCAAS2 0.000 0.000 0.000 ## .BCAAS3 0.000 0.000 0.000 ## .BCAAS4 0.000 0.000 0.000 ## .BCAAS5 0.000 0.000 0.000 ## .BCAAS6 0.000 0.000 0.000 ## .BCAAS7 0.000 0.000 0.000 ## .BCAAS8 0.000 0.000 0.000 ## .BCAAS9 0.000 0.000 0.000 ## .BCAAS10 0.000 0.000 0.000 ## .BCAAS11 0.000 0.000 0.000 ## .BCAAS12 0.000 0.000 0.000 ## .concern 0.000 0.000 0.000 ## .control 0.000 0.000 0.000 ## .curiosity 0.000 0.000 0.000 ## .confidence 0.000 0.000 0.000 ## caradapt 0.000 0.000 0.000 ## ## Thresholds: ## Estimate Std.Err z-value P(>|z|) Std.lv Std.all ## BCAAS1|t1 -1.309 0.040 -32.726 0.000 -1.309 -1.309 ## BCAAS1|t2 -0.229 0.029 -7.858 0.000 -0.229 -0.229 ## BCAAS1|t3 0.507 0.030 16.731 0.000 0.507 0.507 ## BCAAS1|t4 1.432 0.043 33.494 0.000 1.432 1.432 ## BCAAS2|t1 -1.066 0.036 -29.811 0.000 -1.066 -1.066 ## BCAAS2|t2 -0.018 0.029 -0.623 0.533 -0.018 -0.018 ## BCAAS2|t3 0.757 0.032 23.545 0.000 0.757 0.757 ## BCAAS2|t4 1.693 0.050 33.602 0.000 1.693 1.693 ## BCAAS3|t1 -1.368 0.041 -33.153 0.000 -1.368 -1.368 ## BCAAS3|t2 -0.406 0.030 -13.637 0.000 -0.406 -0.406 ## BCAAS3|t3 0.446 0.030 14.868 0.000 0.446 0.446 ## BCAAS3|t4 1.466 0.044 33.625 0.000 1.466 1.466 ## BCAAS4|t1 -1.624 0.048 -33.767 0.000 -1.624 -1.624 ## BCAAS4|t2 -0.681 0.031 -21.617 0.000 -0.681 -0.681 ## BCAAS4|t3 0.260 0.029 8.870 0.000 0.260 0.260 ## BCAAS4|t4 1.228 0.038 31.964 0.000 1.228 1.228 ## BCAAS5|t1 -1.988 0.063 -31.513 0.000 -1.988 -1.988 ## BCAAS5|t2 -1.016 0.035 -28.977 0.000 -1.016 -1.016 ## BCAAS5|t3 -0.051 0.029 -1.776 0.076 -0.051 -0.051 ## BCAAS5|t4 1.032 0.035 29.246 0.000 1.032 1.032 ## BCAAS6|t1 -1.746 0.052 -33.388 0.000 -1.746 -1.746 ## BCAAS6|t2 -0.870 0.033 -26.150 0.000 -0.870 -0.870 ## BCAAS6|t3 0.001 0.029 0.023 0.982 0.001 0.001 ## BCAAS6|t4 0.940 0.034 27.591 0.000 0.940 0.940 ## BCAAS7|t1 -1.540 0.046 -33.785 0.000 -1.540 -1.540 ## BCAAS7|t2 -0.556 0.031 -18.177 0.000 -0.556 -0.556 ## BCAAS7|t3 0.272 0.029 9.283 0.000 0.272 0.272 ## BCAAS7|t4 1.220 0.038 31.872 0.000 1.220 1.220 ## BCAAS8|t1 -1.900 0.059 -32.353 0.000 -1.900 -1.900 ## BCAAS8|t2 -0.860 0.033 -25.940 0.000 -0.860 -0.860 ## BCAAS8|t3 0.113 0.029 3.897 0.000 0.113 0.113 ## BCAAS8|t4 1.125 0.037 30.679 0.000 1.125 1.125 ## BCAAS9|t1 -1.892 0.058 -32.421 0.000 -1.892 -1.892 ## BCAAS9|t2 -0.753 0.032 -23.459 0.000 -0.753 -0.753 ## BCAAS9|t3 0.191 0.029 6.569 0.000 0.191 0.191 ## BCAAS9|t4 1.260 0.039 32.289 0.000 1.260 1.260 ## BCAAS10|t1 -1.831 0.056 -32.884 0.000 -1.831 -1.831 ## BCAAS10|t2 -0.815 0.033 -24.924 0.000 -0.815 -0.815 ## BCAAS10|t3 0.151 0.029 5.187 0.000 0.151 0.151 ## BCAAS10|t4 1.195 0.038 31.588 0.000 1.195 1.195 ## BCAAS11|t1 -1.650 0.049 -33.721 0.000 -1.650 -1.650 ## BCAAS11|t2 -0.533 0.030 -17.500 0.000 -0.533 -0.533 ## BCAAS11|t3 0.385 0.030 12.951 0.000 0.385 0.385 ## BCAAS11|t4 1.354 0.041 33.065 0.000 1.354 1.354 ## BCAAS12|t1 -1.704 0.051 -33.563 0.000 -1.704 -1.704 ## BCAAS12|t2 -0.599 0.031 -19.390 0.000 -0.599 -0.599 ## BCAAS12|t3 0.375 0.030 12.631 0.000 0.375 0.375 ## BCAAS12|t4 1.378 0.041 33.216 0.000 1.378 1.378 ## ## Variances: ## Estimate Std.Err z-value P(>|z|) Std.lv Std.all ## .BCAAS1 0.420 0.420 0.420 ## .BCAAS2 0.282 0.282 0.282 ## .BCAAS3 0.230 0.230 0.230 ## .BCAAS4 0.276 0.276 0.276 ## .BCAAS5 0.241 0.241 0.241 ## .BCAAS6 0.310 0.310 0.310 ## .BCAAS7 0.330 0.330 0.330 ## .BCAAS8 0.406 0.406 0.406 ## .BCAAS9 0.346 0.346 0.346 ## .BCAAS10 0.303 0.303 0.303 ## .BCAAS11 0.303 0.303 0.303 ## .BCAAS12 0.257 0.257 0.257 ## .concern 0.205 0.011 17.933 0.000 0.354 0.354 ## .control 0.153 0.010 15.375 0.000 0.211 0.211 ## .curiosity 0.032 0.009 3.641 0.000 0.048 0.048 ## .confidence 0.108 0.009 12.125 0.000 0.154 0.154 ## caradapt 0.375 0.017 22.379 0.000 1.000 1.000 ## ## Scales y*: ## Estimate Std.Err z-value P(>|z|) Std.lv Std.all ## BCAAS1 1.000 1.000 1.000 ## BCAAS2 1.000 1.000 1.000 ## BCAAS3 1.000 1.000 1.000 ## BCAAS4 1.000 1.000 1.000 ## BCAAS5 1.000 1.000 1.000 ## BCAAS6 1.000 1.000 1.000 ## BCAAS7 1.000 1.000 1.000 ## BCAAS8 1.000 1.000 1.000 ## BCAAS9 1.000 1.000 1.000 ## BCAAS10 1.000 1.000 1.000 ## BCAAS11 1.000 1.000 1.000 ## BCAAS12 1.000 1.000 1.000 ``` ] Modifications: - residual correlation among items 1 and 2 (_concern_ dimension); and, - residual correlation among items 7 and 9 (_curiosity_ dimension). --- # Lambdas `\((\lambda)\)` .font60[ <table class="table" style="margin-left: auto; margin-right: auto;"> <caption>Standardized Factor Loadings</caption> <thead> <tr> <th style="text-align:left;"> </th> <th style="text-align:left;"> concern </th> <th style="text-align:left;"> control </th> <th style="text-align:left;"> curiosity </th> <th style="text-align:left;"> confidence </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;"> BCAAS1 </td> <td style="text-align:left;"> 0.762 </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;"> BCAAS2 </td> <td style="text-align:left;"> 0.847 </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;"> BCAAS3 </td> <td style="text-align:left;"> 0.878 </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;"> BCAAS4 </td> <td style="text-align:left;"> </td> <td style="text-align:left;"> 0.851 </td> <td style="text-align:left;"> </td> <td style="text-align:left;"> </td> </tr> <tr> <td style="text-align:left;"> BCAAS5 </td> <td style="text-align:left;"> </td> <td style="text-align:left;"> 0.871 </td> <td style="text-align:left;"> </td> <td style="text-align:left;"> </td> </tr> <tr> <td style="text-align:left;"> BCAAS6 </td> <td style="text-align:left;"> </td> <td style="text-align:left;"> 0.831 </td> <td style="text-align:left;"> </td> <td style="text-align:left;"> </td> </tr> <tr> <td style="text-align:left;"> BCAAS7 </td> <td style="text-align:left;"> </td> <td style="text-align:left;"> </td> <td style="text-align:left;"> 0.818 </td> <td style="text-align:left;"> </td> </tr> <tr> <td style="text-align:left;"> BCAAS8 </td> <td style="text-align:left;"> </td> <td style="text-align:left;"> </td> <td style="text-align:left;"> 0.771 </td> <td style="text-align:left;"> </td> </tr> <tr> <td style="text-align:left;"> BCAAS9 </td> <td style="text-align:left;"> </td> <td style="text-align:left;"> </td> <td style="text-align:left;"> 0.809 </td> <td style="text-align:left;"> </td> </tr> <tr> <td style="text-align:left;"> BCAAS10 </td> <td style="text-align:left;"> </td> <td style="text-align:left;"> </td> <td style="text-align:left;"> </td> <td style="text-align:left;"> 0.835 </td> </tr> <tr> <td style="text-align:left;"> BCAAS11 </td> <td style="text-align:left;"> </td> <td style="text-align:left;"> </td> <td style="text-align:left;"> </td> <td style="text-align:left;"> 0.835 </td> </tr> <tr> <td style="text-align:left;"> BCAAS12 </td> <td style="text-align:left;"> </td> <td style="text-align:left;"> </td> <td style="text-align:left;"> </td> <td style="text-align:left;"> 0.862 </td> </tr> </tbody> </table> ] --- # Gammas `\((\gamma)\)` .font80[ <table class="table" style="margin-left: auto; margin-right: auto;"> <caption>Standardized Structural Weights</caption> <thead> <tr> <th style="text-align:left;"> </th> <th style="text-align:right;"> Career Adaptability </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;"> Concern </td> <td style="text-align:right;"> 0.804 </td> </tr> <tr> <td style="text-align:left;"> Control </td> <td style="text-align:right;"> 0.888 </td> </tr> <tr> <td style="text-align:left;"> Curiosity </td> <td style="text-align:right;"> 0.976 </td> </tr> <tr> <td style="text-align:left;"> Confidence </td> <td style="text-align:right;"> 0.920 </td> </tr> </tbody> </table> ] --- # Goodness-of-fit The model presented a satisfactory fit `\((\chi^2_{scaled (48)}=1,421.13;p< .001; CFI_{robust}=0.95;TLI_{robust}=0.92;\)` `\(NFI_{scaled}=0.96;SRMR=0.04; RMSEA_{robust}=0.10;p_{(rmsea \leq 0.05)}< .001; 90\%CI[0.10, 0.11])\)` accordingly with the usual cutoff standards (Hu and Bentler, 1999). --- # Diagram The diagram showing the standardized estimates. <div class="grViz html-widget html-fill-item" id="htmlwidget-e652455d6366b4bc25bf" style="width:100%;height:432px;"></div> <script type="application/json" data-for="htmlwidget-e652455d6366b4bc25bf">{"x":{"diagram":" digraph plot { \n graph [ layout = dot, rankdir = LR ] \n node [ shape = box, fontname = Helvetica ] \n node [shape = box] \n BCAAS1; BCAAS2; BCAAS3; BCAAS4; BCAAS5; BCAAS6; BCAAS7; BCAAS8; BCAAS9; BCAAS10; BCAAS11; BCAAS12 \n node [shape = oval] \n concern; control; curiosity; confidence; caradapt \n \n edge [ color = grey ] \n concern->BCAAS1 [label = \"0.76***\"] concern->BCAAS2 [label = \"0.85***\"] concern->BCAAS3 [label = \"0.88***\"] control->BCAAS4 [label = \"0.85***\"] control->BCAAS5 [label = \"0.87***\"] control->BCAAS6 [label = \"0.83***\"] curiosity->BCAAS7 [label = \"0.82***\"] curiosity->BCAAS8 [label = \"0.77***\"] curiosity->BCAAS9 [label = \"0.81***\"] confidence->BCAAS10 [label = \"0.83***\"] confidence->BCAAS11 [label = \"0.83***\"] confidence->BCAAS12 [label = \"0.86***\"] caradapt->concern [label = \"0.8***\"] caradapt->control [label = \"0.89***\"] caradapt->curiosity [label = \"0.98***\"] caradapt->confidence [label = \"0.92***\"] BCAAS2 -> BCAAS1 [label = \"0.39***\", dir = \"both\"] BCAAS9 -> BCAAS7 [label = \"-0.29***\", dir = \"both\"]\n}","config":{"engine":"dot","options":null}},"evals":[],"jsHooks":[]}</script> --- # Item Fit Note that there is much disagreement among measurement scholars about how to classify an infit our outfit statistic as “fitting” or "misfitting." However, you should be aware of commonly accepted rule-of-thumb values among Rasch researchers: > Expected value is about 1.00 when data fit the model > Less than 1.00: Responses are too predictable; they resemble a Guttman-like (deterministic) pattern ("muted") > More than 1.00: Responses are too haphazard ("noisy"); there is too much variation to suggest that the estimate is a good representation of the response pattern Some variation is expected, but noisy responses are usually more cause for concern than muted responses. Frequently used critical values for mean square fit statistics . | *Type of Instrument* | *"Acceptable Range"* | | :---: | :----: | | Multiple-choice test (high-stakes) | 0.80 – 1.20 | | Multiple-choice test (not high-stakes)| 0.70 – 1.30 | | Rating scale | 0.60 – 1.40 | | Clinical observation | 0.50 – 1.70 | | Judgment (when agreement is encouraged) | 0.40 – 1.20| --- # Item Fit .font80[ <table class="table" style="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;"> BCAAS1 </td> <td style="text-align:right;"> 1.018 </td> <td style="text-align:right;"> 1.023 </td> </tr> <tr> <td style="text-align:left;"> BCAAS2 </td> <td style="text-align:right;"> 0.872 </td> <td style="text-align:right;"> 0.892 </td> </tr> <tr> <td style="text-align:left;"> BCAAS3 </td> <td style="text-align:right;"> 0.972 </td> <td style="text-align:right;"> 0.981 </td> </tr> <tr> <td style="text-align:left;"> BCAAS4 </td> <td style="text-align:right;"> 1.029 </td> <td style="text-align:right;"> 1.028 </td> </tr> <tr> <td style="text-align:left;"> BCAAS5 </td> <td style="text-align:right;"> 0.869 </td> <td style="text-align:right;"> 0.883 </td> </tr> <tr> <td style="text-align:left;"> BCAAS6 </td> <td style="text-align:right;"> 1.014 </td> <td style="text-align:right;"> 1.027 </td> </tr> <tr> <td style="text-align:left;"> BCAAS7 </td> <td style="text-align:right;"> 0.992 </td> <td style="text-align:right;"> 1.011 </td> </tr> <tr> <td style="text-align:left;"> BCAAS8 </td> <td style="text-align:right;"> 1.013 </td> <td style="text-align:right;"> 1.024 </td> </tr> <tr> <td style="text-align:left;"> BCAAS9 </td> <td style="text-align:right;"> 1.045 </td> <td style="text-align:right;"> 1.060 </td> </tr> <tr> <td style="text-align:left;"> BCAAS10 </td> <td style="text-align:right;"> 1.007 </td> <td style="text-align:right;"> 1.022 </td> </tr> <tr> <td style="text-align:left;"> BCAAS11 </td> <td style="text-align:right;"> 1.006 </td> <td style="text-align:right;"> 1.015 </td> </tr> <tr> <td style="text-align:left;"> BCAAS12 </td> <td style="text-align:right;"> 0.883 </td> <td style="text-align:right;"> 0.897 </td> </tr> </tbody> </table> ] --- # Item Fit <table class="table" style="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;"> 0.064 </td> </tr> <tr> <td style="text-align:left;"> Infit </td> <td style="text-align:right;"> 0.989 </td> <td style="text-align:right;"> 0.062 </td> </tr> </tbody> </table> --- # Wright Map .center[ <img src="data:image/png;base64,#presentation_files/figure-html/unnamed-chunk-28-1.png" width="80%" /> ] --- # Reliability: Internal consistency **First-order** The model's first-order internal consistency estimates are presented in the following table. <table class="table" style="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;"> Concern </th> <th style="text-align:right;"> Control </th> <th style="text-align:right;"> Curiosity </th> <th style="text-align:right;"> Confidence </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;"> \( \alpha_{ord} \) </td> <td style="text-align:right;"> 0.890 </td> <td style="text-align:right;"> 0.882 </td> <td style="text-align:right;"> 0.821 </td> <td style="text-align:right;"> 0.873 </td> </tr> <tr> <td style="text-align:left;"> \( \omega_{ord} \) </td> <td style="text-align:right;"> 0.807 </td> <td style="text-align:right;"> 0.854 </td> <td style="text-align:right;"> 0.833 </td> <td style="text-align:right;"> 0.848 </td> </tr> <tr> <td style="text-align:left;"> \( AVE \) </td> <td style="text-align:right;"> 0.689 </td> <td style="text-align:right;"> 0.725 </td> <td style="text-align:right;"> 0.639 </td> <td style="text-align:right;"> 0.712 </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="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;"> Career Adaptability </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;"> \( \omega_{L1} \) </td> <td style="text-align:right;"> 0.903 </td> </tr> <tr> <td style="text-align:left;"> \( \omega_{L2} \) </td> <td style="text-align:right;"> 0.945 </td> </tr> <tr> <td style="text-align:left;"> \( \omega_{Partial~L1} \) </td> <td style="text-align:right;"> 0.955 </td> </tr> </tbody> </table> --- # Reliability: Test-Retest .scroll-box-20[ ```r model_measurement_w1w2 <- " ## wave 1 concern concernw1 =~ ACAAS1 + ACAAS2 + ACAAS3 ## wave 1 control controlw1 =~ ACAAS4 + ACAAS5 + ACAAS6 ## wave 1 curiosity curiosityw1 =~ ACAAS7 + ACAAS8 + ACAAS9 ## wave 1 confidence confidencew1 =~ ACAAS10 + ACAAS11 + ACAAS12 ## wave 1 career adaptability caradaptw1 =~ concernw1 + controlw1 + curiosityw1 + confidencew1 ACAAS1 ~~ ACAAS2 ACAAS11 ~~ ACAAS12 ## wave 2 concern concernw2 =~ BCAAS1 + BCAAS2 + BCAAS3 ## wave 2 control controlw2 =~ BCAAS4 + BCAAS5 + BCAAS6 ## wave 2 curiosity curiosityw2 =~ BCAAS7 + BCAAS8 + BCAAS9 ## wave 2 confidence confidencew2 =~ BCAAS10 + BCAAS11 + BCAAS12 ## wave 2 career adaptability caradaptw2 =~ concernw2 + controlw2 + curiosityw2 + confidencew2 BCAAS1 ~~ BCAAS2 BCAAS11 ~~ BCAAS12 #correlation between residuals ACAAS1~~BCAAS1 ACAAS2~~BCAAS2 ACAAS3~~BCAAS3 ACAAS4~~BCAAS4 ACAAS5~~BCAAS5 ACAAS6~~BCAAS6 ACAAS7~~BCAAS7 ACAAS8~~BCAAS8 ACAAS9~~BCAAS9 ACAAS10~~BCAAS10 ACAAS11~~BCAAS11 ACAAS12~~BCAAS12 " ds <- base::readRDS(file = "assets/data/ds.rds") fit_model <- cfa(model = model_measurement_w1w2, data = ds, ordered = T, estimator="wlsmv") 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 = 2) test_restest <- inspect(object = fit_model, what = "std")$psi["caradaptw2","caradaptw1"] |> round(2) gof <- c("df.scaled", "chisq.scaled", "pvalue.scaled", "cfi.robust", "nfi.scaled", "tli.robust", "srmr", "rmsea.robust", "rmsea.ci.lower.robust", "rmsea.ci.upper.robust", "rmsea.pvalue.robust") ``` ] The model presented a satisfactory fit `\((\chi^2_{scaled (227)}=2,579.43;p< .001;CFI_{scaled}=0.96;TLI_{scaled}=0.95;\)` `\(NFI_{scaled}=0.96;SRMR=0.04; RMSEA_{scaled}=0.07;p_{(rmsea \leq 0.05)}< .001; 90\%CI[0.07, 0.08])\)` accordingly with the usual cutoff standards(Hu and Bentler, 1999). The latent correlation was positive and very strong `\((r_{wave 1, wave 2}= 0.65)\)`. --- # Measurement Invariance ## Sex Following Wu and Estabrook Wu and Estabrook (2016) recommendations. **Configural model**: .orange[no constraints] across groups or repeated measures .scroll-box-20[ ```r mod.config <- " ## LOADINGS: concern =~ c(1, 1)*ACAAS1 + c(lambda.1_1.g1, lambda.1_1.g2)*ACAAS1 concern =~ c(NA, NA)*ACAAS2 + c(lambda.2_1.g1, lambda.2_1.g2)*ACAAS2 concern =~ c(NA, NA)*ACAAS3 + c(lambda.3_1.g1, lambda.3_1.g2)*ACAAS3 control =~ c(1, 1)*ACAAS4 + c(lambda.4_2.g1, lambda.4_2.g2)*ACAAS4 control =~ c(NA, NA)*ACAAS5 + c(lambda.5_2.g1, lambda.5_2.g2)*ACAAS5 control =~ c(NA, NA)*ACAAS6 + c(lambda.6_2.g1, lambda.6_2.g2)*ACAAS6 curiosity =~ c(1, 1)*ACAAS7 + c(lambda.7_3.g1, lambda.7_3.g2)*ACAAS7 curiosity =~ c(NA, NA)*ACAAS8 + c(lambda.8_3.g1, lambda.8_3.g2)*ACAAS8 curiosity =~ c(NA, NA)*ACAAS9 + c(lambda.9_3.g1, lambda.9_3.g2)*ACAAS9 confidence =~ c(1, 1)*ACAAS10 + c(lambda.10_4.g1, lambda.10_4.g2)*ACAAS10 confidence =~ c(NA, NA)*ACAAS11 + c(lambda.11_4.g1, lambda.11_4.g2)*ACAAS11 confidence =~ c(NA, NA)*ACAAS12 + c(lambda.12_4.g1, lambda.12_4.g2)*ACAAS12 caradapt =~ c(1, 1)*concern + c(beta.1_5.g1, beta.1_5.g2)*concern caradapt =~ c(NA, NA)*control + c(beta.2_5.g1, beta.2_5.g2)*control caradapt =~ c(NA, NA)*curiosity + c(beta.3_5.g1, beta.3_5.g2)*curiosity caradapt =~ c(NA, NA)*confidence + c(beta.4_5.g1, beta.4_5.g2)*confidence ## THRESHOLDS: ACAAS1 | c(NA, NA)*t1 + c(ACAAS1.thr1.g1, ACAAS1.thr1.g2)*t1 ACAAS1 | c(NA, NA)*t2 + c(ACAAS1.thr2.g1, ACAAS1.thr2.g2)*t2 ACAAS1 | c(NA, NA)*t3 + c(ACAAS1.thr3.g1, ACAAS1.thr3.g2)*t3 ACAAS1 | c(NA, NA)*t4 + c(ACAAS1.thr4.g1, ACAAS1.thr4.g2)*t4 ACAAS2 | c(NA, NA)*t1 + c(ACAAS2.thr1.g1, ACAAS2.thr1.g2)*t1 ACAAS2 | c(NA, NA)*t2 + c(ACAAS2.thr2.g1, ACAAS2.thr2.g2)*t2 ACAAS2 | c(NA, NA)*t3 + c(ACAAS2.thr3.g1, ACAAS2.thr3.g2)*t3 ACAAS2 | c(NA, NA)*t4 + c(ACAAS2.thr4.g1, ACAAS2.thr4.g2)*t4 ACAAS3 | c(NA, NA)*t1 + c(ACAAS3.thr1.g1, ACAAS3.thr1.g2)*t1 ACAAS3 | c(NA, NA)*t2 + c(ACAAS3.thr2.g1, ACAAS3.thr2.g2)*t2 ACAAS3 | c(NA, NA)*t3 + c(ACAAS3.thr3.g1, ACAAS3.thr3.g2)*t3 ACAAS3 | c(NA, NA)*t4 + c(ACAAS3.thr4.g1, ACAAS3.thr4.g2)*t4 ACAAS4 | c(NA, NA)*t1 + c(ACAAS4.thr1.g1, ACAAS4.thr1.g2)*t1 ACAAS4 | c(NA, NA)*t2 + c(ACAAS4.thr2.g1, ACAAS4.thr2.g2)*t2 ACAAS4 | c(NA, NA)*t3 + c(ACAAS4.thr3.g1, ACAAS4.thr3.g2)*t3 ACAAS4 | c(NA, NA)*t4 + c(ACAAS4.thr4.g1, ACAAS4.thr4.g2)*t4 ACAAS5 | c(NA, NA)*t1 + c(ACAAS5.thr1.g1, ACAAS5.thr1.g2)*t1 ACAAS5 | c(NA, NA)*t2 + c(ACAAS5.thr2.g1, ACAAS5.thr2.g2)*t2 ACAAS5 | c(NA, NA)*t3 + c(ACAAS5.thr3.g1, ACAAS5.thr3.g2)*t3 ACAAS5 | c(NA, NA)*t4 + c(ACAAS5.thr4.g1, ACAAS5.thr4.g2)*t4 ACAAS6 | c(NA, NA)*t1 + c(ACAAS6.thr1.g1, ACAAS6.thr1.g2)*t1 ACAAS6 | c(NA, NA)*t2 + c(ACAAS6.thr2.g1, ACAAS6.thr2.g2)*t2 ACAAS6 | c(NA, NA)*t3 + c(ACAAS6.thr3.g1, ACAAS6.thr3.g2)*t3 ACAAS6 | c(NA, NA)*t4 + c(ACAAS6.thr4.g1, ACAAS6.thr4.g2)*t4 ACAAS7 | c(NA, NA)*t1 + c(ACAAS7.thr1.g1, ACAAS7.thr1.g2)*t1 ACAAS7 | c(NA, NA)*t2 + c(ACAAS7.thr2.g1, ACAAS7.thr2.g2)*t2 ACAAS7 | c(NA, NA)*t3 + c(ACAAS7.thr3.g1, ACAAS7.thr3.g2)*t3 ACAAS7 | c(NA, NA)*t4 + c(ACAAS7.thr4.g1, ACAAS7.thr4.g2)*t4 ACAAS8 | c(NA, NA)*t1 + c(ACAAS8.thr1.g1, ACAAS8.thr1.g2)*t1 ACAAS8 | c(NA, NA)*t2 + c(ACAAS8.thr2.g1, ACAAS8.thr2.g2)*t2 ACAAS8 | c(NA, NA)*t3 + c(ACAAS8.thr3.g1, ACAAS8.thr3.g2)*t3 ACAAS8 | c(NA, NA)*t4 + c(ACAAS8.thr4.g1, ACAAS8.thr4.g2)*t4 ACAAS9 | c(NA, NA)*t1 + c(ACAAS9.thr1.g1, ACAAS9.thr1.g2)*t1 ACAAS9 | c(NA, NA)*t2 + c(ACAAS9.thr2.g1, ACAAS9.thr2.g2)*t2 ACAAS9 | c(NA, NA)*t3 + c(ACAAS9.thr3.g1, ACAAS9.thr3.g2)*t3 ACAAS9 | c(NA, NA)*t4 + c(ACAAS9.thr4.g1, ACAAS9.thr4.g2)*t4 ACAAS10 | c(NA, NA)*t1 + c(ACAAS10.thr1.g1, ACAAS10.thr1.g2)*t1 ACAAS10 | c(NA, NA)*t2 + c(ACAAS10.thr2.g1, ACAAS10.thr2.g2)*t2 ACAAS10 | c(NA, NA)*t3 + c(ACAAS10.thr3.g1, ACAAS10.thr3.g2)*t3 ACAAS10 | c(NA, NA)*t4 + c(ACAAS10.thr4.g1, ACAAS10.thr4.g2)*t4 ACAAS11 | c(NA, NA)*t1 + c(ACAAS11.thr1.g1, ACAAS11.thr1.g2)*t1 ACAAS11 | c(NA, NA)*t2 + c(ACAAS11.thr2.g1, ACAAS11.thr2.g2)*t2 ACAAS11 | c(NA, NA)*t3 + c(ACAAS11.thr3.g1, ACAAS11.thr3.g2)*t3 ACAAS11 | c(NA, NA)*t4 + c(ACAAS11.thr4.g1, ACAAS11.thr4.g2)*t4 ACAAS12 | c(NA, NA)*t1 + c(ACAAS12.thr1.g1, ACAAS12.thr1.g2)*t1 ACAAS12 | c(NA, NA)*t2 + c(ACAAS12.thr2.g1, ACAAS12.thr2.g2)*t2 ACAAS12 | c(NA, NA)*t3 + c(ACAAS12.thr3.g1, ACAAS12.thr3.g2)*t3 ACAAS12 | c(NA, NA)*t4 + c(ACAAS12.thr4.g1, ACAAS12.thr4.g2)*t4 ## INTERCEPTS: ACAAS1 ~ c(0, 0)*1 + c(nu.1.g1, nu.1.g2)*1 ACAAS2 ~ c(0, 0)*1 + c(nu.2.g1, nu.2.g2)*1 ACAAS3 ~ c(0, 0)*1 + c(nu.3.g1, nu.3.g2)*1 ACAAS4 ~ c(0, 0)*1 + c(nu.4.g1, nu.4.g2)*1 ACAAS5 ~ c(0, 0)*1 + c(nu.5.g1, nu.5.g2)*1 ACAAS6 ~ c(0, 0)*1 + c(nu.6.g1, nu.6.g2)*1 ACAAS7 ~ c(0, 0)*1 + c(nu.7.g1, nu.7.g2)*1 ACAAS8 ~ c(0, 0)*1 + c(nu.8.g1, nu.8.g2)*1 ACAAS9 ~ c(0, 0)*1 + c(nu.9.g1, nu.9.g2)*1 ACAAS10 ~ c(0, 0)*1 + c(nu.10.g1, nu.10.g2)*1 ACAAS11 ~ c(0, 0)*1 + c(nu.11.g1, nu.11.g2)*1 ACAAS12 ~ c(0, 0)*1 + c(nu.12.g1, nu.12.g2)*1 ## UNIQUE-FACTOR VARIANCES: ACAAS1 ~~ c(1, 1)*ACAAS1 + c(theta.1_1.g1, theta.1_1.g2)*ACAAS1 ACAAS2 ~~ c(1, 1)*ACAAS2 + c(theta.2_2.g1, theta.2_2.g2)*ACAAS2 ACAAS3 ~~ c(1, 1)*ACAAS3 + c(theta.3_3.g1, theta.3_3.g2)*ACAAS3 ACAAS4 ~~ c(1, 1)*ACAAS4 + c(theta.4_4.g1, theta.4_4.g2)*ACAAS4 ACAAS5 ~~ c(1, 1)*ACAAS5 + c(theta.5_5.g1, theta.5_5.g2)*ACAAS5 ACAAS6 ~~ c(1, 1)*ACAAS6 + c(theta.6_6.g1, theta.6_6.g2)*ACAAS6 ACAAS7 ~~ c(1, 1)*ACAAS7 + c(theta.7_7.g1, theta.7_7.g2)*ACAAS7 ACAAS8 ~~ c(1, 1)*ACAAS8 + c(theta.8_8.g1, theta.8_8.g2)*ACAAS8 ACAAS9 ~~ c(1, 1)*ACAAS9 + c(theta.9_9.g1, theta.9_9.g2)*ACAAS9 ACAAS10 ~~ c(1, 1)*ACAAS10 + c(theta.10_10.g1, theta.10_10.g2)*ACAAS10 ACAAS11 ~~ c(1, 1)*ACAAS11 + c(theta.11_11.g1, theta.11_11.g2)*ACAAS11 ACAAS12 ~~ c(1, 1)*ACAAS12 + c(theta.12_12.g1, theta.12_12.g2)*ACAAS12 ## UNIQUE-FACTOR COVARIANCES: ACAAS1 ~~ c(NA, NA)*ACAAS2 + c(theta.2_1.g1, theta.2_1.g2)*ACAAS2 ACAAS7 ~~ c(NA, NA)*ACAAS9 + c(theta.9_7.g1, theta.9_7.g2)*ACAAS9 ## LATENT MEANS/INTERCEPTS: concern ~ c(0, 0)*1 + c(alpha.1.g1, alpha.1.g2)*1 control ~ c(0, 0)*1 + c(alpha.2.g1, alpha.2.g2)*1 curiosity ~ c(0, 0)*1 + c(alpha.3.g1, alpha.3.g2)*1 confidence ~ c(0, 0)*1 + c(alpha.4.g1, alpha.4.g2)*1 caradapt ~ c(0, 0)*1 + c(alpha.5.g1, alpha.5.g2)*1 ## COMMON-FACTOR VARIANCES: concern ~~ c(NA, NA)*concern + c(psi.1_1.g1, psi.1_1.g2)*concern control ~~ c(NA, NA)*control + c(psi.2_2.g1, psi.2_2.g2)*control curiosity ~~ c(NA, NA)*curiosity + c(psi.3_3.g1, psi.3_3.g2)*curiosity confidence ~~ c(NA, NA)*confidence + c(psi.4_4.g1, psi.4_4.g2)*confidence caradapt ~~ c(NA, NA)*caradapt + c(psi.5_5.g1, psi.5_5.g2)*caradapt ## COMMON-FACTOR COVARIANCES: concern ~~ c(0, 0)*control + c(psi.2_1.g1, psi.2_1.g2)*control concern ~~ c(0, 0)*curiosity + c(psi.3_1.g1, psi.3_1.g2)*curiosity concern ~~ c(0, 0)*confidence + c(psi.4_1.g1, psi.4_1.g2)*confidence concern ~~ c(0, 0)*caradapt + c(psi.5_1.g1, psi.5_1.g2)*caradapt control ~~ c(0, 0)*curiosity + c(psi.3_2.g1, psi.3_2.g2)*curiosity control ~~ c(0, 0)*confidence + c(psi.4_2.g1, psi.4_2.g2)*confidence control ~~ c(0, 0)*caradapt + c(psi.5_2.g1, psi.5_2.g2)*caradapt curiosity ~~ c(0, 0)*confidence + c(psi.4_3.g1, psi.4_3.g2)*confidence curiosity ~~ c(0, 0)*caradapt + c(psi.5_3.g1, psi.5_3.g2)*caradapt confidence ~~ c(0, 0)*caradapt + c(psi.5_4.g1, psi.5_4.g2)*caradapt" fit.config <- cfa(mod.config, data = ds_w1[complete.cases(ds_w1[,c(caas_w1,"ASEX")]),], group = "ASEX", ordered = T, parameterization = "theta") ``` ] --- # Measurement Invariance ## Sex **Threshold invariance model**: equal .orange[thresholds] across groups or repeated measures .scroll-box-20[ ```r mod.thresh <- " ## LOADINGS: concern =~ c(1, 1)*ACAAS1 + c(lambda.1_1.g1, lambda.1_1.g2)*ACAAS1 concern =~ c(NA, NA)*ACAAS2 + c(lambda.2_1.g1, lambda.2_1.g2)*ACAAS2 concern =~ c(NA, NA)*ACAAS3 + c(lambda.3_1.g1, lambda.3_1.g2)*ACAAS3 control =~ c(1, 1)*ACAAS4 + c(lambda.4_2.g1, lambda.4_2.g2)*ACAAS4 control =~ c(NA, NA)*ACAAS5 + c(lambda.5_2.g1, lambda.5_2.g2)*ACAAS5 control =~ c(NA, NA)*ACAAS6 + c(lambda.6_2.g1, lambda.6_2.g2)*ACAAS6 curiosity =~ c(1, 1)*ACAAS7 + c(lambda.7_3.g1, lambda.7_3.g2)*ACAAS7 curiosity =~ c(NA, NA)*ACAAS8 + c(lambda.8_3.g1, lambda.8_3.g2)*ACAAS8 curiosity =~ c(NA, NA)*ACAAS9 + c(lambda.9_3.g1, lambda.9_3.g2)*ACAAS9 confidence =~ c(1, 1)*ACAAS10 + c(lambda.10_4.g1, lambda.10_4.g2)*ACAAS10 confidence =~ c(NA, NA)*ACAAS11 + c(lambda.11_4.g1, lambda.11_4.g2)*ACAAS11 confidence =~ c(NA, NA)*ACAAS12 + c(lambda.12_4.g1, lambda.12_4.g2)*ACAAS12 caradapt =~ c(1, 1)*concern + c(beta.1_5.g1, beta.1_5.g2)*concern caradapt =~ c(NA, NA)*control + c(beta.2_5.g1, beta.2_5.g2)*control caradapt =~ c(NA, NA)*curiosity + c(beta.3_5.g1, beta.3_5.g2)*curiosity caradapt =~ c(NA, NA)*confidence + c(beta.4_5.g1, beta.4_5.g2)*confidence ## THRESHOLDS: ACAAS1 | c(NA, NA)*t1 + c(ACAAS1.thr1, ACAAS1.thr1)*t1 ACAAS1 | c(NA, NA)*t2 + c(ACAAS1.thr2, ACAAS1.thr2)*t2 ACAAS1 | c(NA, NA)*t3 + c(ACAAS1.thr3, ACAAS1.thr3)*t3 ACAAS1 | c(NA, NA)*t4 + c(ACAAS1.thr4, ACAAS1.thr4)*t4 ACAAS2 | c(NA, NA)*t1 + c(ACAAS2.thr1, ACAAS2.thr1)*t1 ACAAS2 | c(NA, NA)*t2 + c(ACAAS2.thr2, ACAAS2.thr2)*t2 ACAAS2 | c(NA, NA)*t3 + c(ACAAS2.thr3, ACAAS2.thr3)*t3 ACAAS2 | c(NA, NA)*t4 + c(ACAAS2.thr4, ACAAS2.thr4)*t4 ACAAS3 | c(NA, NA)*t1 + c(ACAAS3.thr1, ACAAS3.thr1)*t1 ACAAS3 | c(NA, NA)*t2 + c(ACAAS3.thr2, ACAAS3.thr2)*t2 ACAAS3 | c(NA, NA)*t3 + c(ACAAS3.thr3, ACAAS3.thr3)*t3 ACAAS3 | c(NA, NA)*t4 + c(ACAAS3.thr4, ACAAS3.thr4)*t4 ACAAS4 | c(NA, NA)*t1 + c(ACAAS4.thr1, ACAAS4.thr1)*t1 ACAAS4 | c(NA, NA)*t2 + c(ACAAS4.thr2, ACAAS4.thr2)*t2 ACAAS4 | c(NA, NA)*t3 + c(ACAAS4.thr3, ACAAS4.thr3)*t3 ACAAS4 | c(NA, NA)*t4 + c(ACAAS4.thr4, ACAAS4.thr4)*t4 ACAAS5 | c(NA, NA)*t1 + c(ACAAS5.thr1, ACAAS5.thr1)*t1 ACAAS5 | c(NA, NA)*t2 + c(ACAAS5.thr2, ACAAS5.thr2)*t2 ACAAS5 | c(NA, NA)*t3 + c(ACAAS5.thr3, ACAAS5.thr3)*t3 ACAAS5 | c(NA, NA)*t4 + c(ACAAS5.thr4, ACAAS5.thr4)*t4 ACAAS6 | c(NA, NA)*t1 + c(ACAAS6.thr1, ACAAS6.thr1)*t1 ACAAS6 | c(NA, NA)*t2 + c(ACAAS6.thr2, ACAAS6.thr2)*t2 ACAAS6 | c(NA, NA)*t3 + c(ACAAS6.thr3, ACAAS6.thr3)*t3 ACAAS6 | c(NA, NA)*t4 + c(ACAAS6.thr4, ACAAS6.thr4)*t4 ACAAS7 | c(NA, NA)*t1 + c(ACAAS7.thr1, ACAAS7.thr1)*t1 ACAAS7 | c(NA, NA)*t2 + c(ACAAS7.thr2, ACAAS7.thr2)*t2 ACAAS7 | c(NA, NA)*t3 + c(ACAAS7.thr3, ACAAS7.thr3)*t3 ACAAS7 | c(NA, NA)*t4 + c(ACAAS7.thr4, ACAAS7.thr4)*t4 ACAAS8 | c(NA, NA)*t1 + c(ACAAS8.thr1, ACAAS8.thr1)*t1 ACAAS8 | c(NA, NA)*t2 + c(ACAAS8.thr2, ACAAS8.thr2)*t2 ACAAS8 | c(NA, NA)*t3 + c(ACAAS8.thr3, ACAAS8.thr3)*t3 ACAAS8 | c(NA, NA)*t4 + c(ACAAS8.thr4, ACAAS8.thr4)*t4 ACAAS9 | c(NA, NA)*t1 + c(ACAAS9.thr1, ACAAS9.thr1)*t1 ACAAS9 | c(NA, NA)*t2 + c(ACAAS9.thr2, ACAAS9.thr2)*t2 ACAAS9 | c(NA, NA)*t3 + c(ACAAS9.thr3, ACAAS9.thr3)*t3 ACAAS9 | c(NA, NA)*t4 + c(ACAAS9.thr4, ACAAS9.thr4)*t4 ACAAS10 | c(NA, NA)*t1 + c(ACAAS10.thr1, ACAAS10.thr1)*t1 ACAAS10 | c(NA, NA)*t2 + c(ACAAS10.thr2, ACAAS10.thr2)*t2 ACAAS10 | c(NA, NA)*t3 + c(ACAAS10.thr3, ACAAS10.thr3)*t3 ACAAS10 | c(NA, NA)*t4 + c(ACAAS10.thr4, ACAAS10.thr4)*t4 ACAAS11 | c(NA, NA)*t1 + c(ACAAS11.thr1, ACAAS11.thr1)*t1 ACAAS11 | c(NA, NA)*t2 + c(ACAAS11.thr2, ACAAS11.thr2)*t2 ACAAS11 | c(NA, NA)*t3 + c(ACAAS11.thr3, ACAAS11.thr3)*t3 ACAAS11 | c(NA, NA)*t4 + c(ACAAS11.thr4, ACAAS11.thr4)*t4 ACAAS12 | c(NA, NA)*t1 + c(ACAAS12.thr1, ACAAS12.thr1)*t1 ACAAS12 | c(NA, NA)*t2 + c(ACAAS12.thr2, ACAAS12.thr2)*t2 ACAAS12 | c(NA, NA)*t3 + c(ACAAS12.thr3, ACAAS12.thr3)*t3 ACAAS12 | c(NA, NA)*t4 + c(ACAAS12.thr4, ACAAS12.thr4)*t4 ## INTERCEPTS: ACAAS1 ~ c(0, NA)*1 + c(nu.1.g1, nu.1.g2)*1 ACAAS2 ~ c(0, NA)*1 + c(nu.2.g1, nu.2.g2)*1 ACAAS3 ~ c(0, NA)*1 + c(nu.3.g1, nu.3.g2)*1 ACAAS4 ~ c(0, NA)*1 + c(nu.4.g1, nu.4.g2)*1 ACAAS5 ~ c(0, NA)*1 + c(nu.5.g1, nu.5.g2)*1 ACAAS6 ~ c(0, NA)*1 + c(nu.6.g1, nu.6.g2)*1 ACAAS7 ~ c(0, NA)*1 + c(nu.7.g1, nu.7.g2)*1 ACAAS8 ~ c(0, NA)*1 + c(nu.8.g1, nu.8.g2)*1 ACAAS9 ~ c(0, NA)*1 + c(nu.9.g1, nu.9.g2)*1 ACAAS10 ~ c(0, NA)*1 + c(nu.10.g1, nu.10.g2)*1 ACAAS11 ~ c(0, NA)*1 + c(nu.11.g1, nu.11.g2)*1 ACAAS12 ~ c(0, NA)*1 + c(nu.12.g1, nu.12.g2)*1 ## UNIQUE-FACTOR VARIANCES: ACAAS1 ~~ c(1, NA)*ACAAS1 + c(theta.1_1.g1, theta.1_1.g2)*ACAAS1 ACAAS2 ~~ c(1, NA)*ACAAS2 + c(theta.2_2.g1, theta.2_2.g2)*ACAAS2 ACAAS3 ~~ c(1, NA)*ACAAS3 + c(theta.3_3.g1, theta.3_3.g2)*ACAAS3 ACAAS4 ~~ c(1, NA)*ACAAS4 + c(theta.4_4.g1, theta.4_4.g2)*ACAAS4 ACAAS5 ~~ c(1, NA)*ACAAS5 + c(theta.5_5.g1, theta.5_5.g2)*ACAAS5 ACAAS6 ~~ c(1, NA)*ACAAS6 + c(theta.6_6.g1, theta.6_6.g2)*ACAAS6 ACAAS7 ~~ c(1, NA)*ACAAS7 + c(theta.7_7.g1, theta.7_7.g2)*ACAAS7 ACAAS8 ~~ c(1, NA)*ACAAS8 + c(theta.8_8.g1, theta.8_8.g2)*ACAAS8 ACAAS9 ~~ c(1, NA)*ACAAS9 + c(theta.9_9.g1, theta.9_9.g2)*ACAAS9 ACAAS10 ~~ c(1, NA)*ACAAS10 + c(theta.10_10.g1, theta.10_10.g2)*ACAAS10 ACAAS11 ~~ c(1, NA)*ACAAS11 + c(theta.11_11.g1, theta.11_11.g2)*ACAAS11 ACAAS12 ~~ c(1, NA)*ACAAS12 + c(theta.12_12.g1, theta.12_12.g2)*ACAAS12 ## UNIQUE-FACTOR COVARIANCES: ACAAS1 ~~ c(NA, NA)*ACAAS2 + c(theta.2_1.g1, theta.2_1.g2)*ACAAS2 ACAAS7 ~~ c(NA, NA)*ACAAS9 + c(theta.9_7.g1, theta.9_7.g2)*ACAAS9 ## LATENT MEANS/INTERCEPTS: concern ~ c(0, 0)*1 + c(alpha.1.g1, alpha.1.g2)*1 control ~ c(0, NA)*1 + c(alpha.2.g1, alpha.2.g2)*1 curiosity ~ c(0, NA)*1 + c(alpha.3.g1, alpha.3.g2)*1 confidence ~ c(0, NA)*1 + c(alpha.4.g1, alpha.4.g2)*1 caradapt ~ c(0, NA)*1 + c(alpha.5.g1, alpha.5.g2)*1 ## COMMON-FACTOR VARIANCES: concern ~~ c(NA, NA)*concern + c(psi.1_1.g1, psi.1_1.g2)*concern control ~~ c(NA, NA)*control + c(psi.2_2.g1, psi.2_2.g2)*control curiosity ~~ c(NA, NA)*curiosity + c(psi.3_3.g1, psi.3_3.g2)*curiosity confidence ~~ c(NA, NA)*confidence + c(psi.4_4.g1, psi.4_4.g2)*confidence caradapt ~~ c(NA, NA)*caradapt + c(psi.5_5.g1, psi.5_5.g2)*caradapt ## COMMON-FACTOR COVARIANCES: concern ~~ c(0, 0)*control + c(psi.2_1.g1, psi.2_1.g2)*control concern ~~ c(0, 0)*curiosity + c(psi.3_1.g1, psi.3_1.g2)*curiosity concern ~~ c(0, 0)*confidence + c(psi.4_1.g1, psi.4_1.g2)*confidence concern ~~ c(0, 0)*caradapt + c(psi.5_1.g1, psi.5_1.g2)*caradapt control ~~ c(0, 0)*curiosity + c(psi.3_2.g1, psi.3_2.g2)*curiosity control ~~ c(0, 0)*confidence + c(psi.4_2.g1, psi.4_2.g2)*confidence control ~~ c(0, 0)*caradapt + c(psi.5_2.g1, psi.5_2.g2)*caradapt curiosity ~~ c(0, 0)*confidence + c(psi.4_3.g1, psi.4_3.g2)*confidence curiosity ~~ c(0, 0)*caradapt + c(psi.5_3.g1, psi.5_3.g2)*caradapt confidence ~~ c(0, 0)*caradapt + c(psi.5_4.g1, psi.5_4.g2)*caradapt" fit.thresh <- cfa(model = mod.thresh, data = ds_w1[complete.cases(ds_w1[,c(caas_w1,"ASEX")]),], group = "ASEX", ordered = T, parameterization = "theta") ``` ] --- # Measurement Invariance ## Sex **Metric (first-order) invariance model**: equal thresholds and .orange[loadings] across groups or repeated measures .scroll-box-20[ ```r mod.metric_1l <- " ## LOADINGS: concern =~ c(1, 1)*ACAAS1 + c(lambda.1_1, lambda.1_1)*ACAAS1 concern =~ c(NA, NA)*ACAAS2 + c(lambda.2_1, lambda.2_1)*ACAAS2 concern =~ c(NA, NA)*ACAAS3 + c(lambda.3_1, lambda.3_1)*ACAAS3 control =~ c(1, 1)*ACAAS4 + c(lambda.4_2, lambda.4_2)*ACAAS4 control =~ c(NA, NA)*ACAAS5 + c(lambda.5_2, lambda.5_2)*ACAAS5 control =~ c(NA, NA)*ACAAS6 + c(lambda.6_2, lambda.6_2)*ACAAS6 curiosity =~ c(1, 1)*ACAAS7 + c(lambda.7_3, lambda.7_3)*ACAAS7 curiosity =~ c(NA, NA)*ACAAS8 + c(lambda.8_3, lambda.8_3)*ACAAS8 curiosity =~ c(NA, NA)*ACAAS9 + c(lambda.9_3, lambda.9_3)*ACAAS9 confidence =~ c(1, 1)*ACAAS10 + c(lambda.10_4, lambda.10_4)*ACAAS10 confidence =~ c(NA, NA)*ACAAS11 + c(lambda.11_4, lambda.11_4)*ACAAS11 confidence =~ c(NA, NA)*ACAAS12 + c(lambda.12_4, lambda.12_4)*ACAAS12 caradapt =~ c(1, 1)*concern + c(beta.1_5.g1, beta.1_5.g2)*concern caradapt =~ c(NA, NA)*control + c(beta.2_5.g1, beta.2_5.g2)*control caradapt =~ c(NA, NA)*curiosity + c(beta.3_5.g1, beta.3_5.g2)*curiosity caradapt =~ c(NA, NA)*confidence + c(beta.4_5.g1, beta.4_5.g2)*confidence ## THRESHOLDS: ACAAS1 | c(NA, NA)*t1 + c(ACAAS1.thr1, ACAAS1.thr1)*t1 ACAAS1 | c(NA, NA)*t2 + c(ACAAS1.thr2, ACAAS1.thr2)*t2 ACAAS1 | c(NA, NA)*t3 + c(ACAAS1.thr3, ACAAS1.thr3)*t3 ACAAS1 | c(NA, NA)*t4 + c(ACAAS1.thr4, ACAAS1.thr4)*t4 ACAAS2 | c(NA, NA)*t1 + c(ACAAS2.thr1, ACAAS2.thr1)*t1 ACAAS2 | c(NA, NA)*t2 + c(ACAAS2.thr2, ACAAS2.thr2)*t2 ACAAS2 | c(NA, NA)*t3 + c(ACAAS2.thr3, ACAAS2.thr3)*t3 ACAAS2 | c(NA, NA)*t4 + c(ACAAS2.thr4, ACAAS2.thr4)*t4 ACAAS3 | c(NA, NA)*t1 + c(ACAAS3.thr1, ACAAS3.thr1)*t1 ACAAS3 | c(NA, NA)*t2 + c(ACAAS3.thr2, ACAAS3.thr2)*t2 ACAAS3 | c(NA, NA)*t3 + c(ACAAS3.thr3, ACAAS3.thr3)*t3 ACAAS3 | c(NA, NA)*t4 + c(ACAAS3.thr4, ACAAS3.thr4)*t4 ACAAS4 | c(NA, NA)*t1 + c(ACAAS4.thr1, ACAAS4.thr1)*t1 ACAAS4 | c(NA, NA)*t2 + c(ACAAS4.thr2, ACAAS4.thr2)*t2 ACAAS4 | c(NA, NA)*t3 + c(ACAAS4.thr3, ACAAS4.thr3)*t3 ACAAS4 | c(NA, NA)*t4 + c(ACAAS4.thr4, ACAAS4.thr4)*t4 ACAAS5 | c(NA, NA)*t1 + c(ACAAS5.thr1, ACAAS5.thr1)*t1 ACAAS5 | c(NA, NA)*t2 + c(ACAAS5.thr2, ACAAS5.thr2)*t2 ACAAS5 | c(NA, NA)*t3 + c(ACAAS5.thr3, ACAAS5.thr3)*t3 ACAAS5 | c(NA, NA)*t4 + c(ACAAS5.thr4, ACAAS5.thr4)*t4 ACAAS6 | c(NA, NA)*t1 + c(ACAAS6.thr1, ACAAS6.thr1)*t1 ACAAS6 | c(NA, NA)*t2 + c(ACAAS6.thr2, ACAAS6.thr2)*t2 ACAAS6 | c(NA, NA)*t3 + c(ACAAS6.thr3, ACAAS6.thr3)*t3 ACAAS6 | c(NA, NA)*t4 + c(ACAAS6.thr4, ACAAS6.thr4)*t4 ACAAS7 | c(NA, NA)*t1 + c(ACAAS7.thr1, ACAAS7.thr1)*t1 ACAAS7 | c(NA, NA)*t2 + c(ACAAS7.thr2, ACAAS7.thr2)*t2 ACAAS7 | c(NA, NA)*t3 + c(ACAAS7.thr3, ACAAS7.thr3)*t3 ACAAS7 | c(NA, NA)*t4 + c(ACAAS7.thr4, ACAAS7.thr4)*t4 ACAAS8 | c(NA, NA)*t1 + c(ACAAS8.thr1, ACAAS8.thr1)*t1 ACAAS8 | c(NA, NA)*t2 + c(ACAAS8.thr2, ACAAS8.thr2)*t2 ACAAS8 | c(NA, NA)*t3 + c(ACAAS8.thr3, ACAAS8.thr3)*t3 ACAAS8 | c(NA, NA)*t4 + c(ACAAS8.thr4, ACAAS8.thr4)*t4 ACAAS9 | c(NA, NA)*t1 + c(ACAAS9.thr1, ACAAS9.thr1)*t1 ACAAS9 | c(NA, NA)*t2 + c(ACAAS9.thr2, ACAAS9.thr2)*t2 ACAAS9 | c(NA, NA)*t3 + c(ACAAS9.thr3, ACAAS9.thr3)*t3 ACAAS9 | c(NA, NA)*t4 + c(ACAAS9.thr4, ACAAS9.thr4)*t4 ACAAS10 | c(NA, NA)*t1 + c(ACAAS10.thr1, ACAAS10.thr1)*t1 ACAAS10 | c(NA, NA)*t2 + c(ACAAS10.thr2, ACAAS10.thr2)*t2 ACAAS10 | c(NA, NA)*t3 + c(ACAAS10.thr3, ACAAS10.thr3)*t3 ACAAS10 | c(NA, NA)*t4 + c(ACAAS10.thr4, ACAAS10.thr4)*t4 ACAAS11 | c(NA, NA)*t1 + c(ACAAS11.thr1, ACAAS11.thr1)*t1 ACAAS11 | c(NA, NA)*t2 + c(ACAAS11.thr2, ACAAS11.thr2)*t2 ACAAS11 | c(NA, NA)*t3 + c(ACAAS11.thr3, ACAAS11.thr3)*t3 ACAAS11 | c(NA, NA)*t4 + c(ACAAS11.thr4, ACAAS11.thr4)*t4 ACAAS12 | c(NA, NA)*t1 + c(ACAAS12.thr1, ACAAS12.thr1)*t1 ACAAS12 | c(NA, NA)*t2 + c(ACAAS12.thr2, ACAAS12.thr2)*t2 ACAAS12 | c(NA, NA)*t3 + c(ACAAS12.thr3, ACAAS12.thr3)*t3 ACAAS12 | c(NA, NA)*t4 + c(ACAAS12.thr4, ACAAS12.thr4)*t4 ## INTERCEPTS: ACAAS1 ~ c(0, NA)*1 + c(nu.1.g1, nu.1.g2)*1 ACAAS2 ~ c(0, NA)*1 + c(nu.2.g1, nu.2.g2)*1 ACAAS3 ~ c(0, NA)*1 + c(nu.3.g1, nu.3.g2)*1 ACAAS4 ~ c(0, NA)*1 + c(nu.4.g1, nu.4.g2)*1 ACAAS5 ~ c(0, NA)*1 + c(nu.5.g1, nu.5.g2)*1 ACAAS6 ~ c(0, NA)*1 + c(nu.6.g1, nu.6.g2)*1 ACAAS7 ~ c(0, NA)*1 + c(nu.7.g1, nu.7.g2)*1 ACAAS8 ~ c(0, NA)*1 + c(nu.8.g1, nu.8.g2)*1 ACAAS9 ~ c(0, NA)*1 + c(nu.9.g1, nu.9.g2)*1 ACAAS10 ~ c(0, NA)*1 + c(nu.10.g1, nu.10.g2)*1 ACAAS11 ~ c(0, NA)*1 + c(nu.11.g1, nu.11.g2)*1 ACAAS12 ~ c(0, NA)*1 + c(nu.12.g1, nu.12.g2)*1 ## UNIQUE-FACTOR VARIANCES: ACAAS1 ~~ c(1, NA)*ACAAS1 + c(theta.1_1.g1, theta.1_1.g2)*ACAAS1 ACAAS2 ~~ c(1, NA)*ACAAS2 + c(theta.2_2.g1, theta.2_2.g2)*ACAAS2 ACAAS3 ~~ c(1, NA)*ACAAS3 + c(theta.3_3.g1, theta.3_3.g2)*ACAAS3 ACAAS4 ~~ c(1, NA)*ACAAS4 + c(theta.4_4.g1, theta.4_4.g2)*ACAAS4 ACAAS5 ~~ c(1, NA)*ACAAS5 + c(theta.5_5.g1, theta.5_5.g2)*ACAAS5 ACAAS6 ~~ c(1, NA)*ACAAS6 + c(theta.6_6.g1, theta.6_6.g2)*ACAAS6 ACAAS7 ~~ c(1, NA)*ACAAS7 + c(theta.7_7.g1, theta.7_7.g2)*ACAAS7 ACAAS8 ~~ c(1, NA)*ACAAS8 + c(theta.8_8.g1, theta.8_8.g2)*ACAAS8 ACAAS9 ~~ c(1, NA)*ACAAS9 + c(theta.9_9.g1, theta.9_9.g2)*ACAAS9 ACAAS10 ~~ c(1, NA)*ACAAS10 + c(theta.10_10.g1, theta.10_10.g2)*ACAAS10 ACAAS11 ~~ c(1, NA)*ACAAS11 + c(theta.11_11.g1, theta.11_11.g2)*ACAAS11 ACAAS12 ~~ c(1, NA)*ACAAS12 + c(theta.12_12.g1, theta.12_12.g2)*ACAAS12 ## UNIQUE-FACTOR COVARIANCES: ACAAS1 ~~ c(NA, NA)*ACAAS2 + c(theta.2_1.g1, theta.2_1.g2)*ACAAS2 ACAAS7 ~~ c(NA, NA)*ACAAS9 + c(theta.9_7.g1, theta.9_7.g2)*ACAAS9 ## LATENT MEANS/INTERCEPTS: concern ~ c(0, 0)*1 + c(alpha.1.g1, alpha.1.g2)*1 control ~ c(0, NA)*1 + c(alpha.2.g1, alpha.2.g2)*1 curiosity ~ c(0, NA)*1 + c(alpha.3.g1, alpha.3.g2)*1 confidence ~ c(0, NA)*1 + c(alpha.4.g1, alpha.4.g2)*1 caradapt ~ c(0, NA)*1 + c(alpha.5.g1, alpha.5.g2)*1 ## COMMON-FACTOR VARIANCES: concern ~~ c(NA, NA)*concern + c(psi.1_1.g1, psi.1_1.g2)*concern control ~~ c(NA, NA)*control + c(psi.2_2.g1, psi.2_2.g2)*control curiosity ~~ c(NA, NA)*curiosity + c(psi.3_3.g1, psi.3_3.g2)*curiosity confidence ~~ c(NA, NA)*confidence + c(psi.4_4.g1, psi.4_4.g2)*confidence caradapt ~~ c(NA, NA)*caradapt + c(psi.5_5.g1, psi.5_5.g2)*caradapt ## COMMON-FACTOR COVARIANCES: concern ~~ c(0, 0)*control + c(psi.2_1.g1, psi.2_1.g2)*control concern ~~ c(0, 0)*curiosity + c(psi.3_1.g1, psi.3_1.g2)*curiosity concern ~~ c(0, 0)*confidence + c(psi.4_1.g1, psi.4_1.g2)*confidence concern ~~ c(0, 0)*caradapt + c(psi.5_1.g1, psi.5_1.g2)*caradapt control ~~ c(0, 0)*curiosity + c(psi.3_2.g1, psi.3_2.g2)*curiosity control ~~ c(0, 0)*confidence + c(psi.4_2.g1, psi.4_2.g2)*confidence control ~~ c(0, 0)*caradapt + c(psi.5_2.g1, psi.5_2.g2)*caradapt curiosity ~~ c(0, 0)*confidence + c(psi.4_3.g1, psi.4_3.g2)*confidence curiosity ~~ c(0, 0)*caradapt + c(psi.5_3.g1, psi.5_3.g2)*caradapt confidence ~~ c(0, 0)*caradapt + c(psi.5_4.g1, psi.5_4.g2)*caradapt " fit.metric_1l <- cfa(model = mod.metric_1l, data = ds_w1, group = "ASEX", ordered = T, parameterization = "theta") ``` ] --- # Measurement Invariance ## Sex **Metric (second-order) invariance model**: equal thresholds, loadings and .orange[structural weights] across groups or repeated measures .scroll-box-20[ ```r mod.metric_2l <- " ## LOADINGS: concern =~ c(1, 1)*ACAAS1 + c(lambda.1_1, lambda.1_1)*ACAAS1 concern =~ c(NA, NA)*ACAAS2 + c(lambda.2_1, lambda.2_1)*ACAAS2 concern =~ c(NA, NA)*ACAAS3 + c(lambda.3_1, lambda.3_1)*ACAAS3 control =~ c(1, 1)*ACAAS4 + c(lambda.4_2, lambda.4_2)*ACAAS4 control =~ c(NA, NA)*ACAAS5 + c(lambda.5_2, lambda.5_2)*ACAAS5 control =~ c(NA, NA)*ACAAS6 + c(lambda.6_2, lambda.6_2)*ACAAS6 curiosity =~ c(1, 1)*ACAAS7 + c(lambda.7_3, lambda.7_3)*ACAAS7 curiosity =~ c(NA, NA)*ACAAS8 + c(lambda.8_3, lambda.8_3)*ACAAS8 curiosity =~ c(NA, NA)*ACAAS9 + c(lambda.9_3, lambda.9_3)*ACAAS9 confidence =~ c(1, 1)*ACAAS10 + c(lambda.10_4, lambda.10_4)*ACAAS10 confidence =~ c(NA, NA)*ACAAS11 + c(lambda.11_4, lambda.11_4)*ACAAS11 confidence =~ c(NA, NA)*ACAAS12 + c(lambda.12_4, lambda.12_4)*ACAAS12 caradapt =~ c(1, 1)*concern + c(beta.1_5, beta.1_5)*concern caradapt =~ c(NA, NA)*control + c(beta.2_5, beta.2_5)*control caradapt =~ c(NA, NA)*curiosity + c(beta.3_5, beta.3_5)*curiosity caradapt =~ c(NA, NA)*confidence + c(beta.4_5, beta.4_5)*confidence ## THRESHOLDS: ACAAS1 | c(NA, NA)*t1 + c(ACAAS1.thr1, ACAAS1.thr1)*t1 ACAAS1 | c(NA, NA)*t2 + c(ACAAS1.thr2, ACAAS1.thr2)*t2 ACAAS1 | c(NA, NA)*t3 + c(ACAAS1.thr3, ACAAS1.thr3)*t3 ACAAS1 | c(NA, NA)*t4 + c(ACAAS1.thr4, ACAAS1.thr4)*t4 ACAAS2 | c(NA, NA)*t1 + c(ACAAS2.thr1, ACAAS2.thr1)*t1 ACAAS2 | c(NA, NA)*t2 + c(ACAAS2.thr2, ACAAS2.thr2)*t2 ACAAS2 | c(NA, NA)*t3 + c(ACAAS2.thr3, ACAAS2.thr3)*t3 ACAAS2 | c(NA, NA)*t4 + c(ACAAS2.thr4, ACAAS2.thr4)*t4 ACAAS3 | c(NA, NA)*t1 + c(ACAAS3.thr1, ACAAS3.thr1)*t1 ACAAS3 | c(NA, NA)*t2 + c(ACAAS3.thr2, ACAAS3.thr2)*t2 ACAAS3 | c(NA, NA)*t3 + c(ACAAS3.thr3, ACAAS3.thr3)*t3 ACAAS3 | c(NA, NA)*t4 + c(ACAAS3.thr4, ACAAS3.thr4)*t4 ACAAS4 | c(NA, NA)*t1 + c(ACAAS4.thr1, ACAAS4.thr1)*t1 ACAAS4 | c(NA, NA)*t2 + c(ACAAS4.thr2, ACAAS4.thr2)*t2 ACAAS4 | c(NA, NA)*t3 + c(ACAAS4.thr3, ACAAS4.thr3)*t3 ACAAS4 | c(NA, NA)*t4 + c(ACAAS4.thr4, ACAAS4.thr4)*t4 ACAAS5 | c(NA, NA)*t1 + c(ACAAS5.thr1, ACAAS5.thr1)*t1 ACAAS5 | c(NA, NA)*t2 + c(ACAAS5.thr2, ACAAS5.thr2)*t2 ACAAS5 | c(NA, NA)*t3 + c(ACAAS5.thr3, ACAAS5.thr3)*t3 ACAAS5 | c(NA, NA)*t4 + c(ACAAS5.thr4, ACAAS5.thr4)*t4 ACAAS6 | c(NA, NA)*t1 + c(ACAAS6.thr1, ACAAS6.thr1)*t1 ACAAS6 | c(NA, NA)*t2 + c(ACAAS6.thr2, ACAAS6.thr2)*t2 ACAAS6 | c(NA, NA)*t3 + c(ACAAS6.thr3, ACAAS6.thr3)*t3 ACAAS6 | c(NA, NA)*t4 + c(ACAAS6.thr4, ACAAS6.thr4)*t4 ACAAS7 | c(NA, NA)*t1 + c(ACAAS7.thr1, ACAAS7.thr1)*t1 ACAAS7 | c(NA, NA)*t2 + c(ACAAS7.thr2, ACAAS7.thr2)*t2 ACAAS7 | c(NA, NA)*t3 + c(ACAAS7.thr3, ACAAS7.thr3)*t3 ACAAS7 | c(NA, NA)*t4 + c(ACAAS7.thr4, ACAAS7.thr4)*t4 ACAAS8 | c(NA, NA)*t1 + c(ACAAS8.thr1, ACAAS8.thr1)*t1 ACAAS8 | c(NA, NA)*t2 + c(ACAAS8.thr2, ACAAS8.thr2)*t2 ACAAS8 | c(NA, NA)*t3 + c(ACAAS8.thr3, ACAAS8.thr3)*t3 ACAAS8 | c(NA, NA)*t4 + c(ACAAS8.thr4, ACAAS8.thr4)*t4 ACAAS9 | c(NA, NA)*t1 + c(ACAAS9.thr1, ACAAS9.thr1)*t1 ACAAS9 | c(NA, NA)*t2 + c(ACAAS9.thr2, ACAAS9.thr2)*t2 ACAAS9 | c(NA, NA)*t3 + c(ACAAS9.thr3, ACAAS9.thr3)*t3 ACAAS9 | c(NA, NA)*t4 + c(ACAAS9.thr4, ACAAS9.thr4)*t4 ACAAS10 | c(NA, NA)*t1 + c(ACAAS10.thr1, ACAAS10.thr1)*t1 ACAAS10 | c(NA, NA)*t2 + c(ACAAS10.thr2, ACAAS10.thr2)*t2 ACAAS10 | c(NA, NA)*t3 + c(ACAAS10.thr3, ACAAS10.thr3)*t3 ACAAS10 | c(NA, NA)*t4 + c(ACAAS10.thr4, ACAAS10.thr4)*t4 ACAAS11 | c(NA, NA)*t1 + c(ACAAS11.thr1, ACAAS11.thr1)*t1 ACAAS11 | c(NA, NA)*t2 + c(ACAAS11.thr2, ACAAS11.thr2)*t2 ACAAS11 | c(NA, NA)*t3 + c(ACAAS11.thr3, ACAAS11.thr3)*t3 ACAAS11 | c(NA, NA)*t4 + c(ACAAS11.thr4, ACAAS11.thr4)*t4 ACAAS12 | c(NA, NA)*t1 + c(ACAAS12.thr1, ACAAS12.thr1)*t1 ACAAS12 | c(NA, NA)*t2 + c(ACAAS12.thr2, ACAAS12.thr2)*t2 ACAAS12 | c(NA, NA)*t3 + c(ACAAS12.thr3, ACAAS12.thr3)*t3 ACAAS12 | c(NA, NA)*t4 + c(ACAAS12.thr4, ACAAS12.thr4)*t4 ## INTERCEPTS: ACAAS1 ~ c(0, NA)*1 + c(nu.1.g1, nu.1.g2)*1 ACAAS2 ~ c(0, NA)*1 + c(nu.2.g1, nu.2.g2)*1 ACAAS3 ~ c(0, NA)*1 + c(nu.3.g1, nu.3.g2)*1 ACAAS4 ~ c(0, NA)*1 + c(nu.4.g1, nu.4.g2)*1 ACAAS5 ~ c(0, NA)*1 + c(nu.5.g1, nu.5.g2)*1 ACAAS6 ~ c(0, NA)*1 + c(nu.6.g1, nu.6.g2)*1 ACAAS7 ~ c(0, NA)*1 + c(nu.7.g1, nu.7.g2)*1 ACAAS8 ~ c(0, NA)*1 + c(nu.8.g1, nu.8.g2)*1 ACAAS9 ~ c(0, NA)*1 + c(nu.9.g1, nu.9.g2)*1 ACAAS10 ~ c(0, NA)*1 + c(nu.10.g1, nu.10.g2)*1 ACAAS11 ~ c(0, NA)*1 + c(nu.11.g1, nu.11.g2)*1 ACAAS12 ~ c(0, NA)*1 + c(nu.12.g1, nu.12.g2)*1 ## UNIQUE-FACTOR VARIANCES: ACAAS1 ~~ c(1, NA)*ACAAS1 + c(theta.1_1.g1, theta.1_1.g2)*ACAAS1 ACAAS2 ~~ c(1, NA)*ACAAS2 + c(theta.2_2.g1, theta.2_2.g2)*ACAAS2 ACAAS3 ~~ c(1, NA)*ACAAS3 + c(theta.3_3.g1, theta.3_3.g2)*ACAAS3 ACAAS4 ~~ c(1, NA)*ACAAS4 + c(theta.4_4.g1, theta.4_4.g2)*ACAAS4 ACAAS5 ~~ c(1, NA)*ACAAS5 + c(theta.5_5.g1, theta.5_5.g2)*ACAAS5 ACAAS6 ~~ c(1, NA)*ACAAS6 + c(theta.6_6.g1, theta.6_6.g2)*ACAAS6 ACAAS7 ~~ c(1, NA)*ACAAS7 + c(theta.7_7.g1, theta.7_7.g2)*ACAAS7 ACAAS8 ~~ c(1, NA)*ACAAS8 + c(theta.8_8.g1, theta.8_8.g2)*ACAAS8 ACAAS9 ~~ c(1, NA)*ACAAS9 + c(theta.9_9.g1, theta.9_9.g2)*ACAAS9 ACAAS10 ~~ c(1, NA)*ACAAS10 + c(theta.10_10.g1, theta.10_10.g2)*ACAAS10 ACAAS11 ~~ c(1, NA)*ACAAS11 + c(theta.11_11.g1, theta.11_11.g2)*ACAAS11 ACAAS12 ~~ c(1, NA)*ACAAS12 + c(theta.12_12.g1, theta.12_12.g2)*ACAAS12 ## UNIQUE-FACTOR COVARIANCES: ACAAS1 ~~ c(NA, NA)*ACAAS2 + c(theta.2_1.g1, theta.2_1.g2)*ACAAS2 ACAAS7 ~~ c(NA, NA)*ACAAS9 + c(theta.9_7.g1, theta.9_7.g2)*ACAAS9 ## LATENT MEANS/INTERCEPTS: concern ~ c(0, 0)*1 + c(alpha.1.g1, alpha.1.g2)*1 control ~ c(0, NA)*1 + c(alpha.2.g1, alpha.2.g2)*1 curiosity ~ c(0, NA)*1 + c(alpha.3.g1, alpha.3.g2)*1 confidence ~ c(0, NA)*1 + c(alpha.4.g1, alpha.4.g2)*1 caradapt ~ c(0, NA)*1 + c(alpha.5.g1, alpha.5.g2)*1 ## COMMON-FACTOR VARIANCES: concern ~~ c(NA, NA)*concern + c(psi.1_1.g1, psi.1_1.g2)*concern control ~~ c(NA, NA)*control + c(psi.2_2.g1, psi.2_2.g2)*control curiosity ~~ c(NA, NA)*curiosity + c(psi.3_3.g1, psi.3_3.g2)*curiosity confidence ~~ c(NA, NA)*confidence + c(psi.4_4.g1, psi.4_4.g2)*confidence caradapt ~~ c(NA, NA)*caradapt + c(psi.5_5.g1, psi.5_5.g2)*caradapt ## COMMON-FACTOR COVARIANCES: concern ~~ c(0, 0)*control + c(psi.2_1.g1, psi.2_1.g2)*control concern ~~ c(0, 0)*curiosity + c(psi.3_1.g1, psi.3_1.g2)*curiosity concern ~~ c(0, 0)*confidence + c(psi.4_1.g1, psi.4_1.g2)*confidence concern ~~ c(0, 0)*caradapt + c(psi.5_1.g1, psi.5_1.g2)*caradapt control ~~ c(0, 0)*curiosity + c(psi.3_2.g1, psi.3_2.g2)*curiosity control ~~ c(0, 0)*confidence + c(psi.4_2.g1, psi.4_2.g2)*confidence control ~~ c(0, 0)*caradapt + c(psi.5_2.g1, psi.5_2.g2)*caradapt curiosity ~~ c(0, 0)*confidence + c(psi.4_3.g1, psi.4_3.g2)*confidence curiosity ~~ c(0, 0)*caradapt + c(psi.5_3.g1, psi.5_3.g2)*caradapt confidence ~~ c(0, 0)*caradapt + c(psi.5_4.g1, psi.5_4.g2)*caradapt " ## fit model to data fit.metric_2l <- cfa(model = mod.metric_2l, data = ds_w1, group = "ASEX", ordered = T, parameterization = "theta") ``` ] --- # Measurement Invariance ## Sex **Scalar (second-order) invariance model**: equal thresholds, loadings, structural weights and .orange[intercepts (of first-order latent factors)] across groups or repeated measures .scroll-box-20[ ```r mod.scalar <- " ## LOADINGS: concern =~ c(1, 1)*ACAAS1 + c(lambda.1_1, lambda.1_1)*ACAAS1 concern =~ c(NA, NA)*ACAAS2 + c(lambda.2_1, lambda.2_1)*ACAAS2 concern =~ c(NA, NA)*ACAAS3 + c(lambda.3_1, lambda.3_1)*ACAAS3 control =~ c(1, 1)*ACAAS4 + c(lambda.4_2, lambda.4_2)*ACAAS4 control =~ c(NA, NA)*ACAAS5 + c(lambda.5_2, lambda.5_2)*ACAAS5 control =~ c(NA, NA)*ACAAS6 + c(lambda.6_2, lambda.6_2)*ACAAS6 curiosity =~ c(1, 1)*ACAAS7 + c(lambda.7_3, lambda.7_3)*ACAAS7 curiosity =~ c(NA, NA)*ACAAS8 + c(lambda.8_3, lambda.8_3)*ACAAS8 curiosity =~ c(NA, NA)*ACAAS9 + c(lambda.9_3, lambda.9_3)*ACAAS9 confidence =~ c(1, 1)*ACAAS10 + c(lambda.10_4, lambda.10_4)*ACAAS10 confidence =~ c(NA, NA)*ACAAS11 + c(lambda.11_4, lambda.11_4)*ACAAS11 confidence =~ c(NA, NA)*ACAAS12 + c(lambda.12_4, lambda.12_4)*ACAAS12 caradapt =~ c(1, 1)*concern + c(beta.1_5, beta.1_5)*concern caradapt =~ c(NA, NA)*control + c(beta.2_5, beta.2_5)*control caradapt =~ c(NA, NA)*curiosity + c(beta.3_5, beta.3_5)*curiosity caradapt =~ c(NA, NA)*confidence + c(beta.4_5, beta.4_5)*confidence ## THRESHOLDS: ACAAS1 | c(NA, NA)*t1 + c(ACAAS1.thr1, ACAAS1.thr1)*t1 ACAAS1 | c(NA, NA)*t2 + c(ACAAS1.thr2, ACAAS1.thr2)*t2 ACAAS1 | c(NA, NA)*t3 + c(ACAAS1.thr3, ACAAS1.thr3)*t3 ACAAS1 | c(NA, NA)*t4 + c(ACAAS1.thr4, ACAAS1.thr4)*t4 ACAAS2 | c(NA, NA)*t1 + c(ACAAS2.thr1, ACAAS2.thr1)*t1 ACAAS2 | c(NA, NA)*t2 + c(ACAAS2.thr2, ACAAS2.thr2)*t2 ACAAS2 | c(NA, NA)*t3 + c(ACAAS2.thr3, ACAAS2.thr3)*t3 ACAAS2 | c(NA, NA)*t4 + c(ACAAS2.thr4, ACAAS2.thr4)*t4 ACAAS3 | c(NA, NA)*t1 + c(ACAAS3.thr1, ACAAS3.thr1)*t1 ACAAS3 | c(NA, NA)*t2 + c(ACAAS3.thr2, ACAAS3.thr2)*t2 ACAAS3 | c(NA, NA)*t3 + c(ACAAS3.thr3, ACAAS3.thr3)*t3 ACAAS3 | c(NA, NA)*t4 + c(ACAAS3.thr4, ACAAS3.thr4)*t4 ACAAS4 | c(NA, NA)*t1 + c(ACAAS4.thr1, ACAAS4.thr1)*t1 ACAAS4 | c(NA, NA)*t2 + c(ACAAS4.thr2, ACAAS4.thr2)*t2 ACAAS4 | c(NA, NA)*t3 + c(ACAAS4.thr3, ACAAS4.thr3)*t3 ACAAS4 | c(NA, NA)*t4 + c(ACAAS4.thr4, ACAAS4.thr4)*t4 ACAAS5 | c(NA, NA)*t1 + c(ACAAS5.thr1, ACAAS5.thr1)*t1 ACAAS5 | c(NA, NA)*t2 + c(ACAAS5.thr2, ACAAS5.thr2)*t2 ACAAS5 | c(NA, NA)*t3 + c(ACAAS5.thr3, ACAAS5.thr3)*t3 ACAAS5 | c(NA, NA)*t4 + c(ACAAS5.thr4, ACAAS5.thr4)*t4 ACAAS6 | c(NA, NA)*t1 + c(ACAAS6.thr1, ACAAS6.thr1)*t1 ACAAS6 | c(NA, NA)*t2 + c(ACAAS6.thr2, ACAAS6.thr2)*t2 ACAAS6 | c(NA, NA)*t3 + c(ACAAS6.thr3, ACAAS6.thr3)*t3 ACAAS6 | c(NA, NA)*t4 + c(ACAAS6.thr4, ACAAS6.thr4)*t4 ACAAS7 | c(NA, NA)*t1 + c(ACAAS7.thr1, ACAAS7.thr1)*t1 ACAAS7 | c(NA, NA)*t2 + c(ACAAS7.thr2, ACAAS7.thr2)*t2 ACAAS7 | c(NA, NA)*t3 + c(ACAAS7.thr3, ACAAS7.thr3)*t3 ACAAS7 | c(NA, NA)*t4 + c(ACAAS7.thr4, ACAAS7.thr4)*t4 ACAAS8 | c(NA, NA)*t1 + c(ACAAS8.thr1, ACAAS8.thr1)*t1 ACAAS8 | c(NA, NA)*t2 + c(ACAAS8.thr2, ACAAS8.thr2)*t2 ACAAS8 | c(NA, NA)*t3 + c(ACAAS8.thr3, ACAAS8.thr3)*t3 ACAAS8 | c(NA, NA)*t4 + c(ACAAS8.thr4, ACAAS8.thr4)*t4 ACAAS9 | c(NA, NA)*t1 + c(ACAAS9.thr1, ACAAS9.thr1)*t1 ACAAS9 | c(NA, NA)*t2 + c(ACAAS9.thr2, ACAAS9.thr2)*t2 ACAAS9 | c(NA, NA)*t3 + c(ACAAS9.thr3, ACAAS9.thr3)*t3 ACAAS9 | c(NA, NA)*t4 + c(ACAAS9.thr4, ACAAS9.thr4)*t4 ACAAS10 | c(NA, NA)*t1 + c(ACAAS10.thr1, ACAAS10.thr1)*t1 ACAAS10 | c(NA, NA)*t2 + c(ACAAS10.thr2, ACAAS10.thr2)*t2 ACAAS10 | c(NA, NA)*t3 + c(ACAAS10.thr3, ACAAS10.thr3)*t3 ACAAS10 | c(NA, NA)*t4 + c(ACAAS10.thr4, ACAAS10.thr4)*t4 ACAAS11 | c(NA, NA)*t1 + c(ACAAS11.thr1, ACAAS11.thr1)*t1 ACAAS11 | c(NA, NA)*t2 + c(ACAAS11.thr2, ACAAS11.thr2)*t2 ACAAS11 | c(NA, NA)*t3 + c(ACAAS11.thr3, ACAAS11.thr3)*t3 ACAAS11 | c(NA, NA)*t4 + c(ACAAS11.thr4, ACAAS11.thr4)*t4 ACAAS12 | c(NA, NA)*t1 + c(ACAAS12.thr1, ACAAS12.thr1)*t1 ACAAS12 | c(NA, NA)*t2 + c(ACAAS12.thr2, ACAAS12.thr2)*t2 ACAAS12 | c(NA, NA)*t3 + c(ACAAS12.thr3, ACAAS12.thr3)*t3 ACAAS12 | c(NA, NA)*t4 + c(ACAAS12.thr4, ACAAS12.thr4)*t4 ## INTERCEPTS: ACAAS1 ~ c(0, 0)*1 + c(nu.1, nu.1)*1 ACAAS2 ~ c(0, 0)*1 + c(nu.2, nu.2)*1 ACAAS3 ~ c(0, 0)*1 + c(nu.3, nu.3)*1 ACAAS4 ~ c(0, 0)*1 + c(nu.4, nu.4)*1 ACAAS5 ~ c(0, 0)*1 + c(nu.5, nu.5)*1 ACAAS6 ~ c(0, 0)*1 + c(nu.6, nu.6)*1 ACAAS7 ~ c(0, 0)*1 + c(nu.7, nu.7)*1 ACAAS8 ~ c(0, 0)*1 + c(nu.8, nu.8)*1 ACAAS9 ~ c(0, 0)*1 + c(nu.9, nu.9)*1 ACAAS10 ~ c(0, 0)*1 + c(nu.10, nu.10)*1 ACAAS11 ~ c(0, 0)*1 + c(nu.11, nu.11)*1 ACAAS12 ~ c(0, 0)*1 + c(nu.12, nu.12)*1 ## UNIQUE-FACTOR VARIANCES: ACAAS1 ~~ c(1, NA)*ACAAS1 + c(theta.1_1.g1, theta.1_1.g2)*ACAAS1 ACAAS2 ~~ c(1, NA)*ACAAS2 + c(theta.2_2.g1, theta.2_2.g2)*ACAAS2 ACAAS3 ~~ c(1, NA)*ACAAS3 + c(theta.3_3.g1, theta.3_3.g2)*ACAAS3 ACAAS4 ~~ c(1, NA)*ACAAS4 + c(theta.4_4.g1, theta.4_4.g2)*ACAAS4 ACAAS5 ~~ c(1, NA)*ACAAS5 + c(theta.5_5.g1, theta.5_5.g2)*ACAAS5 ACAAS6 ~~ c(1, NA)*ACAAS6 + c(theta.6_6.g1, theta.6_6.g2)*ACAAS6 ACAAS7 ~~ c(1, NA)*ACAAS7 + c(theta.7_7.g1, theta.7_7.g2)*ACAAS7 ACAAS8 ~~ c(1, NA)*ACAAS8 + c(theta.8_8.g1, theta.8_8.g2)*ACAAS8 ACAAS9 ~~ c(1, NA)*ACAAS9 + c(theta.9_9.g1, theta.9_9.g2)*ACAAS9 ACAAS10 ~~ c(1, NA)*ACAAS10 + c(theta.10_10.g1, theta.10_10.g2)*ACAAS10 ACAAS11 ~~ c(1, NA)*ACAAS11 + c(theta.11_11.g1, theta.11_11.g2)*ACAAS11 ACAAS12 ~~ c(1, NA)*ACAAS12 + c(theta.12_12.g1, theta.12_12.g2)*ACAAS12 ## UNIQUE-FACTOR COVARIANCES: ACAAS1 ~~ c(NA, NA)*ACAAS2 + c(theta.2_1.g1, theta.2_1.g2)*ACAAS2 ACAAS7 ~~ c(NA, NA)*ACAAS9 + c(theta.9_7.g1, theta.9_7.g2)*ACAAS9 ## LATENT MEANS/INTERCEPTS: concern ~ c(0, 0)*1 + c(alpha.1.g1, alpha.1.g2)*1 control ~ c(0, NA)*1 + c(alpha.2.g1, alpha.2.g2)*1 curiosity ~ c(0, NA)*1 + c(alpha.3.g1, alpha.3.g2)*1 confidence ~ c(0, NA)*1 + c(alpha.4.g1, alpha.4.g2)*1 caradapt ~ c(0, NA)*1 + c(alpha.5.g1, alpha.5.g2)*1 ## COMMON-FACTOR VARIANCES: concern ~~ c(NA, NA)*concern + c(psi.1_1.g1, psi.1_1.g2)*concern control ~~ c(NA, NA)*control + c(psi.2_2.g1, psi.2_2.g2)*control curiosity ~~ c(NA, NA)*curiosity + c(psi.3_3.g1, psi.3_3.g2)*curiosity confidence ~~ c(NA, NA)*confidence + c(psi.4_4.g1, psi.4_4.g2)*confidence caradapt ~~ c(NA, NA)*caradapt + c(psi.5_5.g1, psi.5_5.g2)*caradapt ## COMMON-FACTOR COVARIANCES: concern ~~ c(0, 0)*control + c(psi.2_1.g1, psi.2_1.g2)*control concern ~~ c(0, 0)*curiosity + c(psi.3_1.g1, psi.3_1.g2)*curiosity concern ~~ c(0, 0)*confidence + c(psi.4_1.g1, psi.4_1.g2)*confidence concern ~~ c(0, 0)*caradapt + c(psi.5_1.g1, psi.5_1.g2)*caradapt control ~~ c(0, 0)*curiosity + c(psi.3_2.g1, psi.3_2.g2)*curiosity control ~~ c(0, 0)*confidence + c(psi.4_2.g1, psi.4_2.g2)*confidence control ~~ c(0, 0)*caradapt + c(psi.5_2.g1, psi.5_2.g2)*caradapt curiosity ~~ c(0, 0)*confidence + c(psi.4_3.g1, psi.4_3.g2)*confidence curiosity ~~ c(0, 0)*caradapt + c(psi.5_3.g1, psi.5_3.g2)*caradapt confidence ~~ c(0, 0)*caradapt + c(psi.5_4.g1, psi.5_4.g2)*caradapt " ## fit model to data fit.scalar <- cfa(model = mod.scalar, data = ds_w1, group = "ASEX", ordered = T, parameterization = "theta") ``` ] --- # Measurement Invariance ## Sex **Means invariance model**: equal thresholds, loadings, structural weights, intercepts (of first-order latent factors) and .orange[means] across groups or repeated measures .scroll-box-20[ ```r mod.means <- " ## LOADINGS: concern =~ c(1, 1)*ACAAS1 + c(lambda.1_1, lambda.1_1)*ACAAS1 concern =~ c(NA, NA)*ACAAS2 + c(lambda.2_1, lambda.2_1)*ACAAS2 concern =~ c(NA, NA)*ACAAS3 + c(lambda.3_1, lambda.3_1)*ACAAS3 control =~ c(1, 1)*ACAAS4 + c(lambda.4_2, lambda.4_2)*ACAAS4 control =~ c(NA, NA)*ACAAS5 + c(lambda.5_2, lambda.5_2)*ACAAS5 control =~ c(NA, NA)*ACAAS6 + c(lambda.6_2, lambda.6_2)*ACAAS6 curiosity =~ c(1, 1)*ACAAS7 + c(lambda.7_3, lambda.7_3)*ACAAS7 curiosity =~ c(NA, NA)*ACAAS8 + c(lambda.8_3, lambda.8_3)*ACAAS8 curiosity =~ c(NA, NA)*ACAAS9 + c(lambda.9_3, lambda.9_3)*ACAAS9 confidence =~ c(1, 1)*ACAAS10 + c(lambda.10_4, lambda.10_4)*ACAAS10 confidence =~ c(NA, NA)*ACAAS11 + c(lambda.11_4, lambda.11_4)*ACAAS11 confidence =~ c(NA, NA)*ACAAS12 + c(lambda.12_4, lambda.12_4)*ACAAS12 caradapt =~ c(1, 1)*concern + c(beta.1_5, beta.1_5)*concern caradapt =~ c(NA, NA)*control + c(beta.2_5, beta.2_5)*control caradapt =~ c(NA, NA)*curiosity + c(beta.3_5, beta.3_5)*curiosity caradapt =~ c(NA, NA)*confidence + c(beta.4_5, beta.4_5)*confidence ## THRESHOLDS: ACAAS1 | c(NA, NA)*t1 + c(ACAAS1.thr1, ACAAS1.thr1)*t1 ACAAS1 | c(NA, NA)*t2 + c(ACAAS1.thr2, ACAAS1.thr2)*t2 ACAAS1 | c(NA, NA)*t3 + c(ACAAS1.thr3, ACAAS1.thr3)*t3 ACAAS1 | c(NA, NA)*t4 + c(ACAAS1.thr4, ACAAS1.thr4)*t4 ACAAS2 | c(NA, NA)*t1 + c(ACAAS2.thr1, ACAAS2.thr1)*t1 ACAAS2 | c(NA, NA)*t2 + c(ACAAS2.thr2, ACAAS2.thr2)*t2 ACAAS2 | c(NA, NA)*t3 + c(ACAAS2.thr3, ACAAS2.thr3)*t3 ACAAS2 | c(NA, NA)*t4 + c(ACAAS2.thr4, ACAAS2.thr4)*t4 ACAAS3 | c(NA, NA)*t1 + c(ACAAS3.thr1, ACAAS3.thr1)*t1 ACAAS3 | c(NA, NA)*t2 + c(ACAAS3.thr2, ACAAS3.thr2)*t2 ACAAS3 | c(NA, NA)*t3 + c(ACAAS3.thr3, ACAAS3.thr3)*t3 ACAAS3 | c(NA, NA)*t4 + c(ACAAS3.thr4, ACAAS3.thr4)*t4 ACAAS4 | c(NA, NA)*t1 + c(ACAAS4.thr1, ACAAS4.thr1)*t1 ACAAS4 | c(NA, NA)*t2 + c(ACAAS4.thr2, ACAAS4.thr2)*t2 ACAAS4 | c(NA, NA)*t3 + c(ACAAS4.thr3, ACAAS4.thr3)*t3 ACAAS4 | c(NA, NA)*t4 + c(ACAAS4.thr4, ACAAS4.thr4)*t4 ACAAS5 | c(NA, NA)*t1 + c(ACAAS5.thr1, ACAAS5.thr1)*t1 ACAAS5 | c(NA, NA)*t2 + c(ACAAS5.thr2, ACAAS5.thr2)*t2 ACAAS5 | c(NA, NA)*t3 + c(ACAAS5.thr3, ACAAS5.thr3)*t3 ACAAS5 | c(NA, NA)*t4 + c(ACAAS5.thr4, ACAAS5.thr4)*t4 ACAAS6 | c(NA, NA)*t1 + c(ACAAS6.thr1, ACAAS6.thr1)*t1 ACAAS6 | c(NA, NA)*t2 + c(ACAAS6.thr2, ACAAS6.thr2)*t2 ACAAS6 | c(NA, NA)*t3 + c(ACAAS6.thr3, ACAAS6.thr3)*t3 ACAAS6 | c(NA, NA)*t4 + c(ACAAS6.thr4, ACAAS6.thr4)*t4 ACAAS7 | c(NA, NA)*t1 + c(ACAAS7.thr1, ACAAS7.thr1)*t1 ACAAS7 | c(NA, NA)*t2 + c(ACAAS7.thr2, ACAAS7.thr2)*t2 ACAAS7 | c(NA, NA)*t3 + c(ACAAS7.thr3, ACAAS7.thr3)*t3 ACAAS7 | c(NA, NA)*t4 + c(ACAAS7.thr4, ACAAS7.thr4)*t4 ACAAS8 | c(NA, NA)*t1 + c(ACAAS8.thr1, ACAAS8.thr1)*t1 ACAAS8 | c(NA, NA)*t2 + c(ACAAS8.thr2, ACAAS8.thr2)*t2 ACAAS8 | c(NA, NA)*t3 + c(ACAAS8.thr3, ACAAS8.thr3)*t3 ACAAS8 | c(NA, NA)*t4 + c(ACAAS8.thr4, ACAAS8.thr4)*t4 ACAAS9 | c(NA, NA)*t1 + c(ACAAS9.thr1, ACAAS9.thr1)*t1 ACAAS9 | c(NA, NA)*t2 + c(ACAAS9.thr2, ACAAS9.thr2)*t2 ACAAS9 | c(NA, NA)*t3 + c(ACAAS9.thr3, ACAAS9.thr3)*t3 ACAAS9 | c(NA, NA)*t4 + c(ACAAS9.thr4, ACAAS9.thr4)*t4 ACAAS10 | c(NA, NA)*t1 + c(ACAAS10.thr1, ACAAS10.thr1)*t1 ACAAS10 | c(NA, NA)*t2 + c(ACAAS10.thr2, ACAAS10.thr2)*t2 ACAAS10 | c(NA, NA)*t3 + c(ACAAS10.thr3, ACAAS10.thr3)*t3 ACAAS10 | c(NA, NA)*t4 + c(ACAAS10.thr4, ACAAS10.thr4)*t4 ACAAS11 | c(NA, NA)*t1 + c(ACAAS11.thr1, ACAAS11.thr1)*t1 ACAAS11 | c(NA, NA)*t2 + c(ACAAS11.thr2, ACAAS11.thr2)*t2 ACAAS11 | c(NA, NA)*t3 + c(ACAAS11.thr3, ACAAS11.thr3)*t3 ACAAS11 | c(NA, NA)*t4 + c(ACAAS11.thr4, ACAAS11.thr4)*t4 ACAAS12 | c(NA, NA)*t1 + c(ACAAS12.thr1, ACAAS12.thr1)*t1 ACAAS12 | c(NA, NA)*t2 + c(ACAAS12.thr2, ACAAS12.thr2)*t2 ACAAS12 | c(NA, NA)*t3 + c(ACAAS12.thr3, ACAAS12.thr3)*t3 ACAAS12 | c(NA, NA)*t4 + c(ACAAS12.thr4, ACAAS12.thr4)*t4 ## INTERCEPTS: ACAAS1 ~ c(0, 0)*1 + c(nu.1, nu.1)*1 ACAAS2 ~ c(0, 0)*1 + c(nu.2, nu.2)*1 ACAAS3 ~ c(0, 0)*1 + c(nu.3, nu.3)*1 ACAAS4 ~ c(0, 0)*1 + c(nu.4, nu.4)*1 ACAAS5 ~ c(0, 0)*1 + c(nu.5, nu.5)*1 ACAAS6 ~ c(0, 0)*1 + c(nu.6, nu.6)*1 ACAAS7 ~ c(0, 0)*1 + c(nu.7, nu.7)*1 ACAAS8 ~ c(0, 0)*1 + c(nu.8, nu.8)*1 ACAAS9 ~ c(0, 0)*1 + c(nu.9, nu.9)*1 ACAAS10 ~ c(0, 0)*1 + c(nu.10, nu.10)*1 ACAAS11 ~ c(0, 0)*1 + c(nu.11, nu.11)*1 ACAAS12 ~ c(0, 0)*1 + c(nu.12, nu.12)*1 ## UNIQUE-FACTOR VARIANCES: ACAAS1 ~~ c(1, NA)*ACAAS1 + c(theta.1_1.g1, theta.1_1.g2)*ACAAS1 ACAAS2 ~~ c(1, NA)*ACAAS2 + c(theta.2_2.g1, theta.2_2.g2)*ACAAS2 ACAAS3 ~~ c(1, NA)*ACAAS3 + c(theta.3_3.g1, theta.3_3.g2)*ACAAS3 ACAAS4 ~~ c(1, NA)*ACAAS4 + c(theta.4_4.g1, theta.4_4.g2)*ACAAS4 ACAAS5 ~~ c(1, NA)*ACAAS5 + c(theta.5_5.g1, theta.5_5.g2)*ACAAS5 ACAAS6 ~~ c(1, NA)*ACAAS6 + c(theta.6_6.g1, theta.6_6.g2)*ACAAS6 ACAAS7 ~~ c(1, NA)*ACAAS7 + c(theta.7_7.g1, theta.7_7.g2)*ACAAS7 ACAAS8 ~~ c(1, NA)*ACAAS8 + c(theta.8_8.g1, theta.8_8.g2)*ACAAS8 ACAAS9 ~~ c(1, NA)*ACAAS9 + c(theta.9_9.g1, theta.9_9.g2)*ACAAS9 ACAAS10 ~~ c(1, NA)*ACAAS10 + c(theta.10_10.g1, theta.10_10.g2)*ACAAS10 ACAAS11 ~~ c(1, NA)*ACAAS11 + c(theta.11_11.g1, theta.11_11.g2)*ACAAS11 ACAAS12 ~~ c(1, NA)*ACAAS12 + c(theta.12_12.g1, theta.12_12.g2)*ACAAS12 ## UNIQUE-FACTOR COVARIANCES: ACAAS1 ~~ c(NA, NA)*ACAAS2 + c(theta.2_1.g1, theta.2_1.g2)*ACAAS2 ACAAS7 ~~ c(NA, NA)*ACAAS9 + c(theta.9_7.g1, theta.9_7.g2)*ACAAS9 ## LATENT MEANS/INTERCEPTS: concern ~ c(0, 0)*1 + c(alpha.1, alpha.1)*1 control ~ c(0, 0)*1 + c(alpha.2, alpha.2)*1 curiosity ~ c(0, 0)*1 + c(alpha.3, alpha.3)*1 confidence ~ c(0, 0)*1 + c(alpha.4, alpha.4)*1 caradapt ~ c(0, 0)*1 + c(alpha.5, alpha.5)*1 ## COMMON-FACTOR VARIANCES: concern ~~ c(NA, NA)*concern + c(psi.1_1.g1, psi.1_1.g2)*concern control ~~ c(NA, NA)*control + c(psi.2_2.g1, psi.2_2.g2)*control curiosity ~~ c(NA, NA)*curiosity + c(psi.3_3.g1, psi.3_3.g2)*curiosity confidence ~~ c(NA, NA)*confidence + c(psi.4_4.g1, psi.4_4.g2)*confidence caradapt ~~ c(NA, NA)*caradapt + c(psi.5_5.g1, psi.5_5.g2)*caradapt ## COMMON-FACTOR COVARIANCES: concern ~~ c(0, 0)*control + c(psi.2_1.g1, psi.2_1.g2)*control concern ~~ c(0, 0)*curiosity + c(psi.3_1.g1, psi.3_1.g2)*curiosity concern ~~ c(0, 0)*confidence + c(psi.4_1.g1, psi.4_1.g2)*confidence concern ~~ c(0, 0)*caradapt + c(psi.5_1.g1, psi.5_1.g2)*caradapt control ~~ c(0, 0)*curiosity + c(psi.3_2.g1, psi.3_2.g2)*curiosity control ~~ c(0, 0)*confidence + c(psi.4_2.g1, psi.4_2.g2)*confidence control ~~ c(0, 0)*caradapt + c(psi.5_2.g1, psi.5_2.g2)*caradapt curiosity ~~ c(0, 0)*confidence + c(psi.4_3.g1, psi.4_3.g2)*confidence curiosity ~~ c(0, 0)*caradapt + c(psi.5_3.g1, psi.5_3.g2)*caradapt confidence ~~ c(0, 0)*caradapt + c(psi.5_4.g1, psi.5_4.g2)*caradapt " ## fit model to data fit.means <- cfa(model = mod.means, data = ds_w1, group = "ASEX", ordered = T, parameterization = "theta") ``` ] --- # Measurement Invariance ## Sex **Strict (second-order) invariance model**: equal thresholds, loadings, structural weights, intercepts (of first-order latent factors), means and .orange[disturbances] across groups or repeated measures .scroll-box-20[ ```r mod.strict_2l <- " ## LOADINGS: concern =~ c(1, 1)*ACAAS1 + c(lambda.1_1, lambda.1_1)*ACAAS1 concern =~ c(NA, NA)*ACAAS2 + c(lambda.2_1, lambda.2_1)*ACAAS2 concern =~ c(NA, NA)*ACAAS3 + c(lambda.3_1, lambda.3_1)*ACAAS3 control =~ c(1, 1)*ACAAS4 + c(lambda.4_2, lambda.4_2)*ACAAS4 control =~ c(NA, NA)*ACAAS5 + c(lambda.5_2, lambda.5_2)*ACAAS5 control =~ c(NA, NA)*ACAAS6 + c(lambda.6_2, lambda.6_2)*ACAAS6 curiosity =~ c(1, 1)*ACAAS7 + c(lambda.7_3, lambda.7_3)*ACAAS7 curiosity =~ c(NA, NA)*ACAAS8 + c(lambda.8_3, lambda.8_3)*ACAAS8 curiosity =~ c(NA, NA)*ACAAS9 + c(lambda.9_3, lambda.9_3)*ACAAS9 confidence =~ c(1, 1)*ACAAS10 + c(lambda.10_4, lambda.10_4)*ACAAS10 confidence =~ c(NA, NA)*ACAAS11 + c(lambda.11_4, lambda.11_4)*ACAAS11 confidence =~ c(NA, NA)*ACAAS12 + c(lambda.12_4, lambda.12_4)*ACAAS12 caradapt =~ c(1, 1)*concern + c(beta.1_5, beta.1_5)*concern caradapt =~ c(NA, NA)*control + c(beta.2_5, beta.2_5)*control caradapt =~ c(NA, NA)*curiosity + c(beta.3_5, beta.3_5)*curiosity caradapt =~ c(NA, NA)*confidence + c(beta.4_5, beta.4_5)*confidence ## THRESHOLDS: ACAAS1 | c(NA, NA)*t1 + c(ACAAS1.thr1, ACAAS1.thr1)*t1 ACAAS1 | c(NA, NA)*t2 + c(ACAAS1.thr2, ACAAS1.thr2)*t2 ACAAS1 | c(NA, NA)*t3 + c(ACAAS1.thr3, ACAAS1.thr3)*t3 ACAAS1 | c(NA, NA)*t4 + c(ACAAS1.thr4, ACAAS1.thr4)*t4 ACAAS2 | c(NA, NA)*t1 + c(ACAAS2.thr1, ACAAS2.thr1)*t1 ACAAS2 | c(NA, NA)*t2 + c(ACAAS2.thr2, ACAAS2.thr2)*t2 ACAAS2 | c(NA, NA)*t3 + c(ACAAS2.thr3, ACAAS2.thr3)*t3 ACAAS2 | c(NA, NA)*t4 + c(ACAAS2.thr4, ACAAS2.thr4)*t4 ACAAS3 | c(NA, NA)*t1 + c(ACAAS3.thr1, ACAAS3.thr1)*t1 ACAAS3 | c(NA, NA)*t2 + c(ACAAS3.thr2, ACAAS3.thr2)*t2 ACAAS3 | c(NA, NA)*t3 + c(ACAAS3.thr3, ACAAS3.thr3)*t3 ACAAS3 | c(NA, NA)*t4 + c(ACAAS3.thr4, ACAAS3.thr4)*t4 ACAAS4 | c(NA, NA)*t1 + c(ACAAS4.thr1, ACAAS4.thr1)*t1 ACAAS4 | c(NA, NA)*t2 + c(ACAAS4.thr2, ACAAS4.thr2)*t2 ACAAS4 | c(NA, NA)*t3 + c(ACAAS4.thr3, ACAAS4.thr3)*t3 ACAAS4 | c(NA, NA)*t4 + c(ACAAS4.thr4, ACAAS4.thr4)*t4 ACAAS5 | c(NA, NA)*t1 + c(ACAAS5.thr1, ACAAS5.thr1)*t1 ACAAS5 | c(NA, NA)*t2 + c(ACAAS5.thr2, ACAAS5.thr2)*t2 ACAAS5 | c(NA, NA)*t3 + c(ACAAS5.thr3, ACAAS5.thr3)*t3 ACAAS5 | c(NA, NA)*t4 + c(ACAAS5.thr4, ACAAS5.thr4)*t4 ACAAS6 | c(NA, NA)*t1 + c(ACAAS6.thr1, ACAAS6.thr1)*t1 ACAAS6 | c(NA, NA)*t2 + c(ACAAS6.thr2, ACAAS6.thr2)*t2 ACAAS6 | c(NA, NA)*t3 + c(ACAAS6.thr3, ACAAS6.thr3)*t3 ACAAS6 | c(NA, NA)*t4 + c(ACAAS6.thr4, ACAAS6.thr4)*t4 ACAAS7 | c(NA, NA)*t1 + c(ACAAS7.thr1, ACAAS7.thr1)*t1 ACAAS7 | c(NA, NA)*t2 + c(ACAAS7.thr2, ACAAS7.thr2)*t2 ACAAS7 | c(NA, NA)*t3 + c(ACAAS7.thr3, ACAAS7.thr3)*t3 ACAAS7 | c(NA, NA)*t4 + c(ACAAS7.thr4, ACAAS7.thr4)*t4 ACAAS8 | c(NA, NA)*t1 + c(ACAAS8.thr1, ACAAS8.thr1)*t1 ACAAS8 | c(NA, NA)*t2 + c(ACAAS8.thr2, ACAAS8.thr2)*t2 ACAAS8 | c(NA, NA)*t3 + c(ACAAS8.thr3, ACAAS8.thr3)*t3 ACAAS8 | c(NA, NA)*t4 + c(ACAAS8.thr4, ACAAS8.thr4)*t4 ACAAS9 | c(NA, NA)*t1 + c(ACAAS9.thr1, ACAAS9.thr1)*t1 ACAAS9 | c(NA, NA)*t2 + c(ACAAS9.thr2, ACAAS9.thr2)*t2 ACAAS9 | c(NA, NA)*t3 + c(ACAAS9.thr3, ACAAS9.thr3)*t3 ACAAS9 | c(NA, NA)*t4 + c(ACAAS9.thr4, ACAAS9.thr4)*t4 ACAAS10 | c(NA, NA)*t1 + c(ACAAS10.thr1, ACAAS10.thr1)*t1 ACAAS10 | c(NA, NA)*t2 + c(ACAAS10.thr2, ACAAS10.thr2)*t2 ACAAS10 | c(NA, NA)*t3 + c(ACAAS10.thr3, ACAAS10.thr3)*t3 ACAAS10 | c(NA, NA)*t4 + c(ACAAS10.thr4, ACAAS10.thr4)*t4 ACAAS11 | c(NA, NA)*t1 + c(ACAAS11.thr1, ACAAS11.thr1)*t1 ACAAS11 | c(NA, NA)*t2 + c(ACAAS11.thr2, ACAAS11.thr2)*t2 ACAAS11 | c(NA, NA)*t3 + c(ACAAS11.thr3, ACAAS11.thr3)*t3 ACAAS11 | c(NA, NA)*t4 + c(ACAAS11.thr4, ACAAS11.thr4)*t4 ACAAS12 | c(NA, NA)*t1 + c(ACAAS12.thr1, ACAAS12.thr1)*t1 ACAAS12 | c(NA, NA)*t2 + c(ACAAS12.thr2, ACAAS12.thr2)*t2 ACAAS12 | c(NA, NA)*t3 + c(ACAAS12.thr3, ACAAS12.thr3)*t3 ACAAS12 | c(NA, NA)*t4 + c(ACAAS12.thr4, ACAAS12.thr4)*t4 ## INTERCEPTS: ACAAS1 ~ c(0, 0)*1 + c(nu.1, nu.1)*1 ACAAS2 ~ c(0, 0)*1 + c(nu.2, nu.2)*1 ACAAS3 ~ c(0, 0)*1 + c(nu.3, nu.3)*1 ACAAS4 ~ c(0, 0)*1 + c(nu.4, nu.4)*1 ACAAS5 ~ c(0, 0)*1 + c(nu.5, nu.5)*1 ACAAS6 ~ c(0, 0)*1 + c(nu.6, nu.6)*1 ACAAS7 ~ c(0, 0)*1 + c(nu.7, nu.7)*1 ACAAS8 ~ c(0, 0)*1 + c(nu.8, nu.8)*1 ACAAS9 ~ c(0, 0)*1 + c(nu.9, nu.9)*1 ACAAS10 ~ c(0, 0)*1 + c(nu.10, nu.10)*1 ACAAS11 ~ c(0, 0)*1 + c(nu.11, nu.11)*1 ACAAS12 ~ c(0, 0)*1 + c(nu.12, nu.12)*1 ## UNIQUE-FACTOR VARIANCES: ACAAS1 ~~ c(1, NA)*ACAAS1 + c(theta.1_1.g1, theta.1_1.g2)*ACAAS1 ACAAS2 ~~ c(1, NA)*ACAAS2 + c(theta.2_2.g1, theta.2_2.g2)*ACAAS2 ACAAS3 ~~ c(1, NA)*ACAAS3 + c(theta.3_3.g1, theta.3_3.g2)*ACAAS3 ACAAS4 ~~ c(1, NA)*ACAAS4 + c(theta.4_4.g1, theta.4_4.g2)*ACAAS4 ACAAS5 ~~ c(1, NA)*ACAAS5 + c(theta.5_5.g1, theta.5_5.g2)*ACAAS5 ACAAS6 ~~ c(1, NA)*ACAAS6 + c(theta.6_6.g1, theta.6_6.g2)*ACAAS6 ACAAS7 ~~ c(1, NA)*ACAAS7 + c(theta.7_7.g1, theta.7_7.g2)*ACAAS7 ACAAS8 ~~ c(1, NA)*ACAAS8 + c(theta.8_8.g1, theta.8_8.g2)*ACAAS8 ACAAS9 ~~ c(1, NA)*ACAAS9 + c(theta.9_9.g1, theta.9_9.g2)*ACAAS9 ACAAS10 ~~ c(1, NA)*ACAAS10 + c(theta.10_10.g1, theta.10_10.g2)*ACAAS10 ACAAS11 ~~ c(1, NA)*ACAAS11 + c(theta.11_11.g1, theta.11_11.g2)*ACAAS11 ACAAS12 ~~ c(1, NA)*ACAAS12 + c(theta.12_12.g1, theta.12_12.g2)*ACAAS12 ## UNIQUE-FACTOR COVARIANCES: ACAAS1 ~~ c(NA, NA)*ACAAS2 + c(theta.2_1.g1, theta.2_1.g2)*ACAAS2 ACAAS7 ~~ c(NA, NA)*ACAAS9 + c(theta.9_7.g1, theta.9_7.g2)*ACAAS9 ## LATENT MEANS/INTERCEPTS: concern ~ c(0, 0)*1 + c(alpha.1.g1, alpha.1.g2)*1 control ~ c(0, NA)*1 + c(alpha.2.g1, alpha.2.g2)*1 curiosity ~ c(0, NA)*1 + c(alpha.3.g1, alpha.3.g2)*1 confidence ~ c(0, NA)*1 + c(alpha.4.g1, alpha.4.g2)*1 caradapt ~ c(0, NA)*1 + c(alpha.5.g1, alpha.5.g2)*1 ## COMMON-FACTOR VARIANCES: concern ~~ c(1, 1)*concern + c(psi.1_1.g1, psi.1_1.g2)*concern control ~~ c(1, 1)*control + c(psi.2_2.g1, psi.2_2.g2)*control curiosity ~~ c(1, 1)*curiosity + c(psi.3_3.g1, psi.3_3.g2)*curiosity confidence ~~ c(1, 1)*confidence + c(psi.4_4.g1, psi.4_4.g2)*confidence caradapt ~~ c(NA, NA)*caradapt + c(psi.5_5.g1, psi.5_5.g2)*caradapt ## COMMON-FACTOR COVARIANCES: concern ~~ c(0, 0)*control + c(psi.2_1.g1, psi.2_1.g2)*control concern ~~ c(0, 0)*curiosity + c(psi.3_1.g1, psi.3_1.g2)*curiosity concern ~~ c(0, 0)*confidence + c(psi.4_1.g1, psi.4_1.g2)*confidence concern ~~ c(0, 0)*caradapt + c(psi.5_1.g1, psi.5_1.g2)*caradapt control ~~ c(0, 0)*curiosity + c(psi.3_2.g1, psi.3_2.g2)*curiosity control ~~ c(0, 0)*confidence + c(psi.4_2.g1, psi.4_2.g2)*confidence control ~~ c(0, 0)*caradapt + c(psi.5_2.g1, psi.5_2.g2)*caradapt curiosity ~~ c(0, 0)*confidence + c(psi.4_3.g1, psi.4_3.g2)*confidence curiosity ~~ c(0, 0)*caradapt + c(psi.5_3.g1, psi.5_3.g2)*caradapt confidence ~~ c(0, 0)*caradapt + c(psi.5_4.g1, psi.5_4.g2)*caradapt" ## fit model to data fit.strict_2l <- cfa(model = mod.strict_2l, data = ds_w1, group = "ASEX", ordered = T, parameterization = "theta") ``` ] --- # Measurement Invariance ## Sex **Strict (first-order) invariance model**: equal thresholds, loadings, structural weights, intercepts (of first-order latent factors), means, disturbances and .orange[residuals] across groups or repeated measures .scroll-box-20[ ```r mod.strict_1l <- " ## LOADINGS: concern =~ c(1, 1)*ACAAS1 + c(lambda.1_1, lambda.1_1)*ACAAS1 concern =~ c(NA, NA)*ACAAS2 + c(lambda.2_1, lambda.2_1)*ACAAS2 concern =~ c(NA, NA)*ACAAS3 + c(lambda.3_1, lambda.3_1)*ACAAS3 control =~ c(1, 1)*ACAAS4 + c(lambda.4_2, lambda.4_2)*ACAAS4 control =~ c(NA, NA)*ACAAS5 + c(lambda.5_2, lambda.5_2)*ACAAS5 control =~ c(NA, NA)*ACAAS6 + c(lambda.6_2, lambda.6_2)*ACAAS6 curiosity =~ c(1, 1)*ACAAS7 + c(lambda.7_3, lambda.7_3)*ACAAS7 curiosity =~ c(NA, NA)*ACAAS8 + c(lambda.8_3, lambda.8_3)*ACAAS8 curiosity =~ c(NA, NA)*ACAAS9 + c(lambda.9_3, lambda.9_3)*ACAAS9 confidence =~ c(1, 1)*ACAAS10 + c(lambda.10_4, lambda.10_4)*ACAAS10 confidence =~ c(NA, NA)*ACAAS11 + c(lambda.11_4, lambda.11_4)*ACAAS11 confidence =~ c(NA, NA)*ACAAS12 + c(lambda.12_4, lambda.12_4)*ACAAS12 caradapt =~ c(1, 1)*concern + c(beta.1_5, beta.1_5)*concern caradapt =~ c(NA, NA)*control + c(beta.2_5, beta.2_5)*control caradapt =~ c(NA, NA)*curiosity + c(beta.3_5, beta.3_5)*curiosity caradapt =~ c(NA, NA)*confidence + c(beta.4_5, beta.4_5)*confidence ## THRESHOLDS: ACAAS1 | c(NA, NA)*t1 + c(ACAAS1.thr1, ACAAS1.thr1)*t1 ACAAS1 | c(NA, NA)*t2 + c(ACAAS1.thr2, ACAAS1.thr2)*t2 ACAAS1 | c(NA, NA)*t3 + c(ACAAS1.thr3, ACAAS1.thr3)*t3 ACAAS1 | c(NA, NA)*t4 + c(ACAAS1.thr4, ACAAS1.thr4)*t4 ACAAS2 | c(NA, NA)*t1 + c(ACAAS2.thr1, ACAAS2.thr1)*t1 ACAAS2 | c(NA, NA)*t2 + c(ACAAS2.thr2, ACAAS2.thr2)*t2 ACAAS2 | c(NA, NA)*t3 + c(ACAAS2.thr3, ACAAS2.thr3)*t3 ACAAS2 | c(NA, NA)*t4 + c(ACAAS2.thr4, ACAAS2.thr4)*t4 ACAAS3 | c(NA, NA)*t1 + c(ACAAS3.thr1, ACAAS3.thr1)*t1 ACAAS3 | c(NA, NA)*t2 + c(ACAAS3.thr2, ACAAS3.thr2)*t2 ACAAS3 | c(NA, NA)*t3 + c(ACAAS3.thr3, ACAAS3.thr3)*t3 ACAAS3 | c(NA, NA)*t4 + c(ACAAS3.thr4, ACAAS3.thr4)*t4 ACAAS4 | c(NA, NA)*t1 + c(ACAAS4.thr1, ACAAS4.thr1)*t1 ACAAS4 | c(NA, NA)*t2 + c(ACAAS4.thr2, ACAAS4.thr2)*t2 ACAAS4 | c(NA, NA)*t3 + c(ACAAS4.thr3, ACAAS4.thr3)*t3 ACAAS4 | c(NA, NA)*t4 + c(ACAAS4.thr4, ACAAS4.thr4)*t4 ACAAS5 | c(NA, NA)*t1 + c(ACAAS5.thr1, ACAAS5.thr1)*t1 ACAAS5 | c(NA, NA)*t2 + c(ACAAS5.thr2, ACAAS5.thr2)*t2 ACAAS5 | c(NA, NA)*t3 + c(ACAAS5.thr3, ACAAS5.thr3)*t3 ACAAS5 | c(NA, NA)*t4 + c(ACAAS5.thr4, ACAAS5.thr4)*t4 ACAAS6 | c(NA, NA)*t1 + c(ACAAS6.thr1, ACAAS6.thr1)*t1 ACAAS6 | c(NA, NA)*t2 + c(ACAAS6.thr2, ACAAS6.thr2)*t2 ACAAS6 | c(NA, NA)*t3 + c(ACAAS6.thr3, ACAAS6.thr3)*t3 ACAAS6 | c(NA, NA)*t4 + c(ACAAS6.thr4, ACAAS6.thr4)*t4 ACAAS7 | c(NA, NA)*t1 + c(ACAAS7.thr1, ACAAS7.thr1)*t1 ACAAS7 | c(NA, NA)*t2 + c(ACAAS7.thr2, ACAAS7.thr2)*t2 ACAAS7 | c(NA, NA)*t3 + c(ACAAS7.thr3, ACAAS7.thr3)*t3 ACAAS7 | c(NA, NA)*t4 + c(ACAAS7.thr4, ACAAS7.thr4)*t4 ACAAS8 | c(NA, NA)*t1 + c(ACAAS8.thr1, ACAAS8.thr1)*t1 ACAAS8 | c(NA, NA)*t2 + c(ACAAS8.thr2, ACAAS8.thr2)*t2 ACAAS8 | c(NA, NA)*t3 + c(ACAAS8.thr3, ACAAS8.thr3)*t3 ACAAS8 | c(NA, NA)*t4 + c(ACAAS8.thr4, ACAAS8.thr4)*t4 ACAAS9 | c(NA, NA)*t1 + c(ACAAS9.thr1, ACAAS9.thr1)*t1 ACAAS9 | c(NA, NA)*t2 + c(ACAAS9.thr2, ACAAS9.thr2)*t2 ACAAS9 | c(NA, NA)*t3 + c(ACAAS9.thr3, ACAAS9.thr3)*t3 ACAAS9 | c(NA, NA)*t4 + c(ACAAS9.thr4, ACAAS9.thr4)*t4 ACAAS10 | c(NA, NA)*t1 + c(ACAAS10.thr1, ACAAS10.thr1)*t1 ACAAS10 | c(NA, NA)*t2 + c(ACAAS10.thr2, ACAAS10.thr2)*t2 ACAAS10 | c(NA, NA)*t3 + c(ACAAS10.thr3, ACAAS10.thr3)*t3 ACAAS10 | c(NA, NA)*t4 + c(ACAAS10.thr4, ACAAS10.thr4)*t4 ACAAS11 | c(NA, NA)*t1 + c(ACAAS11.thr1, ACAAS11.thr1)*t1 ACAAS11 | c(NA, NA)*t2 + c(ACAAS11.thr2, ACAAS11.thr2)*t2 ACAAS11 | c(NA, NA)*t3 + c(ACAAS11.thr3, ACAAS11.thr3)*t3 ACAAS11 | c(NA, NA)*t4 + c(ACAAS11.thr4, ACAAS11.thr4)*t4 ACAAS12 | c(NA, NA)*t1 + c(ACAAS12.thr1, ACAAS12.thr1)*t1 ACAAS12 | c(NA, NA)*t2 + c(ACAAS12.thr2, ACAAS12.thr2)*t2 ACAAS12 | c(NA, NA)*t3 + c(ACAAS12.thr3, ACAAS12.thr3)*t3 ACAAS12 | c(NA, NA)*t4 + c(ACAAS12.thr4, ACAAS12.thr4)*t4 ## INTERCEPTS: ACAAS1 ~ c(0, 0)*1 + c(nu.1, nu.1)*1 ACAAS2 ~ c(0, 0)*1 + c(nu.2, nu.2)*1 ACAAS3 ~ c(0, 0)*1 + c(nu.3, nu.3)*1 ACAAS4 ~ c(0, 0)*1 + c(nu.4, nu.4)*1 ACAAS5 ~ c(0, 0)*1 + c(nu.5, nu.5)*1 ACAAS6 ~ c(0, 0)*1 + c(nu.6, nu.6)*1 ACAAS7 ~ c(0, 0)*1 + c(nu.7, nu.7)*1 ACAAS8 ~ c(0, 0)*1 + c(nu.8, nu.8)*1 ACAAS9 ~ c(0, 0)*1 + c(nu.9, nu.9)*1 ACAAS10 ~ c(0, 0)*1 + c(nu.10, nu.10)*1 ACAAS11 ~ c(0, 0)*1 + c(nu.11, nu.11)*1 ACAAS12 ~ c(0, 0)*1 + c(nu.12, nu.12)*1 ## UNIQUE-FACTOR VARIANCES: ACAAS1 ~~ c(1, 1)*ACAAS1 + c(theta.1_1, theta.1_1)*ACAAS1 ACAAS2 ~~ c(1, 1)*ACAAS2 + c(theta.2_2, theta.2_2)*ACAAS2 ACAAS3 ~~ c(1, 1)*ACAAS3 + c(theta.3_3, theta.3_3)*ACAAS3 ACAAS4 ~~ c(1, 1)*ACAAS4 + c(theta.4_4, theta.4_4)*ACAAS4 ACAAS5 ~~ c(1, 1)*ACAAS5 + c(theta.5_5, theta.5_5)*ACAAS5 ACAAS6 ~~ c(1, 1)*ACAAS6 + c(theta.6_6, theta.6_6)*ACAAS6 ACAAS7 ~~ c(1, 1)*ACAAS7 + c(theta.7_7, theta.7_7)*ACAAS7 ACAAS8 ~~ c(1, 1)*ACAAS8 + c(theta.8_8, theta.8_8)*ACAAS8 ACAAS9 ~~ c(1, 1)*ACAAS9 + c(theta.9_9, theta.9_9)*ACAAS9 ACAAS10 ~~ c(1, 1)*ACAAS10 + c(theta.10_10, theta.10_10)*ACAAS10 ACAAS11 ~~ c(1, 1)*ACAAS11 + c(theta.11_11, theta.11_11)*ACAAS11 ACAAS12 ~~ c(1, 1)*ACAAS12 + c(theta.12_12, theta.12_12)*ACAAS12 ## UNIQUE-FACTOR COVARIANCES: ACAAS1 ~~ c(NA, NA)*ACAAS2 + c(theta.2_1.g1, theta.2_1.g2)*ACAAS2 ACAAS7 ~~ c(NA, NA)*ACAAS9 + c(theta.9_7.g1, theta.9_7.g2)*ACAAS9 ## LATENT MEANS/INTERCEPTS: concern ~ c(0, 0)*1 + c(alpha.1.g1, alpha.1.g2)*1 control ~ c(0, NA)*1 + c(alpha.2.g1, alpha.2.g2)*1 curiosity ~ c(0, NA)*1 + c(alpha.3.g1, alpha.3.g2)*1 confidence ~ c(0, NA)*1 + c(alpha.4.g1, alpha.4.g2)*1 caradapt ~ c(0, NA)*1 + c(alpha.5.g1, alpha.5.g2)*1 ## COMMON-FACTOR VARIANCES: concern ~~ c(1, 1)*concern + c(psi.1_1.g1, psi.1_1.g2)*concern control ~~ c(1, 1)*control + c(psi.2_2.g1, psi.2_2.g2)*control curiosity ~~ c(1, 1)*curiosity + c(psi.3_3.g1, psi.3_3.g2)*curiosity confidence ~~ c(1, 1)*confidence + c(psi.4_4.g1, psi.4_4.g2)*confidence caradapt ~~ c(NA, NA)*caradapt + c(psi.5_5.g1, psi.5_5.g2)*caradapt ## COMMON-FACTOR COVARIANCES: concern ~~ c(0, 0)*control + c(psi.2_1.g1, psi.2_1.g2)*control concern ~~ c(0, 0)*curiosity + c(psi.3_1.g1, psi.3_1.g2)*curiosity concern ~~ c(0, 0)*confidence + c(psi.4_1.g1, psi.4_1.g2)*confidence concern ~~ c(0, 0)*caradapt + c(psi.5_1.g1, psi.5_1.g2)*caradapt control ~~ c(0, 0)*curiosity + c(psi.3_2.g1, psi.3_2.g2)*curiosity control ~~ c(0, 0)*confidence + c(psi.4_2.g1, psi.4_2.g2)*confidence control ~~ c(0, 0)*caradapt + c(psi.5_2.g1, psi.5_2.g2)*caradapt curiosity ~~ c(0, 0)*confidence + c(psi.4_3.g1, psi.4_3.g2)*confidence curiosity ~~ c(0, 0)*caradapt + c(psi.5_3.g1, psi.5_3.g2)*caradapt confidence ~~ c(0, 0)*caradapt + c(psi.5_4.g1, psi.5_4.g2)*caradapt" ## fit model to data fit.strict_1l <- cfa(model = mod.strict_1l, data = ds_w1, group = "ASEX", ordered = T, parameterization = "theta") ``` ] --- # Measurement Invariance ## Sex <table class="table" style="margin-left: auto; margin-right: auto;"> <thead> <tr> <th style="text-align:left;"> </th> <th style="text-align:left;"> \(\chi^2_{scaled}\) </th> <th style="text-align:right;"> \(df_{scaled}\) </th> <th style="text-align:left;"> \(p_{\Delta\chi^2}\) </th> <th style="text-align:left;"> \(CFI_{scaled}\) </th> <th style="text-align:left;"> \(\Delta CFI_{scaled}\) </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;"> Configural </td> <td style="text-align:left;"> 1,371.170 </td> <td style="text-align:right;"> 96 </td> <td style="text-align:left;"> - </td> <td style="text-align:left;"> 0.966 </td> <td style="text-align:left;"> - </td> </tr> <tr> <td style="text-align:left;"> Thresholds </td> <td style="text-align:left;"> 1,313.314 </td> <td style="text-align:right;"> 116 </td> <td style="text-align:left;"> .184 </td> <td style="text-align:left;"> 0.969 </td> <td style="text-align:left;"> 0.002 </td> </tr> <tr> <td style="text-align:left;"> Factor loadings </td> <td style="text-align:left;"> 1,225.955 </td> <td style="text-align:right;"> 124 </td> <td style="text-align:left;"> .674 </td> <td style="text-align:left;"> 0.971 </td> <td style="text-align:left;"> 0.003 </td> </tr> <tr> <td style="text-align:left;"> Structural weights </td> <td style="text-align:left;"> 1,106.789 </td> <td style="text-align:right;"> 127 </td> <td style="text-align:left;"> .086 </td> <td style="text-align:left;"> 0.974 </td> <td style="text-align:left;"> 0.003 </td> </tr> <tr> <td style="text-align:left;"> Intercepts (first-order) </td> <td style="text-align:left;"> 1,155.274 </td> <td style="text-align:right;"> 139 </td> <td style="text-align:left;"> < .001 </td> <td style="text-align:left;"> 0.973 </td> <td style="text-align:left;"> -0.001 </td> </tr> <tr> <td style="text-align:left;"> Latent means </td> <td style="text-align:left;"> 987.983 </td> <td style="text-align:right;"> 143 </td> <td style="text-align:left;"> < .001 </td> <td style="text-align:left;"> 0.978 </td> <td style="text-align:left;"> 0.005 </td> </tr> <tr> <td style="text-align:left;"> Disturbances </td> <td style="text-align:left;"> 1,467.391 </td> <td style="text-align:right;"> 147 </td> <td style="text-align:left;"> > .999 </td> <td style="text-align:left;"> 0.965 </td> <td style="text-align:left;"> -0.012 </td> </tr> <tr> <td style="text-align:left;"> Residuals </td> <td style="text-align:left;"> 1,441.118 </td> <td style="text-align:right;"> 159 </td> <td style="text-align:left;"> < .001 </td> <td style="text-align:left;"> 0.966 </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> --- # Measurement Invariance ## Wave 1 vs. Wave 2 <table class="table" style="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;"> 2,715.409 </td> <td style="text-align:right;"> 96 </td> <td style="text-align:left;"> - </td> <td style="text-align:left;"> 0.965 </td> <td style="text-align:left;"> - </td> </tr> <tr> <td style="text-align:left;"> Thresholds </td> <td style="text-align:left;"> 2,500.538 </td> <td style="text-align:right;"> 116 </td> <td style="text-align:left;"> .044 </td> <td style="text-align:left;"> 0.969 </td> <td style="text-align:left;"> 0.003 </td> </tr> <tr> <td style="text-align:left;"> Factor loadings </td> <td style="text-align:left;"> 2,359.375 </td> <td style="text-align:right;"> 124 </td> <td style="text-align:left;"> .141 </td> <td style="text-align:left;"> 0.971 </td> <td style="text-align:left;"> 0.002 </td> </tr> <tr> <td style="text-align:left;"> Structural weights </td> <td style="text-align:left;"> 2,089.867 </td> <td style="text-align:right;"> 127 </td> <td style="text-align:left;"> .815 </td> <td style="text-align:left;"> 0.974 </td> <td style="text-align:left;"> 0.004 </td> </tr> <tr> <td style="text-align:left;"> Intercepts (first-order) </td> <td style="text-align:left;"> 2,133.669 </td> <td style="text-align:right;"> 139 </td> <td style="text-align:left;"> < .001 </td> <td style="text-align:left;"> 0.974 </td> <td style="text-align:left;"> 0.000 </td> </tr> <tr> <td style="text-align:left;"> Latent means </td> <td style="text-align:left;"> 1,229.733 </td> <td style="text-align:right;"> 143 </td> <td style="text-align:left;"> .143 </td> <td style="text-align:left;"> 0.986 </td> <td style="text-align:left;"> 0.012 </td> </tr> <tr> <td style="text-align:left;"> Disturbances </td> <td style="text-align:left;"> 2,942.785 </td> <td style="text-align:right;"> 147 </td> <td style="text-align:left;"> < .001 </td> <td style="text-align:left;"> 0.963 </td> <td style="text-align:left;"> -0.023 </td> </tr> <tr> <td style="text-align:left;"> Residuals </td> <td style="text-align:left;"> 2,723.190 </td> <td style="text-align:right;"> 159 </td> <td style="text-align:left;"> < .001 </td> <td style="text-align:left;"> 0.966 </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> --- class: inverse, center, middle # Validity Evidence based on the Relations to Other Variables <html><div style='float:left'></div><hr color='#EB811B' size=1px width=800px></html> --- exclude: true # Raw Correlations: Wave 1 ```r #caas-sf ds_w1$caa <- rowMeans(x = ds_w1[,caas_w1], na.rm = TRUE) #Stress-Related Growth Scale-15 ds_w1$growth <- rowMeans(x = ds_w1[,srgs15_items_w1], na.rm = TRUE) #Demographics #age #should not correlate #Fear of Losing Out Scale-4 #negative correlation #one dimension ds_w1$kiasuism <- rowMeans(x = ds_w1[,folo4_items_w1], na.rm = TRUE) #Conformity Scale-11 #negative correlation #one dimension ds_w1$colectivism <- rowMeans(x = ds_w1[,cf11_items_w1], na.rm = TRUE) #Life Orientation Test-10 #positive correlation #one dimension ds_w1$life_o <- rowMeans(x = ds_w1[,lot10_items_w1], na.rm = TRUE) #Adult Resilience Measure-Revised-17 #positive correlation #two dimensions: ##personal resilience c(1,2,3,7,9,10,12,13,14,16) ds_w1$pers_res <- rowMeans(ds_w1[,armr17_items_w1[c(1,2,3,7,9,10,12,13,14,16)]], na.rm = TRUE) ##relational resilience c(4,5,6,8,11,15,17) ds_w1$rel_res <- rowMeans(ds_w1[,armr17_items_w1[c(4,5,6,8,11,15,17)]], na.rm = TRUE) #Multidimensional Scale of Perceived Social Support-12 #positive correlation #three dimensions: ##family c(3,4,8,11) ds_w1$sup_fam <- rowMeans(ds_w1[,mspss12_items_w1[c(3,4,8,11)]], na.rm = TRUE) ##friends c(6,7,9,12) ds_w1$sup_frd <- rowMeans(ds_w1[,mspss12_items_w1[c(6,7,9,12)]], na.rm = TRUE) ##significant others c(1,2,5,10) ds_w1$sup_oth <- rowMeans(ds_w1[,mspss12_items_w1[c(1,2,5,10)]], na.rm = TRUE) #Career Guidance Subscale-4 #one dimension #positive correlation ds_w1$car_guid <- rowMeans(ds_w1[,spiscg4_items_w1], na.rm = TRUE) #Breadth of Extracurricular Activities Scale-8 #one dimension #positive correlation ds_w1$ext_act <- rowMeans(ds_w1[,beca7_items_w1], na.rm = TRUE) ``` Variables: - caas — Career Adaptability; - growth — Stress-Related Growth; - kiasuism — Fear of Losing Out; - colectivism — Conformity; - life_o — Life Orientation; - pers_res — Personal Resilience; - rel_res — Relational Resilience; - sup_fam — Family Support; - sup_frd — Friends Support; - sup_oth — Significant Others Support; - car_guid — Career Guidance; - ext_act — Breadth of Extracurricular Activities. --- exclude: true # Raw Correlations: Wave 1 <div class="figure"> <img src="data:image/png;base64,#presentation_files/figure-html/unnamed-chunk-47-1.png" alt="Raw correlations plot: Wave 1" width="100%" /> <p class="caption">Raw correlations plot: Wave 1</p> </div> --- exclude: true # Raw Correlations: Wave 2 Variables: - caas — Career Adaptability; - growth — Stress-Related Growth; - life_o — Life Orientation; - pers_res — Personal Resilience; - rel_res — Relational Resilience; - sup_fam — Family Support; - sup_frd — Friends Support; - sup_oth — Significant Others Support; - car_guid — Career Guidance; - ext_act — Breadth of Extracurricular Activities; - pess_view — Pessimistic Views; - anx — Anxiety; - self_ident — Self and Identity. ```r #caas-sf ds_w2$caa <- rowMeans(ds_w2[,caas_w2], na.rm = TRUE) #Stress-Related Growth Scale-15 ds_w2$growth <- rowMeans(ds_w2[,srgs15_items_w2], na.rm = TRUE) #Demographics #age #should not correlate #Life Orientation Test-10 #positive correlation #one dimension ds_w2$life_o <- rowMeans(ds_w2[,lot10_items_w2], na.rm = TRUE) #Adult Resilience Measure-Revised-17 #positive correlation #two dimensions: ##personal resilience c(1,2,3,7,9,10,12,13,14,16) ds_w2$pers_res <- rowMeans(ds_w2[,armr17_items_w2[c(1,2,3,7,9,10,12,13,14,16)]], na.rm = TRUE) ##relational resilience c(4,5,6,8,11,15,17) ds_w2$rel_res <- rowMeans(ds_w2[,armr17_items_w2[c(4,5,6,8,11,15,17)]], na.rm = TRUE) #Multidimensional Scale of Perceived Social Support-12 #positive correlation #three dimensions: ##family c(3,4,8,11) ds_w2$sup_fam <- rowMeans(ds_w2[,mspss12_items_w2[c(3,4,8,11)]], na.rm = TRUE) ##friends c(6,7,9,12) ds_w2$sup_frd <- rowMeans(ds_w2[,mspss12_items_w2[c(6,7,9,12)]], na.rm = TRUE) ##significant others c(1,2,5,10) ds_w2$sup_oth <- rowMeans(ds_w2[,mspss12_items_w2[c(1,2,5,10)]], na.rm = TRUE) #Career Guidance Subscale-4 #one dimension #positive correlation ds_w2$car_guid <- rowMeans(ds_w2[,spiscg4_items_w2], na.rm = TRUE) #Breadth of Extracurricular Activities Scale-8 #one dimension #positive correlation ds_w2$ext_act <- rowMeans(ds_w2[,beca7_items_w2], na.rm = TRUE) #Career Decision-Making questionnaire-23 #three dimensions: ##pessimistic views c(1,2,3,4,5,6,7) #negative correlation ds_w2$pess_view <- rowMeans(ds_w2[,cdm23_items_w2[c(1,2,3,4,5,6,7)]], na.rm = TRUE) ##anxiety c(8,9,10,11,12,13,14,15) #negative correlation ds_w2$anx <- rowMeans(ds_w2[,cdm23_items_w2[c(8,9,10,11,12,13,14,15)]], na.rm = TRUE) ##self and identity c(16,17,18,19,20,21,22,23) #negative correlation ds_w2$self_ident <- rowMeans(ds_w2[,cdm23_items_w2[c(16,17,18,19,20,21,22,23)]], na.rm = TRUE) ``` --- exclude: true # Raw Correlations: Wave 2 <div class="figure"> <img src="data:image/png;base64,#presentation_files/figure-html/unnamed-chunk-49-1.png" alt="Raw correlations plot: Wave 2" width="100%" /> <p class="caption">Raw correlations plot: Wave 2</p> </div> --- # Latent Correlations: Wave 1 .scroll-box-20[ ```r structural_model <- " ########################CAAS-SF ## wave 1 concern concernw1 =~ ACAAS1 + ACAAS2 + ACAAS3 ## wave 1 control controlw1 =~ ACAAS4 + ACAAS5 + ACAAS6 ## wave 1 curiosity curiosityw1 =~ ACAAS7 + ACAAS8 + ACAAS9 ## wave 1 confidence confidencew1 =~ ACAAS10 + ACAAS11 + ACAAS12 ## wave 1 career adaptability caradaptw1 =~ concernw1 + controlw1 + curiosityw1 + confidencew1 ACAAS1 ~~ ACAAS2 ACAAS11 ~~ ACAAS12 #Fear of Losing Out Scale-4 #negative correlation #one dimension Kiasuismw1 =~ AFOLO1+AFOLO2+AFOLO3+AFOLO4 #Conformity Scale-11 #negative correlation #one dimension: 2,7,9,11 are resersed items Conformismw1 =~ ACF6+ACF7+ACF8+ACF9+ACF10+ACF11 #ACF1+ACF2+ACF4+ACF3+ACF5 ########################LOT-R #wave1 #Life Orientation Test-10 #positive correlation optw1 =~ ALOT1+ALOT4+ALOT10 pessw1 =~ ALOT3+ALOT7++ALOT9 ########################ARM-R #Adult Resilience Measure-Revised-17 #positive correlation #WAVE 1 ##personal resilience c(1,2,3,7,9,10,12,13,14,16) #Pers_resw1 =~ AARM1+AARM2+AARM3+AARM7+AARM9+AARM10+AARM12+AARM13+AARM14+AARM16 ##relational resilience c(4,5,6,8,11,15,17) #Rel_resw1 =~ AARM4+AARM5+AARM6+AARM8+AARM11+AARM15+AARM17 ########################MSPSS #Multidimensional Scale of Perceived Social Support-12 #positive correlation #wave 1 #three dimensions: ##family c(3,4,8,11) Sup_famw1 =~ AMS3+AMS4+AMS8+AMS11 ##friends c(6,7,9,12) Sup_frdw1 =~ AMS6+AMS7+AMS9+AMS12 ##significant others c(1,2,5,10) Sup_othw1 =~ AMS1+AMS2+AMS5+AMS10 #second-order Supportw1 =~ Sup_famw1 + Sup_frdw1 + Sup_othw1 #Stress-Related Growth Scale-15 #Growth =~ ASRGS1+ASRGS2+ASRGS3+ASRGS4+ASRGS5+ASRGS6+ASRGS7+ASRGS8+ASRGS9+ASRGS10+ASRGS11+ASRGS12+ASRGS13+ASRGS14+ASRGS15 #Career Guidance Subscale-4 #one dimension #positive correlation #Car_guid =~ ACG1+ACG2+ACG3+ACG4 #Breadth of Extracurricular Activities Scale-8 #one dimension #positive correlation #Ext_act =~ ABECA1+ABECA2+ABECA3+ABECA4+ABECA5+ABECA6+ABECA7 " fit_model <- sem(m=structural_model, d=ds_w1, ord=T, estimator = "wlsmv") gofs_model <- fitmeasures(object = fit_model, fit.measures = gof) %>% round(digits = 2) ``` ] The model presented a satisfactory fit `\((\chi^2_{scaled (716)}=5,122.82;p< .001;CFI_{robust}=0.91;TLI_{robust}=0.90;\)` `\(NFI_{scaled}=0.98;SRMR=0.05; RMSEA_{robust}=0.06;p_{(rmsea \leq 0.05)}< .001; 90\%CI[0.06, 0.06])\)` accordingly with the usual cutoff standards(Hu and Bentler, 1999). --- # Latent Correlations: Wave 1 <table class="table" style="margin-left: auto; margin-right: auto;"> <caption>Latent Correlations</caption> <thead> <tr> <th style="text-align:left;"> </th> <th style="text-align:left;"> 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;"> Career Adaptability (1) </td> <td style="text-align:left;"> - </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;"> Kiasuism (2) </td> <td style="text-align:left;"> 0.09 </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;"> Conformism (3) </td> <td style="text-align:left;"> -0.38 </td> <td style="text-align:right;"> 0.13 </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;"> Optimism (4) </td> <td style="text-align:left;"> 0.36 </td> <td style="text-align:right;"> -0.08 </td> <td style="text-align:right;"> -0.14 </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;"> Pessimism (5) </td> <td style="text-align:left;"> -0.08 </td> <td style="text-align:right;"> 0.25 </td> <td style="text-align:right;"> 0.08 </td> <td style="text-align:right;"> -0.68 </td> <td style="text-align:right;"> - </td> <td style="text-align:right;"> </td> </tr> <tr> <td style="text-align:left;"> Support (6) </td> <td style="text-align:left;"> 0.36 </td> <td style="text-align:right;"> 0.05 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0.49 </td> <td style="text-align:right;"> -0.3 </td> <td style="text-align:right;"> - </td> </tr> </tbody> </table> --- # Latent Correlations: Wave 2 .scroll-box-20[ ```r ds[,c(caas_w2,mspss12_items_w2, lot10_items_w2)] <- sapply(ds[,c(caas_w2,mspss12_items_w2, lot10_items_w2)], sjlabelled::unlabel) structural_model <- " ########################CAAS-SF ## wave 2 concern concernw2 =~ BCAAS1 + BCAAS2 + BCAAS3 ## wave 2 control controlw2 =~ BCAAS4 + BCAAS5 + BCAAS6 ## wave 2 curiosity curiosityw2 =~ BCAAS7 + BCAAS8 + BCAAS9 ## wave 2 confidence confidencew2 =~ BCAAS10 + BCAAS11 + BCAAS12 ## wave 2 career adaptability caradaptw2 =~ concernw2 + controlw2 + curiosityw2 + confidencew2 BCAAS1 ~~ BCAAS2 BCAAS11 ~~ BCAAS12 ########################LOT-R #wave2 #Life Orientation Test-10 #positive correlation optw2 =~ BLOT1+BLOT4+BLOT10 pessw2 =~ BLOT3+BLOT7+BLOT9 ########################ARM-R #Adult Resilience Measure-Revised-17 #positive correlation #WAVE 2 ##personal resilience c(1,2,3,7,9,10,12,13,14,16) #Pers_resw2 =~ BARM1+BARM2+BARM3+BARM7+BARM9+BARM10+BARM12+BARM13+BARM14+BARM16 ##relational resilience c(4,5,6,8,11,15,17) #Rel_resw2 =~ BARM4+BARM5+BARM6+BARM8+BARM11+BARM15+BARM17 ########################MSPSS #Multidimensional Scale of Perceived Social Support-12 #positive correlation #wave 2 #three dimensions: ##family c(3,4,8,11) Sup_famw2 =~ BMS3+BMS4+BMS8+BMS11 ##friends c(6,7,9,12) Sup_frdw2 =~ BMS6+BMS7+BMS9+BMS12 ##significant others c(1,2,5,10) Sup_othw2 =~ BMS1+BMS2+BMS5+BMS10 #second-order Supportw2 =~ Sup_famw2 + Sup_frdw2 + Sup_othw2 " fit_model <- sem(m=structural_model, d=ds, ord=T, estimator = "wlsmv") gofs_model <- fitmeasures(object = fit_model, fit.measures = gof) %>% round(digits = 2) ``` ] The model presented a satisfactory fit `\((\chi^2_{scaled (390)}=1,845.61;p< .001;CFI_{robust}=0.94;TLI_{robust}=0.93;\)` `\(NFI_{scaled}=0.99;SRMR=0.03; RMSEA_{robust}=0.06;p_{(rmsea \leq 0.05)}< .001; 90\%CI[0.06, 0.07])\)` accordingly with the usual cutoff standards(Hu and Bentler, 1999). --- # Latent Correlations: Wave 2 <table class="table" style="margin-left: auto; margin-right: auto;"> <caption>Latent Correlations</caption> <thead> <tr> <th style="text-align:left;"> </th> <th style="text-align:left;"> 1 </th> <th style="text-align:right;"> 2 </th> <th style="text-align:right;"> 3 </th> <th style="text-align:right;"> 4 </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;"> Career Adaptability (1) </td> <td style="text-align:left;"> - </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;"> Optimism (2) </td> <td style="text-align:left;"> 0.45 </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;"> Pessimism (3) </td> <td style="text-align:left;"> -0.04 </td> <td style="text-align:right;"> -0.53 </td> <td style="text-align:right;"> - </td> <td style="text-align:right;"> </td> </tr> <tr> <td style="text-align:left;"> Support (4) </td> <td style="text-align:left;"> 0.41 </td> <td style="text-align:right;"> 0.51 </td> <td style="text-align:right;"> -0.21 </td> <td style="text-align:right;"> - </td> </tr> </tbody> </table> --- # Discussion CAAS-SF demonstrated strong validity evidence, aligning with the expected dimensions of career adaptability, including Concern, Control, Curiosity and Confidence. -- Good reliability was observed for all factors, including test-retest reliability. -- Longitudinal measurement invariance and gender-based measurement invariance. --- # Discussion Convergent validity was supported through positive correlations with optimism, fear of losing out, and social support, as well as negative correlations with pessimism and conformism. -- Cultural aspects (vertical conformity and kiasuism). --- # Conclusion The CAAS-SF was found to have good psychometric properties for assessing career adaptability among Singaporean undergraduate students based on validity evidence from multiple sources and measurement traditions -- The study highlighted the importance of considering sociocultural context variables when examining career-related constructs and offered valuable insights into the applicability of the CAAS-SF in diverse populations. --- # References Adams, R. 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In: _Social Behavior and Personality: an international journal_ 23.3, pp. 253-263. ISSN: 0301-2212. DOI: [10.2224/sbp.1995.23.3.253](https://doi.org/10.2224%2Fsbp.1995.23.3.253). --- # Questions/comments .can-edit.key-measurement[ - ... ]