Comparing Depressive Symptoms, Emotional Exhaustion, and Sleep Disturbances in Self-Employed and Employed Workers: Application of Approximate Bayesian Measurement Invariance

Studies investigating differences in mental health problems between self-employed and employed workers have provided contradictory results. Many of the studies utilized scales validated for employed workers, without collecting validity evidence for making comparisons with self-employed. The aim of this study was (1) to collect validity evidence for three different scales assessing depressive symptoms, emotional exhaustion, and sleep disturbances for employed workers, and combinators; and (2) to test if these groups differed. We first conducted approximate measurement invariance analysis and found that all scales were invariant at the scalar level. Self-employed workers had least mental health problems and employed workers had most, but differences were small. Though we found the scales invariant, we do not find them optimal for comparison of means. To be more precise in describing differences between groups, we recommend using clinical cut-offs or scales developed with the specific purpose of assessing mental health problems at work.

Accounting for Differential Item Functioning Using Bayesian Approximate Measurement Invariance

The main thesis of the present study is to use the Bayesian structural equation modeling (BSEM) methodology of establishing approximate measurement invariance (A-MI) using data from a national examination in Saudi Arabia as an alternative to not meeting strong invariance criteria. Instead, we illustrate how to account for the absence of measurement invariance using relative compared to exact criteria. A secondary goal was to compare latent means across groups using invariant parameters only and through utilizing exact and relative evaluative-MI protocol suggested equivalence of the thresholds using prior variances equal to 0.10. Subsequent differences between groups were evaluated using effect size criteria and the prior-posterior predictive p-value (PPPP), which proved to be invaluable in attesting for differences that are beyond zero, some meaningless nonzero estimate, and the three commonly used indices of effect sizes described by Cohen in 1988 (i.e., .20, .50, and .80). Results substantiated the use of the PPPP for evaluating mean differences across groups when utilizing nonexact evaluative criteria.

An application of Bayesian measurement invariance to modelling cognition over time in the English Longitudinal Study of Ageing

OBJECTIVES

Recommended cut-off criteria for testing measurement invariance (MI) using the comparative fit index (CFI) vary between -0.002 and -0.01. We compared CFI results with those obtained using Bayesian approximate MI for cognitive function.

METHODS

We used cognitive function data from Waves 1-5 of the English Longitudinal Study of Ageing (ELSA; Wave 1 n = 11,951), a nationally representative sample of English adults aged ≥50. We tested for longitudinal invariance using CFI and approximate MI (prior for a difference between intercepts/loadings ~N(0,0.01)) in an attention factor (orientation to date, day, week, and month) and a memory factor (immediate and delayed recall, verbal fluency, and a prospective memory task).

RESULTS

Conventional CFI criteria found strong invariance for the attention factor (CFI + 0.002) but either weak or strong invariance for the memory factor (CFI -0.004). The approximate MI results also supported strong MI for attention but found 9/20 intercepts or thresholds were noninvariant for the memory factor. This supports weak rather than strong invariance.

CONCLUSIONS

Within ELSA, the attention factor is suitable for longitudinal analysis but not the memory factor. More generally, in situations where the appropriate CFI criteria for invariance are unclear, Bayesian approximate MI could alternatively be used.

Psychometric Evaluation of the Overexcitability Questionnaire-Two Applying Bayesian Structural Equation Modeling (BSEM) and Multiple-Group BSEM-Based Alignment with Approximate Measurement Invariance

The Overexcitability Questionnaire-Two (OEQ-II) measures the degree and nature of overexcitability, which assists in determining the developmental potential of an individual according to Dabrowski's Theory of Positive Disintegration. Previous validation studies using frequentist confirmatory factor analysis, which postulates exact parameter constraints, led to model rejection and a long series of model modifications. Bayesian structural equation modeling (BSEM) allows the application of zero-mean, small-variance priors for cross-loadings, residual covariances, and differences in measurement parameters across groups, better reflecting substantive theory and leading to better model fit and less overestimation of factor correlations. Our BSEM analysis with a sample of 516 students in higher education yields positive results regarding the factorial validity of the OEQ-II. Likewise, applying BSEM-based alignment with approximate measurement invariance, the absence of non-invariant factor loadings and intercepts across gender is supportive of the psychometric quality of the OEQ-II. Compared to males, females scored significantly higher on emotional and sensual overexcitability, and significantly lower on psychomotor overexcitability.

Comparing results of an exact vs. an approximate (Bayesian) measurement invariance test: a cross-country illustration with a scale to measure 19 human values

One of the most frequently used procedures for measurement invariance testing is the multigroup confirmatory factor analysis (MGCFA). Muthén and Asparouhov recently proposed a new approach to test for approximate rather than exact measurement invariance using Bayesian MGCFA. Approximate measurement invariance permits small differences between parameters otherwise constrained to be equal in the classical exact approach. However, extant knowledge about how results of approximate measurement invariance tests compare to the results of the exact measurement invariance test is missing. We address this gap by comparing the results of exact and approximate cross-country measurement invariance tests of a revised scale to measure human values. Several studies that measured basic human values with the Portrait Values Questionnaire (PVQ) reported problems of measurement noninvariance (especially scalar noninvariance) across countries. Recently Schwartz et al. proposed a refined value theory and an instrument (PVQ-5X) to measure 19 more narrowly defined values. Cieciuch et al. tested its measurement invariance properties across eight countries and established exact scalar measurement invariance for 10 of the 19 values. The current study applied the approximate measurement invariance procedure on the same data and established approximate scalar measurement invariance even for all 19 values. Thus, the first conclusion is that the approximate approach provides more encouraging results for the usefulness of the scale for cross-cultural research, although this finding needs to be generalized and validated in future research using population data. The second conclusion is that the approximate measurement invariance is more likely than the exact approach to establish measurement invariance, although further simulation studies are needed to determine more precise recommendations about how large the permissible variance of the priors may be.