Approximate Measurement Invariance of Willingness to Sacrifice for the Environment Across 30 Countries: The Importance of Prior Distributions and Their Visualization

Nationwide opinions and international attitudes toward climate and environmental change are receiving increasing attention in both scientific and political communities. An often used way to measure these attitudes is by large-scale social surveys. However, the assumption for a valid country comparison, measurement invariance, is often not met, especially when a large number of countries are being compared. This makes a ranking of countries by the mean of a latent variable potentially unstable, and may lead to untrustworthy conclusions. Recently, more liberal approaches to assessing measurement invariance have been proposed, such as the alignment method in combination with Bayesian approximate measurement invariance. However, the effect of prior variances on the assessment procedure and substantive conclusions is often not well understood. In this article, we tested for measurement invariance of the latent variable “willingness to sacrifice for the environment” using Maximum Likelihood Multigroup Confirmatory Factor Analysis and Bayesian approximate measurement invariance, both with and without alignment optimization. For the Bayesian models, we used multiple priors to assess the impact on the rank order stability of countries. The results are visualized in such a way that the effect of different prior variances and models on group means and rankings becomes clear. We show that even when models appear to be a good fit to the data, there might still be an unwanted impact on the rank ordering of countries. From the results, we can conclude that people in Switzerland and South Korea are most motivated to sacrifice for the environment, while people in Latvia are less motivated to sacrifice for the environment.

Measuring Physical Intimate Partner Violence to Monitor Sustainable Development Goal 5: A Global Psychometric Assessment

Background. One third of women experience IPV and potential sequelae. Sustainable Development Goal (SDG) 5.2, to eliminate all violence against women, including IPV, compels national governments to monitor such violence. We conducted the first global measurement-invariance assessment of standardized physical IPV items. Methods. Thirty-six Demographic and Health Surveys (DHS) from 36 Lower-/Middle-Income Countries (LMICs) administering the same 18 IPV items during 2012-2018 were included. We performed exploratory and confirmatory factor analyses (EFA/CFA) with seven physical IPV items, which are the most behaviorally specific and reliable. Datasets meeting EFA/CFA model fit criteria (loadings>.35, RMSEA<.08, CFI/TLI>.95) were included in multiple-group CFA to test strict measurement invariance, and in alignment optimization (AO) to test approximate measurement invariance. We compared national rankings based on AO-derived scores and lifetime physical IPV prevalences, and correlated AO-dervied scores with physical, sexual, and psychological IPV prevalences. Results. Estimated lifetime physical IPV varied widely (5.6%-50.5%). All loadings and fit statistics met thresholds in country-specific EFA/CFAs. A unidimensional, seven-item physical IPV construct lacked scalar invariance in multiple-group CFA but achieved approximate measurement invariance in AO analysis, as 12.3% (<25%) of model parameters were non-invariant. National rankings of AO-derived scores and estimated physical IPV prevalences were similarly distributed, but national estimates often were not significantly different, so grouped score ranges or prevalence ranges are advised. Three items (slap, twist, choke) warrant cognitive testing to improve their psychometric performance. Correlations of AO-derived scores with IPV prevalences ranged from .48 to .66. Conclusions. Seven DHS physical-IPV items were approximately invariant across 36 LMICs spanning five regions and are reasonable for cross-national, grouped comparison of physical IPV. Measurement-invariance testing over time will inform their utility to monitor SDG5.2.1; cross-national and cross-time measurement-invariance testing of other IPV item sets is warranted.

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.

Mesh simplification algorithm based on edge curvature metrics and local optimization

Aiming at the problem that the mesh simplification algorithm loses the geometric features of the model in large-scale simplification, an improved half-edge collapse mesh simplification algorithm is proposed. The concept of approximate measurement of edge curvature is introduced, and the edge curvature is added to the error measure, so that the order of half-edge collapse of the mesh is changed, and the simplified details of the mesh model can be preserved accurately. At the same time, by analyzing the quality of simplified triangular mesh, optimizing triangular mesh locally, reducing the amount of narrow triangles, the quality of the simplified model is improved. The proposed algorithm was tested on Cow model, Car model and Bunny model, and compared with another three algorithms, one of them is a classical mesh simplification algorithm based on edge collapse, the other is an improved algorithm of the classical one. The experimental results show that the improved algorithm can better retain the detail features of the original model at the same reduction ratio, and has reasonable mesh allocation, fast execution speed and small error.

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 illustration of Bayesian approximate measurement invariance with longitudinal data and a small sample size

This article illustrates the Bayesian approximate measurement invariance (MI) approach in M plus with longitudinal data and small sample size. Approximate MI incorporates zero-mean small variance prior distributions on the differences between parameter estimates over time. Contrary to traditional invariance testing methods, where exact invariance is tested, this method allows for some “wiggle room” in the parameter estimates over time. The procedure is illustrated using longitudinal data on college students’ academic stress as it changes in the period leading up to and right after an important midterm. Results show that traditional invariance testing methods come to a standstill due to the small sample size. Bayesian approximate MI testing was able to identify non-invariant parameters, after which a partially invariant model could be estimated.