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

Estimation Methods of the Multiple-Group One-Dimensional Factor Model: Implied Identification Constraints in the Violation of Measurement Invariance

Factor analysis is one of the most important statistical tools for analyzing multivariate data (i.e., items) in the social sciences. An essential case is the comparison of multiple groups on a one-dimensional factor variable that can be interpreted as a summary of the items. The assumption of measurement invariance is a frequently employed assumption that enables the comparison of the factor variable across groups. This article discusses different estimation methods of the multiple-group one-dimensional factor model under violations of measurement invariance (i.e., measurement noninvariance). In detail, joint estimation, linking methods, and regularized estimation approaches are treated. It is argued that linking approaches and regularization approaches can be equivalent to joint estimation approaches if appropriate (robust) loss functions are employed. Each of the estimation approaches defines identification constraints of parameters that quantify violations of measurement invariance. We argue in the discussion section that the fitted multiple-group one-dimensional factor analysis will likely be misspecified due to the violation of measurement invariance. Hence, because there is always indeterminacy in determining group comparisons of the factor variable under noninvariance, the preference of particular fitting strategies such as partial invariance over alternatives is unjustified. In contrast, researchers purposely define fitting functions that minimize the extent of model misspecification due to the choice of a particular (robust) loss function.

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.

Prior Sensitivity in Bayesian Structural Equation Modeling for Sparse Factor Loading Structures

Bayesian structural equation modeling (BSEM) is a flexible tool for the exploration and estimation of sparse factor loading structures; that is, most cross-loading entries are zero and only a few important cross-loadings are nonzero. The current investigation was focused on the BSEM with small-variance normal distribution priors (BSEM-N) for both variable selection and model estimation. The prior sensitivity in BSEM-N was explored in factor analysis models with sparse loading structures through a simulation study (Study 1) and an empirical example (Study 2). Study 1 examined the prior sensitivity in BSEM-N based on the model fit, population model recovery, true and false positive rates, and parameter estimation. Seven shrinkage priors on cross-loadings and five noninformative/vague priors on other model parameters were examined. Study 2 provided a real data example to illustrate the impact of various priors on model fit and parameter selection and estimation. Results indicated that when the 95% credible intervals of shrinkage priors barely covered the population cross-loading values, it resulted in the best balance between true and false positives. If the goal is to perform variable selection, a sparse cross-loading structure is required, preferably with a minimal number of nontrivial cross-loadings and relatively high primary loading values. To improve parameter estimates, a relatively large prior variance is preferred. When cross-loadings are relatively large, BSEM-N with zero-mean priors is not recommended for the estimation of cross-loadings and factor correlations.

Lp Loss Functions in Invariance Alignment and Haberman Linking with Few or Many Groups

The comparison of group means in latent variable models plays a vital role in empirical research in the social sciences. The present article discusses an extension of invariance alignment and Haberman linking by choosing the robust power loss function ρ(x)=|x|p(p>0). This power loss function with power values p smaller than one is particularly suited for item responses that are generated under partial invariance. For a general class of linking functions, asymptotic normality of estimates is shown. Moreover, the theory of M-estimation is applied for obtaining linking errors (i.e., inference with respect to a population of items) for this class of linking functions. In a simulation study, it is shown that invariance alignment and Haberman linking have comparable performance, and in some conditions, the newly proposed robust Haberman linking outperforms invariance alignment. In three examples, the influence of the choice of a particular linking function on the estimation of group means is demonstrated. It is concluded that the choice of the loss function in linking is related to structural assumptions about the pattern of noninvariance in item parameters.

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.

Global mental health: an improved measure of well-being in multiple languages

BACKGROUND

An increasing number of international organisations and national governments have committed to well-being promotion. Unfortunately, important questions regarding how to assess well-being are still unresolved, making policy implementation and evaluation difficult.

METHODS

This research expanded on Huppert and So's (Soc Indic Res. 110, 837-861 2013) multidimensional subjective well-being framework by investigating the replicability of the model in two non-European regions (South America, represented by Brazil and Colombia, and Eastern Africa, represented by Uganda), and the United Kingdom. Additionally, previous limitations of the framework were also addressed. ESS Round Six items were crucially improved in terms of temporal and response scale consistency. Bayesian approximate measurement invariance was applied on a sample of 381 young adult participants to test for consistency across countries.

RESULTS

The Huppert & So (Soc Indic Res. 110, 837-861 2013) model was found to fairly replicate across non-European regions, where meaningful differences in well-being patterns across regions were observed. Additionally, estimated well-being was related with other well-being measures (Five Ways): Learn and Connect were the strongest predictors of general well-being, with Take Notice and Give being associated with specific aspects of it.

CONCLUSIONS

Based on this narrow sample of young adults, it appears the ten-item measure proposed by Huppert & So (Soc Indic Res. 110, 837-861 2013) is useful for assessing population mental health outside of Europe. This is only an initial attempt to assess qualities, so further testing should be done before applying at scale for identifying policy opportunities to address well-being of populations.

Structural Equation Modeling of Vocabulary Size and Depth Using Conventional and Bayesian Methods

In classifications of vocabulary knowledge, vocabulary size and depth have often been separately conceptualized (Schmitt, 2014). Although size and depth are known to be substantially correlated, it is not clear whether they are a single construct or two separate components of vocabulary knowledge (Yanagisawa and Webb, 2020). This issue has not been addressed extensively in the literature and can be better examined using structural equation modeling (SEM), with measurement error modeled separately from the construct of interest. The current study reports on conventional and Bayesian SEM approaches (e.g., Muthén and Asparouhov, 2012) to examine the factor structure of the size and depth of second language vocabulary knowledge of Japanese adult learners of English. A total of 255 participants took five vocabulary tests. One test was designed to measure vocabulary size in terms of the number of words known, while the remaining four were designed to measure vocabulary depth in terms of word association, polysemy, and collocation. All tests used a multiple-choice format. The size test was divided into three subtests according to word frequency. Results from conventional and Bayesian SEM show that a correlated two-factor model of size and depth with three and four indicators, respectively, fit better than a single-factor model of size and depth. In the two-factor model, vocabulary size and depth were strongly correlated (r = 0.945 for conventional SEM and 0.943 for Bayesian SEM with cross-loadings), but they were distinct. The implications of these findings are discussed.

The Temporal Ordering of Motivation and Self-Control: A Cross-Lagged Effects Model

Mechanisms leading to cognitive energy depletion in performance settings such as high-level sports highlight likely associations between individuals' self-control capacity and their motivation. Investigating the temporal ordering of these concepts combining self-determination theory and psychosocial self-control theories, the authors hypothesized that athletes' self-control capacity would be more influenced by their motivation than vice versa and that autonomous and controlled types of motivation would predict self-control capacity positively and negatively, respectively. High-level winter-sport athletes from Norwegian elite sport colleges (N = 321; 16-20 years) consented to participate. Using Bayesian structural equation modeling and 3-wave analyses, findings revealed credible self-control → motivation → self-control cross-lagged effects. Athletes' trait self-control especially initiated the temporal ordering of the least controlled types of motivation (i.e., intrinsic, integrated, and amotivation). Findings indicate that practicing self-control competencies and promoting athletes' autonomous types of motivation are important components in the development toward the elite level. These components will help athletes maintain their persistent goal striving by increasing the value and inherent satisfaction of the development process, avoiding the debilitating effects of self-control depletion and exhaustion.

The Role of Self-Control and Motivation on Exhaustion in Youth Athletes: A Longitudinal Perspective

The depletion of self-control competencies has been explained by an external shift in motivation, and recent research has emphasized that controlled types of motivation and self-control competencies are positively associated with exhaustion in youth athletes. Using the self-determination theory (SDT) and self-control theories, this study examined associations between athletes' motivation, self-control competencies, and exhaustion experiences throughout a competitive season. A total of 321 winter sport youth athletes (173 males, 98 females, and 50 unknown gender; aged 16 to 20 years, M = 17.98, SD = 0.89) participated in this 10-week longitudinal study, including three time points. Using Bayesian structural equation modeling, associations between athletes' reported level of motivation regulations, self-control, and exhaustion throughout their competitive season were examined in two mediation models. Constructs were associated in a conceptual and consistent manner. Simple mediation models showed credible indirect and direct effects of motivation on exhaustion via self-control within amotivation, and intrinsic, integrated, identified, and external regulation analyses. These credible effects were not replicated in the focused mediation model, when controlling for self-control and exhaustion autoregressive effects. However, direction of effects in both models was consistent and congruent. Findings consistently supported the interplay between motivation and exhaustion via self-control in youth athletes over an important competition period of the year. Autonomous and controlled motivation interacted with self-control and, respectively, predicted perceived exhaustion negatively and positively. Thus, autonomous self-control motives are important in preventing negative sport participation development over time. However, simple and focused mediation models showed different results, suggesting a necessity for accurate considerations of analytical methods chosen to investigate longitudinal mediation. Specifically, future studies need to carefully consider the time interval between measurement time points when investigating changes in dynamic psychological constructs, and include autoregressive longitudinal effects in order to predict change in levels of the outcome over time.

Invariância Fatorial e Normatização das Escalas de Sobre-Excitabilidade

Resumo Este estudo teve como objetivos estabelecer normas preliminares e verificar a estrutura e invariância fatorial das Escalas de Sobre-Excitabilidade (ESE) de acordo com o sexo. Trata-se de uma medida destinada à avaliação de sobre-excitabilidade - tendência para reagir intensa e sensivelmente a estímulos nas áreas sensorial, psicomotora, imaginativa, emocional e intelectual. Participaram 1500 estudantes do ensino fundamental de cinco estados brasileiros. Análises fatoriais confirmatórias demonstraram bons índices de ajustes para os modelos testados, revelando a existência de 11 escalas. Apesar de haver diferenças quanto ao sexo nos escores médios de algumas escalas, análises fatoriais confirmatórias multigrupos indicaram a invariância fatorial da medida nos grupos masculino e feminino. A normatização preliminar foi estabelecida a partir do cálculo do percentil acumulado para os escores totais e por sexo. Esses resultados evidenciam propriedades psicométricas adequadas e constituem um avanço para a normatização das ESE.

On Detecting Systematic Measurement Error in Cross-Cultural Research: A Review and Critical Reflection on Equivalence and Invariance Tests

One major threat to revealing cultural influences on psychological states or processes is the presence of bias (i.e., systematic measurement error). When quantitative measures are not targeting the same construct or they differ in metric across cultures, the validity of inferences about cultural variability (and universality) is in doubt. The objectives of this article are to review what can be done about it and what is being done about it. To date, a multitude of useful techniques and methods to reduce or assess bias in cross-cultural research have been developed. We explore the limits of invariance/equivalence testing and suggest more flexible means of dealing with bias. First, we review currently available established and novel methods that reveal bias in cross-cultural research. Second, we analyze current practices in a systematic content analysis. The content analysis of more than 500 culture-comparative quantitative studies (published from 2008 to 2015 in three outlets in cross-cultural, social, and developmental psychology) aims to gauge current practices and approaches in the assessment of measurement equivalence/invariance. Surprisingly, the analysis revealed a rather low penetration of invariance testing in cross-cultural research. Although a multitude of classical and novel approaches for invariance testing is available, these are employed infrequent rather than habitual. We discuss reasons for this hesitation, and we derive suggestions for creatively assessing and handling biases across different research paradigms and designs.