A Comparison of ML, WLSMV, and Bayesian Methods for Multilevel Structural Equation Models in Small Samples: A Simulation Study

Estimating nonlinear effects of random slopes: A comparison of multilevel structural equation modeling with a two-step, a single-indicator, and a plausible values approach

Multilevel structural equation modeling (MSEM) is a statistical framework of major relevance for research concerned with people's intrapersonal dynamics. An application domain that is rapidly gaining relevance is the study of individual differences in the within-person association (WPA) of variables that fluctuate over time. For instance, an individual's social reactivity - their emotional response to social situations - can be represented as the association between repeated measurements of the individual's social interaction quantity and momentary well-being. MSEM allows researchers to investigate the associations between WPAs and person-level outcome variables (e.g., life satisfaction) by specifying the WPAs as random slopes in the structural equation on level 1 and using the latent representations of the slopes to predict outcomes on level 2. Here, we are concerned with the case in which a researcher is interested in nonlinear effects of WPAs on person-level outcomes - a U-shaped effect of a WPA, a moderation effect of two WPAs, or an effect of congruence between two WPAs - such that the corresponding MSEM includes latent interactions between random slopes. We evaluate the nonlinear MSEM approach for the three classes of nonlinear effects (U-shaped, moderation, congruence) and compare it with three simpler approaches: a simple two-step approach, a single-indicator approach, and a plausible values approach. We use a simulation study to compare the approaches on accuracy of parameter estimates and inference. We derive recommendations for practice and provide code templates and an illustrative example to help researchers implement the approaches.

Subsyndromes and symptom clusters: Multilevel factor analysis of behavioral and psychological symptoms of dementia with intensive longitudinal data

INTRODUCTION

Behavioral and psychological symptoms in dementia (BPSD) are dynamic phenomena with a high amount of intraindividual variability. We applied a multilevel framework to identify subsyndromes (between-person factors) that represent clinically relevant profiles of BPSD and identify symptom clusters (within-person factors) that represent contextually driven daily symptom experiences.

METHODS

This study used an intensive longitudinal design in which 68 co-residing family caregivers to persons living with dementia were recruited to proxy report on their care recipient's daily symptom experiences of 23 different BPSD for eight consecutive days (n = 443 diaries). A multilevel exploratory/confirmatory factor analysis was used to account for nested data and separate within-person variances from between-level factor estimates.

RESULTS

Exploratory factor analysis identified a 4-between 3-within factor structure based on fit statistics and clinical interpretability.

DISCUSSION

This study offers major methodological and conceptual advancements for management of BPSD within Alzheimer's disease and related dementias by introducing two related but distinct concepts of subsyndromes and symptom clusters.

HIGHLIGHTS

Because behavioral and psychological symptoms of dementia (BPSD) are dynamic temporal phenomenon, this introduces measurement error into aggregate group-level estimates when trying to create subsyndromes. We propose a multilevel analysis to provide a more valid and reliable estimation by separating out variance due to within-person daily fluctuations. Using a multilevel exploratory factor analysis with intensive longitudinal data, we identified distinct and meaningful groups of BPSD. The four factors at the between-person level represented subsyndromes that are based on how BPSD co-occurred among persons with Alzheimer's disease (AD). These subsyndromes are clinically relevant because they share features of established clinical phenomena and may have similar neurobiological etiologies. We also found three within-person factors representing distinct symptom clusters. They are based on how BPSD clustered together on a given day for an individual with AD and related dementias. These clusters may have shared environmental triggers.

Bayesian multilevel modelling of the association between socio-economic status and stunting among under-five-year children in Tanzania

BACKGROUND

Stunting is associated with socioeconomic status (SES) which is multidimensional. This study aimed to compare different SES indices in predicting stunting.

METHODS

This was the secondary data analysis using Tanzania Demographics and Health Surveys (TDHS). The study used 7492, 6668, and 8790 under-five-year children from TDHS 2004/5, 2010, and 2015/16, respectively. The Household Wealth Index (HWI); Water and Sanitation, Assets, Maternal education and Income (WAMI); Wealth Assets, Education, and Occupation (WEO); and the Multidimensional Poverty Index (MPI) indices were compared. The summated scores, principal component analysis (PCA), and random forest (RF) approaches were used to construct indices. The Bayesian and maximum likelihood multilevel generalized linear mixed models (MGLMM) were constructed to determine the association between each SES index and stunting.

RESULTS

The study revealed that 42.3%, 38.4%, and 32.4% of the studied under-five-year children were stunted in 2004/5, 2010, and 2015/16, respectively. Compared to other indicators of SES, the MPI had a better prediction of stunting for the TDHS 2004/5 and 2015/16, while the WAMI had a better prediction in 2010. For each score increase in WAMI, the odds of stunting were 64% [BPOR = 0.36; 95% CCI 0.3, 0.4] lower in 2010, while for each score increase in MPI there was 1 [BPOR = 1.1; 95% CCI 1.1, 1.2] times higher odds of stunting in 2015/16.

CONCLUSION

The MPI and WAMI under PCA were the best measures of SES that predict stunting. Because MPI was the best predictor of stunting for two surveys (TDHS 2004/5 and 2015/16), studies dealing with stunting should use MPI as a proxy measure of SES. Use of BE-MGLMM in modelling stunting is encouraged. Strengthened availability of items forming MPI is inevitable for child growth potentials. Further studies should investigate the determinants of stunting using Bayesian spatial models to take into account spatial heterogeneity.

Improving the stability of bivariate correlations using informative Bayesian priors: a Monte Carlo simulation study

Objective

Much of psychological research has suffered from small sample sizes and low statistical power, resulting in unstable parameter estimates. The Bayesian approach offers a promising solution by incorporating prior knowledge into statistical models, which may lead to improved stability compared to a frequentist approach.

Methods

Simulated data from four populations with known bivariate correlations (ρ = 0.1, 0.2, 0.3, 0.4) was used to estimate the sample correlation as samples were sequentially added from the population, from n = 10 to n = 500. The impact of three different, subjectively defined prior distributions (weakly, moderately, and highly informative) was investigated and compared to a frequentist model.

Results

The results show that bivariate correlation estimates are unstable, and that the risk of obtaining an estimate that is exaggerated or in the wrong direction is relatively high, for sample sizes for below 100, and considerably so for sample sizes below 50. However, this instability can be constrained by informative Bayesian priors.

Conclusion

Informative Bayesian priors have the potential to significantly reduce sample size requirements and help ensure that obtained estimates are in line with realistic expectations. The combined stabilizing and regularizing effect of a weakly informative prior is particularly useful when conducting research with small samples. The impact of more informative Bayesian priors depends on one's threshold for probability and whether one's goal is to obtain an estimate merely in the correct direction, or to obtain a high precision estimate whose associated interval falls within a narrow range. Implications for sample size requirements and directions for future research are discussed.

Depression-Mediating Pathways From Household Adversity to Antiretroviral Therapy Nonadherence Among Children and Adolescents Living With HIV in Zambia: A Structural Equation Modeling Approach

BACKGROUND

In Zambia, half of children and adolescents living with HIV (CALWH) on antiretroviral therapy (ART) are virologically unsuppressed. Depressive symptoms are associated with ART nonadherence but have received insufficient attention as mediating factors in the relationship between HIV self-management and household-level adversities. We aimed to quantify theorized pathways from indicators of household adversity to ART adherence, partially mediated by depressive symptoms, among CALWH in 2 Zambian provinces.

SETTING

In July-September 2017, we enrolled 544 CALWH aged 5-17 years and their adult caregivers into a year-long prospective cohort study.

METHODS

At baseline, CALWH-caregiver dyads completed an interviewer-administered questionnaire, which included validated measures of recent (past 6 months) depressive symptomatology and self-reported past-month ART adherence (never versus sometimes or often missing medication doses). We used structural equation modeling with theta parameterization to identify statistically significant ( P < 0.05) pathways from household adversities (past-month food insecurity and caregiver self-reported health) to depression (modeled latently), ART adherence, and poor physical health in the past 2 weeks.

RESULTS

Most CALWH (mean age: 11 years, 59% female) exhibited depressive symptomatology (81%). In our structural equation model, food insecurity significantly predicted elevated depressive symptomatology ( ß = 0.128), which was associated inversely with daily ART adherence ( ß = -0.249) and positively with poor physical health ( ß = 0.359). Neither food insecurity nor poor caregiver health was directly associated with ART nonadherence or poor physical health.

CONCLUSIONS

Using structural equation modeling, we found that depressive symptomatology fully mediated the relationship between food insecurity, ART nonadherence, and poor health among CALWH.

Applying Monte Carlo Simulations to a Small Data Analysis of a Case of Economic Growth in COVID-19 Times

Studies on the going-on COVID-19 pandemic face small sample issues. In this context, Bayesian estimation is considered a viable alternative to frequentist estimation. Demonstrating the Bayesian approach's advantage in dealing with this problem, our research conducted a case study concerning ASEAN economic growth during the COVID-19 pandemic. By using Monte Carlo standard errors and interval hypothesis testing to check parameter bias within a Bayesian MCMC simulation study, the author obtained significant conclusions as follows: first, in insufficient sample sizes, in contrast to frequentist estimation, the Bayesian framework can offer meaningful results, that is, expansionary monetary and contractionary fiscal policies are positively associated with economic growth; second, in the face of a small sample, by incorporating more information into prior distributions for the model parameters, Bayesian Monte Carlo simulations perform so far better than naïve Bayesian and frequentist estimation; third, in case of a correctly specified prior, the inferences are robust to different prior specifications. The author strongly recommends applying specific informative priors to Bayesian analyses, particularly in small sample investigations.

Bayesian estimates for genetic and phenotypic parameters of growth traits in Sahiwal cattle

Analyses were carried out for the estimation of (co)variance components and genetic parameters for birth weight (BWT), 6-month weight (6WT), 12-month weight (12WT), 18-month weight (18WT), 24-month weight (24WT), 30-month weight (30WT), 36-month weight (36WT), weight at first service (WFS), and weight at first calving(WFC) in Sahiwal cattle. Data for 802 lifetime records (raw data) were collected over a period of 30 years (1990-2019) for various growth traits in the herd for Sahiwal cows maintained at the livestock farm unit of ICAR-NDRI Karnal, Haryana, India. Bayesian estimates using the multi-trait Gibbs sampling animal model approach were calculated in the present study. Total heritability for BWT, 6WT, 12WT, 18WT, 24WT, 30WT, 36WT, WFS, and WFC by Bayesian modeling was estimated as 0.22 ± 0.0052, 0.47 ± 0.0037, 0.30 ± 0.0025, 0.65 ± 0.0021, 0.32 ± 0.0039, 0.33 ± 0.0027, 0.39 ± 0.0031, 0.49 ± 0.0020, and 0.57 ± 0.0023, respectively, along with its Monte Carlo error in Sahiwal cattle. Direct genetic covariances between body weight traits were ranging from - 2762.5 for 18WT and WFC to 4739.6 between WFS and WFC. Environmental covariances were ranging from - 169.98 for 30WT and 36WT to 4539.4 between WFS and WFC. Family relationships as well as the existing interaction effects between two or more traits in opposite direction effect lead to negative estimates for genetic covariances between some of the combinations with various growth traits. Although most of the estimates for posteriori were somewhat skewed, the marginalization effect enabled them to fit into the Gaussian distribution, by comparing the mean, mode, and median with each other. Results suggest that genetic progress through growth traits can be achieved if the selection is carried out for highly heritable 18-month weight as well as for the selection of pubertal and fertility traits, viz., 24WT, 30WT, 36WT, WFS, and WFC with a balanced feeding and optimum management.

Bayesian Mediation Analysis with Power Prior Distributions

Bayesian methods are often suggested as a solution for issues encountered in small sample research, however, Bayesian methods often require informative priors to outperform classical methods in these settings. Specifying accurate priors with respect to the true value of the parameter of interest is challenging and inaccurate informative priors can have detrimental effects on conclusions from the statistical analysis. This paper proposes an objective procedure for creating informative priors for mediation analysis based on a historical data set; the only requirements for implementing the procedure are that the data from the current study constitute a representative sample from the population of interest, and that the historical and current data sets contain measures of the same covariates and independent variable, mediator, and outcome. The simulation study findings show that the proposed method leads to appropriate amount of borrowing from the historical data set, which leads to increases in precision and power when the historical data and current data are exchangeable, and does not induce bias when the historical and current studies are not exchangeable. The proposed method is illustrated using data from the project PROsetta Stone, and we provide rstan code for implementing the proposed method.

Design and Evaluation among Young Adults of a Financial Literacy Scale Focused on Key Financial Decisions

The present study underpins the design and validation of a Financial Literacy (FL) scale in the Latin American and the Caribbean (LAC) context. Though scales are available, they do not meet contextual characteristics and seem to miss out on a focus on Key Financial Decisions (KFD). Scale design was consistent with an extensive literature review (2010–2021). Forty-four items scale covering the dimensions of Financial Attitude, Financial Behavior, and Financial Knowledge were presented to 478 young adults aged 18–30, and women 58% of them. The results reflect a robust FL scale by applying Confirmatory Factor Analysis (CFA). The data about young adults’ FL can be used as a benchmark in future studies fostering the development of FL in the Latin American and Caribbean contexts.

Where There’s a Will, There’s a Way? Social and Mental Forces of Successful Adaptation of Immigrant Children in Young Adulthood

Although the twenty-first century is deemed as a new era of globalization, waves of immigration continue, due to disparities between politically and economically unstable regions and Western democratized and developed countries. Immigration research has therefore reignited its attention on the successful adaptation of immigrants’ offspring, which has profound implications for Western immigrant-receiving countries, as well as worldwide stability. Although immigration research mainly informed by the conventional assimilation theory and/or segmented assimilation perspective accentuates the importance of structural factors, termed as social forces here, in relation to immigrant children’s successful adaptation in adolescence, an argument of determinism and tenability keeps on and the contribution of human mental resources and determination, termed as mental forces here, in shaping life trajectories of immigrant children should be not ignored. For this, with a representative sample of 3344 immigrant children from the Children of Immigrants Longitudinal Study (CILS), we examined and compared both the effects of social and mental forces measured in adolescence of immigrant children on their multiple adaptation outcomes in terms of college graduation, engagement in postgraduate study, and first and current job attainments in young adulthood with a Bayesian multilevel modeling framework. The results found that both social forces of segmented assimilation theory and mental forces of immigrant children in adolescence were significantly predictive of immigrant children’s successful adaptation in young adulthood (OR = 1.088–2.959 and β = 0.050–0.639 for social forces; OR = 11.290–18.119 and β = 0.293–0.297 for mental forces), in which, although the latter showed stronger effects than the former, the effects of mental forces on adaptation of immigrant children were conditionally shaped by the contexts of the social forces informed by segmented assimilation theory. The findings of the current study highlight the significance of the organism–environment interaction perspective on immigration research and provide an insight to consider a context-driven response thesis proposed.

Estimating and Testing Random Intercept Multilevel Structural Equation Models with Model Implied Instrumental Variables

This study develops a new limited information estimator for random intercept Multilevel Structural Equation Models (MSEM). It is based on the Model Implied Instrumental Variable Two-Stage Least Squares (MIIV-2SLS) estimator, which has been shown to be an excellent alternative or supplement to maximum likelihood (ML) in SEMs (Bollen, 1996). We also develop a multilevel overidentification test statistic that applies to equations at the within or between levels. Our Monte Carlo simulation analysis suggests that MIIV-2SLS is more robust than ML to misspecification at within or between levels, performs well given fewer that 100 clusters, and shows that our multilevel overidentification test for equations performs well at both levels of the model.

Conducting and Evaluating Multilevel Studies: Recommendations, Resources, and a Checklist

Multilevel methods allow researchers to investigate relationships that expand across levels (e.g., individuals, teams, and organizations). The popularity of these methods for studying organizational phenomena has increased in recent decades. Methodologists have examined how these methods work under different conditions, providing an empirical base for making sound decisions when using these methods. In this article, we provide recommendations, tools, resources, and a checklist that can be useful for scholars involved in conducting or assessing multilevel studies. The focus of our article is on two-level designs, in which Level-1 entities are neatly nested within Level-2 entities, and top-down effects are estimated. However, some of our recommendations are also applicable to more complex multilevel designs.

Parenting stress mediates the longitudinal effect of maternal depression on child anxiety/depressive symptoms

BACKGROUND

Evidence is lacking for the longitudinal bidirectional relationship between maternal depression and child anxiety/depressive symptoms through pre-school to adolescence and regarding parenting stress as having a mediating effect on this association.

METHODS

We performed a secondary analysis of data from the Fragile Families and Child Well-being Study (n = 1,446 child-mother dyads in 20 main U.S. cities) collected at baseline, Year-5 (T1), Year-9 (T2) and Year-15 (T3) (from 1998 to 2017). Maternal depression, child anxiety/depressive symptoms and parenting stress were assessed at three time points (T1-T3). The associations were evaluated using autoregressive cross-lagged panel models.

RESULTS

Cross-lagged models indicated that 1) maternal depression significantly predicted subsequent higher child anxiety/depressive symptoms across all time points, and 2) greater child anxiety/depressive symptoms significantly predicted subsequent maternal depression across all time points. Furthermore, T1 maternal depression was indirectly associated with T3 child anxiety/depressive symptoms via T2 parenting stress [b = 0.010 (SE=0.004), p = 0.017]. However, T2 parenting stress did not significantly mediate the association between T1 child anxiety/depressive symptoms and T3 maternal depression [b = 0.004 (SE=0.004), p = 0.256].

LIMITATIONS

The FFCWS oversampled unmarried parents and had a higher proportion of socio-economically disadvantaged racial and ethnic minority families, limiting the generalizability of findings.

CONCLUSIONS

Maternal depression is indirectly linked to child anxiety/depressive symptoms via parenting stress.

The mediating effect of parenting stress and couple relationship quality on the association between material hardship trajectories and maternal mental health status

BACKGROUND

Household material hardships could have a negative impact on maternal mental health. Understanding mechanisms by which material hardship trajectories affect maternal depression and anxiety could aid health care professionals and researchers to design better interventions to improve mental health outcomes among mothers.

METHODS

The study identified family-level mechanisms by which material hardship trajectories affect maternal depression and anxiety using Fragile Families and Child Wellbeing Study data (n = 1,645). Latent growth mixture modelling was used to identify latent classes of material hardship trajectories at Years-1, -3, and -5. Parenting stress and couple relationship quality was measured at Year-9. The outcome measures included maternal depression and generalized anxiety disorder (GAD) at Year-15 based on the Composite International Diagnostic Interview - Short Form.

RESULTS

Parenting stress mediated the association between low-increasing hardship (b = 0.020, 95% confidence interval (CI):0.003, 0.043) and maternal depression. Parenting stress also mediated the association between high-increasing hardship (b = 0.043, 95% CI:0.004, 0.092), high decreasing hardship (b = 0.034, 95% CI=0.001, 0.072), and low-increasing (b = 0.034, 95% CI:0.007, 0.066) and maternal GAD. In all models, current material hardship was directly related to maternal depression (b = 0.188, 95% CI:0.134, 0.242) and GAD (b = 0.174, 95% CI:0.091, 0.239).

LIMITATIONS

Study results need to be interpreted with caution as the FFCWS oversampled non-marital births as part of the original study design.

CONCLUSIONS

While current material hardship appears to be more related to maternal mental health, prior material hardship experiences contribute to greater parenting stress which places mothers at risk for experiencing depression and GAD later on.

Explanatory Model of Perceived Stress in the General Population: A Cross-Sectional Study in Peru During the COVID-19 Context

Background

The COVID-19 pandemic had negatively impact mental health worldwide. High prevalence of stress had been previously reported in populations during this context. Many theoretical frameworks had been proposed for explaining the stress process, we aim to proposed and explanatory model for the genesis of perceived stress in Peruvian general population.

Method

We conducted an online survey in Peruvian general population assessing sociodemographic variables and evaluating mental health conditions by using The Perceived Stress Scale (PSS-10), Positive Affect and Negative Affect Scale (PANAS), Generalized Anxiety Disorder scale (GAD-7), Patient Health Questionnaire (PHQ-9), and a numerical rating scale (NRS) for fear of COVID-19. Correlation analysis was conducted for the variables of interest. Two regression models were constructed to explore related factor to the dimensions of perceived stress. Finally, a structural regression model was performed with the independent variables.

Results

Data of 210 individuals was analyzed. Ages ranged from 15 to 74 years and 39% were women. Additionally, 65.2% of the participants had at least one mental health conditions (depression, anxiety, or stress symptoms). Perceived self-efficacy and positive affect (PA) were correlated, as perceived helplessness with anxious symptoms and negative affect (NA). Regression analysis showed that sex, anxiety symptoms, and NA explained perceived helplessness while positive and NA explained self-efficacy. The structural regression model analysis identified that fear of COVID-19 (composed of fear of infecting others and fear of contagion), predicted mental health conditions (i.e., depressive or anxiety symptoms); also, mental health conditions were predicted by PA and NA. Perceived helplessness and Perceived self-efficacy were interrelated and represented the perceived stress variable.

Conclusion

We proposed an explanatory model of perceived stress based on two correlated dimensions (self-efficacy and helplessness) in the Peruvian general population during the context of the COVID-19 pandemic, with two out of three individuals surveyed having at least one mental health condition.

Evaluating Cluster-Level Factor Models with lavaan and Mplus

Background: Researchers frequently use the responses of individuals in clusters to measure cluster-level constructs. Examples are the use of student evaluations to measure teaching quality, or the use of employee ratings of organizational climate. In earlier research, Stapleton and Johnson (2019) provided advice for measuring cluster-level constructs based on a simulation study with inadvertently confounded design factors. We extended their simulation study using both Mplus and lavaan to reveal how their conclusions were dependent on their study conditions. Methods: We generated data sets from the so-called configural model and the simultaneous shared-and-configural model, both with and without nonzero residual variances at the cluster level. We fitted models to these data sets using different maximum likelihood estimation algorithms. Results: Stapleton and Johnson’s results were highly contingent on their confounded design factors. Convergence rates could be very different across algorithms, depending on whether between-level residual variances were zero in the population or in the fitted model. We discovered a worrying convergence issue with the default settings in Mplus, resulting in seemingly converged solutions that are actually not. Rejection rates of the normal-theory test statistic were as expected, while rejection rates of the scaled test statistic were seriously inflated in several conditions. Conclusions: The defaults in Mplus carry specific risks that are easily checked but not well advertised. Our results also shine a different light on earlier advice on the use of measurement models for shared factors.

Is it possible to find a bifactor structure in the Fear of COVID-19 Scale (FCV-19S)? Psychometric evidence in an Ecuadorian sample

The aim of the study was to evaluate the construct validity based on the internal structure, the relationship with other variables, and the internal consistency among items of the Fear of COVID-19 Scale (FCV-19S) in a sample of 743 Ecuadorians. The findings confirm the presence of a bifactor structure, which includes a general factor and two specific factors: one emotional and the other physiological. The general factor, and the specific factors presented adequate levels of internal consistency. Finally, the FCV-19S showed a highly significant relationship with GAD-7 at the latent level. The scale has adequate psychometric properties for its application.

A Comparison of Penalized Maximum Likelihood Estimation and Markov Chain Monte Carlo Techniques for Estimating Confirmatory Factor Analysis Models With Small Sample Sizes

With small to modest sample sizes and complex models, maximum likelihood (ML) estimation of confirmatory factor analysis (CFA) models can show serious estimation problems such as non-convergence or parameter estimates outside the admissible parameter space. In this article, we distinguish different Bayesian estimators that can be used to stabilize the parameter estimates of a CFA: the mode of the joint posterior distribution that is obtained from penalized maximum likelihood (PML) estimation, and the mean (EAP), median (Med), or mode (MAP) of the marginal posterior distribution that are calculated by using Markov Chain Monte Carlo (MCMC) methods. In two simulation studies, we evaluated the performance of the Bayesian estimators from a frequentist point of view. The results show that the EAP produced more accurate estimates of the latent correlation in many conditions and outperformed the other Bayesian estimators in terms of root mean squared error (RMSE). We also argue that it is often advantageous to choose a parameterization in which the main parameters of interest are bounded, and we suggest the four-parameter beta distribution as a prior distribution for loadings and correlations. Using simulated data, we show that selecting weakly informative four-parameter beta priors can further stabilize parameter estimates, even in cases when the priors were mildly misspecified. Finally, we derive recommendations and propose directions for further research.

Statistical estimation of structural equation models with a mixture of continuous and categorical observed variables

In the social and behavioral sciences, observed variables of mixed scale types (i.e., both continuous and categorical observed variables) have long been included in structural equation models. However, little is known about the impact of mixed continuous and categorical observed variables on the performance of existing estimation methods. This study compares two popular estimation methods with robust corrections, robust maximum likelihood (MLR) and diagonally weighted least squares (DWLS), when mixed continuous and categorical observed data are analyzed, evaluating the behavior of DWLS and MLR estimates in both measurement and full structural equation models. Monte Carlo simulation was carried out to examine the performance of DWLS and MLR in estimating model parameters, standard errors, and chi-square statistics. Two population models, a correlated three-factor measurement model and a five-factor structural equation model, were tested in combination with 36 other experimental conditions characterized by the number of observed variables' categories (2, 3, 4, 5, 6, and 7), categorical observed distribution shape (symmetry and slight asymmetry), and sample size (200, 500, and 1000). Data generation and analysis were performed with Mplus 8. Results reveal that (1) DWLS yields more accurate factor loading estimates for categorical observed variables than MLR, whereas DWLS and MLR produce comparable factor loading estimates for continuous observed variables; (2) inter-factor correlations and structural paths are estimated equally well by DWLS and MLR in nearly all conditions; (3) robust standard errors of parameter estimates obtained by MLR are slightly more accurate than those produced by DWLS in almost every condition, but the superiority of MLR over DWLS is not clearly evident once a medium or large sample is used (i.e., n = 500 or 1000); and (4) DWLS is systematically superior to MLR in controlling Type I error rates, but this superiority is attenuated with increasing sample size. The article concludes with a general discussion of the findings and some recommendations for practice and future research.

Systematically Defined Informative Priors in Bayesian Estimation: An Empirical Application on the Transmission of Internalizing Symptoms Through Mother-Adolescent Interaction Behavior

BACKGROUND

Bayesian estimation with informative priors permits updating previous findings with new data, thus generating cumulative knowledge. To reduce subjectivity in the process, the present study emphasizes how to systematically weigh and specify informative priors and highlights the use of different aggregation methods using an empirical example that examined whether observed mother-adolescent positive and negative interaction behavior mediate the associations between maternal and adolescent internalizing symptoms across early to mid-adolescence in a 3-year longitudinal multi-method design.

METHODS

The sample consisted of 102 mother-adolescent dyads (39.2% girls, M age T1 = 13.0). Mothers and adolescents reported on their internalizing symptoms and their interaction behaviors were observed during a conflict task. We systematically searched for previous studies and used an expert-informed weighting system to account for their relevance. Subsequently, we aggregated the (power) priors using three methods: linear pooling, logarithmic pooling, and fitting a normal distribution to the linear pool by means of maximum likelihood estimation. We compared the impact of the three differently specified informative priors and default priors on the prior predictive distribution, shrinkage, and the posterior estimates.

RESULTS

The prior predictive distributions for the three informative priors were quite similar and centered around the observed data mean. The shrinkage results showed that the logarithmic pooled priors were least affected by the data. Most posterior estimates were similar across the different priors. Some previous studies contained extremely specific information, resulting in bimodal posterior distributions for the analyses with linear pooled prior distributions. The posteriors following the fitted normal priors and default priors were very similar. Overall, we found that maternal, but not adolescent, internalizing symptoms predicted subsequent mother-adolescent interaction behavior, whereas negative interaction behavior seemed to predict subsequent internalizing symptoms. Evidence regarding mediation effects remained limited.

CONCLUSION

A systematic search for previous information and an expert-built weighting system contribute to a clear specification of power priors. How information from multiple previous studies should be included in the prior depends on theoretical considerations (e.g., the prior is an updated Bayesian distribution), and may also be affected by pragmatic considerations regarding the impact of the previous results at hand (e.g., extremely specific previous results).

Adolescent cannabis and tobacco use are associated with opioid use in young adulthood-12-year longitudinal study in an urban cohort

BACKGROUND AND AIMS

Cannabis, tobacco and alcohol use are prevalent among youth in the United States and may be risk factors for opioid use. The current study aimed at investigating associations between developmental trajectories of cannabis, tobacco and alcohol use in adolescence and opioid use in young adulthood in an urban cohort over the span of 12 years.

DESIGN

Cohort study of adolescents originally recruited for a randomized prevention trial with yearly assessments into young adulthood.

SETTING

Nine urban elementary schools in Baltimore, MD in the United States.

PARTICIPANTS

Participants (n = 583, 86.8% African American, 54.7% male) were originally recruited as first grade students.

MEASUREMENTS

Cannabis, tobacco and alcohol use were assessed annually from ages 14-18 years and opioid use from ages 19-26. Socio-demographics were assessed at age 6. Intervention status was also randomly assigned at age 6. Gender, race, free/reduced-priced lunch and intervention status were included as covariates in individual and sequential growth models.

FINDINGS

There were significant positive associations between the cannabis use intercept at age 14 and the opioid use intercept at age 19 (beta = 1.43; P = 0.028), the tobacco use intercept at age 14 and the opioid use intercept at age 19 (beta = 0.82; P = 0.042). Specifically, more frequent use of cannabis or tobacco at age 14 was associated with more frequent use of opioids at age 19.

CONCLUSIONS

Cannabis and tobacco use in early adolescence may be risk factors for opioid use in young adulthood among African Americans living in urban areas.

Dangers of the Defaults: A Tutorial on the Impact of Default Priors When Using Bayesian SEM With Small Samples

When Bayesian estimation is used to analyze Structural Equation Models (SEMs), prior distributions need to be specified for all parameters in the model. Many popular software programs offer default prior distributions, which is helpful for novel users and makes Bayesian SEM accessible for a broad audience. However, when the sample size is small, those prior distributions are not always suitable and can lead to untrustworthy results. In this tutorial, we provide a non-technical discussion of the risks associated with the use of default priors in small sample contexts. We discuss how default priors can unintentionally behave as highly informative priors when samples are small. Also, we demonstrate an online educational Shiny app, in which users can explore the impact of varying prior distributions and sample sizes on model results. We discuss how the Shiny app can be used in teaching; provide a reading list with literature on how to specify suitable prior distributions; and discuss guidelines on how to recognize (mis)behaving priors. It is our hope that this tutorial helps to spread awareness of the importance of specifying suitable priors when Bayesian SEM is used with small samples.

Factor Validity of Alcohol Use Disorders Identification Test (AUDIT) Using Robust Estimations in Ecuadorian Adolescents

OBJECTIVE

Confirm the three correlated factors model of the Alcohol Use Disorders Identification Test (AUDIT) using robust estimations and evaluate its internal consistency with a sample of Ecuadorian adolescents.

METHOD

Descriptive and instrumental analysis that includes confirmatory factor analysis with robust estimation and the calculation of its internal consistency.

PARTICIPANTS

A total of 1113 adolescents in which 56.1% are men and 43.9% are women), and they were between 11 and 19 years old ($\overline{X} $= 14.9 years; s = 1.67). Students from eight educational centres in Cotopaxi (54.1%) and Tungurahua (45.9%) in Ecuador were also included.

RESULTS

The three correlated factors model from the AUDIT is confirmed with χ2 = 95.67; P < 0.001; df = 32; χ2/df = 2.98; comparative adjustment index = 0.93; Tucker-Lewis index = 0.90; standardized root mean square residual = 0.046; root mean square error of approximation = 0.042; 95% confidence interval [0.033-0.052].

CONCLUSIONS

The three correlated factors model from the AUDIT using robust estimations has an adequate fit and is also reliable in a sample of Ecuadorian adolescents.

Multimethod Assessement of Time-Stable and Time-Variable Interindividual Differences

Abstract. The dynamic development of interindividual differences and the temporal interplay between different personality constructs are of major interest to many researchers in the field of personality psychology. Furthermore, the collection of multiple rater-perspectives complementing classical self-report measures in psychological assessment is increasingly applied also in longitudinal research. Nevertheless, models to analyze longitudinal multitrait-multimethod (MTMM) data are scarce. A new Latent State-Trait (LST) Graded Response Model for the analysis of longitudinal MTMM data with ordered categorical response variables is introduced. The model combines advantages of LST theory and MTMM models for different types of raters (interchangeable and structurally different) with an Item Response Theory (IRT) approach. The model allows researchers to analyze the stability and variability of personality constructs, discriminant and convergent validity, as well as rater effects on the item-level. Model application and interpretation are illustrated using subjective well-being data of young adults. Results of an extensive simulation study indicate that the model can be accurately estimated with Bayesian statistics with at least 3 measurement occasions and more than 250 target persons rated by at least 5 interchangeable raters under moderate degrees of convergent validity.

A General Bayesian Multidimensional Item Response Theory Model for Small and Large Samples

Although item response theory (IRT) models such as the bifactor, two-tier, and between-item-dimensionality IRT models have been devised to confirm complex dimensional structures in educational and psychological data, they can be challenging to use in practice. The reason is that these models are multidimensional IRT (MIRT) models and thus are highly parameterized, making them only suitable for data provided by large samples. Unfortunately, many educational and psychological studies are conducted on a small scale, leaving the researchers without the necessary MIRT models to confirm the hypothesized structures in their data. To address the lack of modeling options for these researchers, we present a general Bayesian MIRT model based on adaptive informative priors. Simulations demonstrated that our MIRT model could be used to confirm a two-tier structure (with two general and six specific dimensions), a bifactor structure (with one general and six specific dimensions), and a between-item six-dimensional structure in rating scale data representing sample sizes as small as 100. Although our goal was to provide a general MIRT model suitable for smaller samples, the simulations further revealed that our model was applicable to larger samples. We also analyzed real data from 121 individuals to illustrate that the findings of our simulations are relevant to real situations.

Multilevel Factor Score Regression

Multilevel SEM is an increasingly popular technique to analyze data that are both hierarchical and contain latent variables. The parameters are usually jointly estimated using a maximum likelihood estimator (MLE). This has the disadvantage that a large sample size is needed and misspecifications in one part of the model may influence the whole model. We propose an alternative stepwise estimation method, which is an extension of the Croon method for factor score regression. In this article, we extend this method to the multilevel setting. A simulation study was used to compare this new estimation method to the standard MLE. The Croon method outperformed MLE with regard to convergence rate, bias, MSE, and coverage, in particular when models contained a structural misspecification. In conclusion, the Croon method seems to be a promising alternative to MLE.

The Importance of Type I Error Rates When Studying Bias in Monte Carlo Studies in Statistics

Two common outcomes of Monte Carlo studies in statistics are bias and Type I error rate. Several versions of bias statistics exist but all employ arbitrary cutoffs for deciding when bias is ignorable or non-ignorable. This article argues Type I error rates should be used when assessing bias.

Exploring the Correlation Between Multiple Latent Variables and Covariates in Hierarchical Data Based on the Multilevel Multidimensional IRT Model

In many large-scale tests, it is very common that students are nested within classes or schools and that the test designers try to measure their multidimensional latent traits (e.g., logical reasoning ability and computational ability in the mathematics test). It is particularly important to explore the influences of covariates on multiple abilities for development and improvement of educational quality monitoring mechanism. In this study, motivated by a real dataset of a large-scale English achievement test, we will address how to construct an appropriate multilevel structural models to fit the data in many of multilevel models, and what are the effects of gender and socioeconomic-status differences on English multidimensional abilities at the individual level, and how does the teachers' satisfaction and school climate affect students' English abilities at the school level. A full Gibbs sampling algorithm within the Markov chain Monte Carlo (MCMC) framework is used for model estimation. Moreover, a unique form of the deviance information criterion (DIC) is used as a model comparison index. In order to verify the accuracy of the algorithm estimation, two simulations are considered in this paper. Simulation studies show that the Gibbs sampling algorithm works well in estimating all model parameters across a broad spectrum of scenarios, which can be used to guide the real data analysis. A brief discussion and suggestions for further research are shown in the concluding remarks.

Preventing Neighborhood Disorder: Comparing Alternative Models of Collective Efficacy Theory Using Structural Equation Modeling

Collective efficacy is a widely studied theoretical framework. Originally operationalized as the combination of social cohesion and informal social control, collective efficacy theory is a predictor of multiple positive outcomes. Conceptual and empirical critiques of collective efficacy theory suggest that social cohesion and informal social control should be modeled as unique constructs. Further, the current model of collective efficacy theory does not include an explicit measure of efficacy. Mutual efficacy, defined as community members' beliefs that collective action will be successful at attaining group goals, will be developed in this manuscript. The purpose of mutual efficacy was to make efficacy an explicit component within collective efficacy theory. Three models of collective efficacy theory are compared in this study: (a) a one-factor model of collective efficacy that combines social cohesion and informal social control, (b) a two-factor model of collective efficacy that models social cohesion as a predictor of informal social control, and (c) a mutual efficacy model where the relationship between social cohesion and informal social control is mediated by mutual efficacy. Results suggest that the two-factor model and the mutual efficacy model both fit the data better than the current model of collective efficacy.

Categorical Omega With Small Sample Sizes via Bayesian Estimation: An Alternative to Frequentist Estimators

When item scores are ordered categorical, categorical omega can be computed based on the parameter estimates from a factor analysis model using frequentist estimators such as diagonally weighted least squares. When the sample size is relatively small and thresholds are different across items, using diagonally weighted least squares can yield a substantially biased estimate of categorical omega. In this study, we applied Bayesian estimation methods for computing categorical omega. The simulation study investigated the performance of categorical omega under a variety of conditions through manipulating the scale length, number of response categories, distributions of the categorical variable, heterogeneities of thresholds across items, and prior distributions for model parameters. The Bayes estimator appears to be a promising method for estimating categorical omega. Mplus and SAS codes for computing categorical omega were provided.

Skew t Mixture Latent State-Trait Analysis: A Monte Carlo Simulation Study on Statistical Performance

This simulation study assessed the statistical performance of a skew t mixture latent state-trait (LST) model for the analysis of longitudinal data. The model aims to identify interpretable latent classes with class-specific LST model parameters. A skew t-distribution within classes is allowed to account for non-normal outcomes. This flexible function covers heavy tails and may reduce the risk of identifying spurious classes, e.g., in case of outliers. Sample size, number of occasions and skewness of the trait variable were varied. Generally, parameter estimation accuracy increases with increasing numbers of observations and occasions. Larger bias compared to other parameters occurs for parameters referring to the skew t-distribution and variances of the latent trait variables. Standard error estimation accuracy shows diffuse patterns across conditions and parameters. Overall model performance is acceptable for large conditions, even though none of the models is free from bias. The application of the skew t mixture model in case of large numbers of occasions and observations may be possible, but results should be treated with caution. Moreover, the skew t approach may be useful for other mixture models.

Dysfunction by Disclosure? Stereotype Threat as a Source of Secondary Neurocognitive Malperformance in Obsessive-Compulsive Disorder

OBJECTIVES

There is mixed evidence regarding whether patients with obsessive-compulsive disorder (OCD) display substantial neurocognitive deficits. Several studies implicate poor motivation, comorbid disorders, or distraction due to obsessive thoughts as potential causes of secondary malperformance. The present study examined the impact of stereotype threat (i.e., confrontation with a negative stereotype may impair performance) on neuropsychological functioning in individuals with OCD. We hypothesized that a stereotype threat cue emphasizing neurocognitive deficits in OCD (as is often conveyed in disclosure and consent documents that inform patients about the purpose of a study) would compromise patients' test performance relative to a control group who did not receive such cue.

METHODS

Fifty participants with either a verified or a likely diagnosis of OCD were recruited online and randomly assigned to either an experimental condition aimed to elicit stereotype threat or a control condition. Both groups underwent (objective) memory and attention (Go/NoGo task) assessments and completed questionnaires capturing psychopathology, cognitive complaints, and self-stigma.

RESULTS

As hypothesized, patients in the stereotype threat condition performed worse on the Go/NoGo task. Groups did not differ on any other measures.

CONCLUSIONS

Stereotype threat negatively impacted neuropsychological performance on an attention task. The threat cue was perhaps too weak or the stereotype threat was already internalized by the patients and "saturated" at baseline so that no effect emerged on the other measures. Implications for clinical trials are discussed. (JINS, 2018, 24, 584-592).

Short form of the Spanish adaptation of the State-Trait Anxiety Inventory

Background/Objective: The State-Trait Anxiety Inventory (STAI) is one of the assessment instruments that are most widely used by psychologists around the world and is the seventh most broadly used by clinical psychologists in Spain. Although several short forms of the STAI have been developed since its creation, none are available for the Spanish general population. The aim of the present study was to develop and validate a short form of the STAI. Method: To achieve this, we administered the full STAI to 1,157 healthy adults, and 30 patients with generalized anxiety disorder. We conducted a discriminant analysis using such groups. Results: We obtained a selection of four items for state anxiety and four items for trait anxiety and compared it to other short forms through a confirmatory factor analysis. The short form obtained with the discriminant analysis showed the best fit for Spanish samples. Conclusions: these eight items can be used to facilitate the state and trait anxiety assessment.