The relationship between multilevel models and non‐parametric multilevel mixture models: Discrete approximation of intraclass correlation,random coefficient distributions,and residual heteroscedasticity

Multilevel data structures are common in the social sciences. Often, such nested data are analysed with multilevel models (MLMs) in which heterogeneity between clusters is modelled by continuously distributed random intercepts and/or slopes. Alternatively, the non‐parametric multilevel regression mixture model (NPMM) can accommodate the same nested data structures through discrete latent class variation. The purpose of this article is to delineate analytic relationships between NPMM and MLM parameters that are useful for understanding the indirect interpretation of the NPMM as a non‐parametric approximation of the MLM, with relaxed distributional assumptions. We define how seven standard and non‐standard MLM specifications can be indirectly approximated by particular NPMM specifications. We provide formulas showing how the NPMM can serve as an approximation of the MLM in terms of intraclass correlation, random coefficient means and (co)variances, heteroscedasticity of residuals at level 1, and heteroscedasticity of residuals at level 2. Further, we discuss how these relationships can be useful in practice. The specific relationships are illustrated with simulated graphical demonstrations, and direct and indirect interpretations of NPMM classes are contrasted. We provide an R function to aid in implementing and visualizing an indirect interpretation of NPMM classes. An empirical example is presented and future directions are discussed.     

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

Multilevel structural equation models are increasingly applied in psychological research. With increasing model complexity, estimation becomes computationally demanding, and small sample sizes pose further challenges on estimation methods relying on asymptotic theory. Recent developments of Bayesian estimation techniques may help to overcome the shortcomings of classical estimation techniques. The use of potentially inaccurate prior information may, however, have detrimental effects, especially in small samples. The present Monte Carlo simulation study compares the statistical performance of classical estimation techniques with Bayesian estimation using different prior specifications for a two-level SEM with either continuous or ordinal indicators. Using two software programs (Mplus and Stan), differential effects of between- and within-level sample sizes on estimation accuracy were investigated. Moreover, it was tested to which extent inaccurate priors may have detrimental effects on parameter estimates in categorical indicator models. For continuous indicators, Bayesian estimation did not show performance advantages over ML. For categorical indicators, Bayesian estimation outperformed WLSMV solely in case of strongly informative accurate priors. Weakly informative inaccurate priors did not deteriorate performance of the Bayesian approach, while strong informative inaccurate priors led to severely biased estimates even with large sample sizes. With diffuse priors, Stan yielded better results than Mplus in terms of parameter estimates.     

Multilevel Factor Analysis: Reporting Guidelines and a Review of Reporting Practices

We provide reporting guidelines for multilevel factor analysis (MFA) and use these guidelines to systematically review 72 MFA applications in journals across a range of disciplines (e.g., education, health/nursing, management, and psychology) published between 1994 and 2014. Results are organized in terms of the (a) characteristics of the MFA application (e.g., construct measured), (b) purpose (e.g., measurement validation), (c) data source (e.g., number of cases at Level 1 and Level 2), (d) statistical approach (e.g., maximum likelihood), and (e) results reported (e.g., intraclass correlations for indicators and latent variables, standardized factor loadings, fit indices). Results from this review have implications for applied researchers interested in expanding their approaches to psychometric analyses and construct validation within a multilevel framework and for methodologists using Monte Carlo methods to explore technical and methodological issues grounded in realistic research design conditions.     

From Stigmatized Immigrants to Radical Right Voting: A Multilevel Study on the Role of Threat and Contact

This study examines the interplay between presence of stigmatized immigrants, threat, and intergroup contact that underlies radical right voting (voting propensity and actual district‐level vote results). On the one hand, low‐status immigrants are often stigmatized and depicted as threats. Thus, presence of stigmatized immigrants should heighten threat perceptions, thereby increasing radical right voting. On the other hand, as positive contact with stigmatized immigrants is known to reduce anti‐immigrant prejudice, it should also attenuate radical right voting. As predicted, multilevel path analyses with the Swiss Election Studies 2011 data (N = 1,736 respondents in 136 districts) revealed that the proportion of stigmatized immigrants (from former Yugoslavia and Albania) in districts heightened perceived threat. Threat perceptions, in turn, increased propensity to vote for the Swiss People's Party, the major radical right party. In contrast, experiencing positive, everyday contact with former Yugoslav and Albanian immigrants reduced voting propensity through attenuated threat perceptions. Contact and threat perceptions were also related to the actual vote through voting propensity.     

Finding a Life Worth Living: Meaning in Life and Graduation from College

Graduation from college is an important milestone for young adults, marked by mixed emotions and poignancy, and therefore is an especially salient context for studying meaning in life. The present research used experience‐sampling methodology to examine the antecedents and consequences of students' experience of meaning in life over the course of graduation. Participants were 74 graduating students who provided a total of 538 reports over the span of 3 days, including commencement day. Increased levels of state meaning in life during the days around commencement were linked to spending time with people in general and with family in particular, and thinking about one's years in college. Thinking about one's years in college mediated the effects of present company on state meaning in life. Graduates who experienced higher levels of state meaning in life during the days around their commencement ceremony had higher trait levels of meaning in life 1 week following commencement. We discuss how making meaning of a poignant experience has implications for healthy psychological development. Copyright © 2016 European Association of Personality Psychology     

Sex and age group differences in the associations between sleep duration and BMI from adolescence to young adulthood

Objective: We examine concurrent and longitudinal associations between sleep duration (SD) and body mass index (BMI) from adolescence to young adulthood, controlling for physical activity and internalising symptoms. Sex and age group differences (early adolescent group ages 12–15 years and late adolescent group ages 16–18 years) are examined.

Design: A randomly selected community-based sample of youth (N = 662; 48.3% males) were surveyed biannually from 2003 (T1) to 2014 (T6).

Results: We found sex and age group differences for the concurrent and longitudinal associations between SD and BMI. For males, shorter SD at baseline was concurrently related to higher BMI. For females, shorter SD at baseline was associated with longitudinal increases in BMI, for the late adolescent group only.

Conclusion: Findings show that the association between SD and BMI, previously shown in childhood, continues to be significant in adolescence and young adulthood. Developmentally appropriate and sex-specific strategies for motivating and supporting healthy sleep habits in adolescence that may help to prevent weight gain into young adulthood are discussed.     

Ecological assessments of community disorder: Their relationship to fear of crime and theoretical implications

Researchers suggest that fear of crime arises from community disorder, cues in the social and physical environment that are distinct from crime itself. Three ecological methods of measuring community disorder are presented: resident perceptions reported in surveys and on-site observations by trained raters, both aggregated to the street block level, and content analysis of crime- and disorder-related newspaper articles aggregated to the neighborhood level. Each method demonstrated adequate reliability and roughly equal ability to predict subsequent fear of crime among 412 residents of 50 blocks in 50 neighborhoods in Baltimore, MD. Pearson and partial correlations (controlling for sex, race, age, and victimization) were calculated at multiple levels of analysis: individual, individual deviation from block, and community (block/neighborhood). Hierarchical linear models provided comparable results under more stringent conditions. Results linking different measure of disorder with fear, and individual and aggregated demographics with fear inform theories about fear of crime and extend research on the impact of community social and physical disorder. Implications for ecological assessment of community social and physical environments are discussed.     

Transactional development of parent personality and child temperament

Stability and change in parental extraversion and neuroticism were studied in transaction with their views of their child's temperament from the age of six months to the age of five‐and‐a‐half years in 109 mother–father–child triads (parent–daughter: n = 61, parent–son: n = 48). While parental traits showed high stability, infants' higher positive affectivity predicted an increase in parental extraversion over 5 years, and infant's higher activity predicted a decrease in parental neuroticism. Parent‐rated temperament showed expected heterotypic continuity. Initially higher parental extraversion predicted an increase in the child's effortful control, and higher parental neuroticism predicted an increase in the child's negative affectivity. The results indicate that parental personality and child temperament develop in transaction promoting change in each other. Copyright © 2008 John Wiley & Sons, Ltd.     

多水平随机中介效应估计及其比较

本文在综述各类多水平中介模型的基础上, 聚焦于自变量、中介变量、因变量都来自多水平结构中较低水平的多水平随机中介效应模型, 通过蒙特卡洛模拟研究比较该模型与简化的多水平固定中介效应模型、传统中介效应模型的差别, 并考察了目前用于多水平随机中介效应的三种参数估计方法：限制性极大似然、极大似然、最小方差二次无偏估计在不同情况下对随机中介效应估计的优劣。研究结果显示：当数据符合多水平随机中介效应模型时, 使用简化模型将错误估计中介效应及其标准误, 得到不正确的统计检验结果; 使用多水平随机中介效应模型能够实现对中介效应的正确估计和检验, 其中限制性极大似然或极大似然估计方法优于最小方差二次无偏估计方法。     

Linking personality states,current social roles and major life goals

Employing an experience‐sampling design, the interplay between personality states, social roles and major life goals was examined as it unfolds in the stream of people's daily lives. Multilevel analyses revealed a considerable amount of both within‐ and between‐person variability in state expressions of personality traits justifying further examination of predictors at both levels of analyses. Roles proved as predictors of current personality states albeit effects differed significantly between individuals. Life goals accounted for between‐person differences in average personality states but were not effective in predicting differences in relations between personality states and roles. Altogether, findings testify to the viability of the employed research strategy to analyse the interplay between both dispositional and fluctuating influences on individuals' trait expressions in behaviour. Copyright © 2009 John Wiley & Sons, Ltd.