In small sample contexts, Bayesian estimation is often suggested as a viable alternative to frequentist estimation, such as maximum likelihood estimation. Our systematic literature review is the first study aggregating information from numerous simulation studies to present an overview of the performance of Bayesian and frequentist estimation for structural equation models with small sample sizes. We conclude that with small samples, the use of Bayesian estimation with diffuse default priors can result in severely biased estimatesthe levels of bias are often even higher than when frequentist methods are used. This bias can only be decreased by incorporating prior information. We therefore recommend against naively using Bayesian estimation when samples are small, and encourage researchers to make well-considered decisions about all priors. For this purpose, we provide recommendations on how to construct thoughtful priors.

Purpose European studies demonstrated that immigrant adolescents are at a higher risk for mental health problems than native adolescents, but little is known about the role of socioeconomic status (SES) and gender in this association. This study examined to what extent differences in the mental health problems of non-western immigrant and native Dutch adolescents were explained by adolescents’ family affluence and educational level and differed with the adolescents’ family affluence, educational level, and gender. Methods Adolescents in a Dutch nationally representative sample of 11–16-year old native Dutch (n = 5283) and non-western immigrants (n = 1054) reported on their family affluence, own educational level, conduct problems, emotional symptoms, peer relationship problems, and hyperactivity–inattention problems. Results Non-western immigrant adolescents were at a higher risk for conduct problems and peer relationship problems than native Dutch adolescents, but family affluence and educational level explained only a very small proportion of these differences. With two exceptions, differences in the mental health problems of non-western immigrants and natives were highly comparable for different family affluence levels, educational levels, and for boys and girls. Only for natives, a higher family SES was related to less conduct problems. Furthermore, only for non-western immigrants a high family SES related to more hyperactivity–inattention problems. Conclusions Our findings illustrate that the association between immigration background and adolescent mental health problems is largely independent of SES and gender. Future studies should include other factors to facilitate our understanding of the association between immigration background and adolescent mental health problems.

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.

Latent growth models (LGMs) with a distal outcome allow researchers to assess longer-term patterns, and to detect the need to start a (preventive) treatment or intervention in an early stage. The aim of the current simulation study is to examine the performance of an LGM with a continuous distal outcome under maximum likelihood (ML) and Bayesian estimation with default and informative priors, under varying sample sizes, effect sizes and slope variance values. We conclude that caution is needed when predicting a distal outcome from an LGM when the: (1) sample size is small; and (2) amount of variation around the latent slope is small, even with a large sample size. We recommend against the use of ML and Bayesian estimation with Mplus default priors in these situations to avoid severely biased estimates. Recommendations for substantive researchers working with LGMs with distal outcomes are provided based on the simulation results.

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