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The second version of Kaiser's Measure of Sampling Adequacy (MSA2) has been widely applied to assess the factorability of data in psychological research. The MSA2 is developed in the population and little is known about its behavior in finite samples. If estimated MSA2s are biased due to sampling errors, misleading inferences on the factorability of data are likely to occur. This study investigates the effect of sampling error on MSA2 estimation by systematically examining the accuracy and fluctuations of MSA2 estimates with simulated continuous and ordered categorical data. Features manipulated included the number of factors, number of variables per factor, factor loading, inter-factor correlations, sample size, number of response categories, skewness of variables, and types of correlation analyzed, Pearson and polychoric correlations. Results revealed that the MSA2s were underestimated due to the effect of sampling error. Severely biased MSA2 occurred when analyzing a large number of weakly correlated variables with insufficient participants. The underestimation of MSA2 became worse with categorized data. Polychoric correlations yielded slightly more accurate but relatively unstable MSA2 estimates compared to Pearson correlations. In practice, researchers need to bear in mind the downward bias of MSA2 estimates and interpret the value of sample MSA2s with caution. [ABSTRACT FROM AUTHOR]

Traditional observed variable multilevel models for evaluating indirect effects are limited by their inability to quantify measurement and sampling error. They are further restricted by being unable to fully separate within- and between-level effects without bias. Doubly latent models reduce these biases by decomposing the observed within-level indicators into within- and between-level latent components. This decomposition simultaneously controls for both measurement error at each level, and sampling error in the aggregation of individual values that serve as indicators of higher-level constructs. We illustrate the usefulness of this approach in investigating the mediating role of aggressive attitudes in associations between reports of school climate and prevalence of teasing and bullying. Teacher perceived justness and support in schools were both found to be indirectly associated with the prevalence of teasing and bullying through aggressive attitudes, and teacher perceived support was found to be directly associated with teasing and bullying. [ABSTRACT FROM AUTHOR]