Brief Research Report: Effects of Sampling Error and Categorization on Estimation of Measure of Sampling Adequacy

Abstract

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.

Keywords:

• Factor analysis
• KMO
• measure of sampling adequacy
• ordered categorical data
• polychoric correlations

Data availability statement

Complete results and R code for data generation used in this research is available in the OSF repository: https://osf.io/hx5ng/, and none of the experiments was preregistered.

Additional information

Funding

This research was supported by Grant MOST 107-2410-H-002-116-MY3 from the Ministry of Science and Technology in Taiwan.