Procedures for Analyzing Multidimensional Mixture Data

Hsu Lin Su, Po Hsi Chen*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The multidimensional mixture data structure exists in many test (or inventory) conditions. Heterogeneity also relatively exists in populations. Still, some researchers are interested in deciding to which subpopulation a participant belongs according to the participant’s factor pattern. Thus, in this study, we proposed three analysis procedures based on the factor mixture model to analyze data in the multidimensional mixture context. Simulations were manipulated with different levels of factor numbers, factor correlations, numbers of latent classes, and class separation. Issues with regard to model selection were discussed at first. The results showed that in the two-class situations the procedures of “factor structure first then class number” (Procedure 1) and “factor structure and class number considered simultaneously” (Procedure 3) performed better than the “class number first then factor structure” (Procedure 2) and yielded precise parameter estimation and classification accuracy. It would be appropriate to choose Procedures 1 and 3 when strong measurement invariance is assumed while using an information criterion, but Procedure 1 saved more time than Procedure 3. In the three-class situations, the performance of all three procedures was limited. Implementations and suggestions have been addressed in this research.

Original languageEnglish
Pages (from-to)1173-1201
Number of pages29
JournalEducational and Psychological Measurement
Issue number6
Publication statusPublished - 2023 Dec


  • factor mixture model
  • factor structure
  • latent class
  • multidimensional mixture data

ASJC Scopus subject areas

  • Education
  • Developmental and Educational Psychology
  • Applied Psychology
  • Applied Mathematics


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