Distinguishing Between Latent Classes and Continuous Factors: Resolution by Maximum Likelihood?

Area of Science:

• Statistics
• Psychometrics
• Data Analysis

Background:

• Latent variable models are essential for understanding systematic patterns in observed data.
• These models can incorporate continuous, categorical, or mixed latent variables.
• Accurate identification of latent variable type is critical for valid statistical inference.

Purpose of the Study:

• To determine if observed responses can reliably distinguish between continuous and categorical latent variables.
• To quantify the impact of sample size and class proportions on this distinction.

Main Methods:

• Simulated data were generated under various latent variable model assumptions.
• Latent variable models (categorical, continuous, mixed) were fitted to the simulated data.
• Exploratory factor mixture models were employed to compare model fit and differentiate latent variable types.

Main Results:

• Restricting analyses to only continuous or only categorical models can lead to overextraction of factors or classes, respectively, when the underlying data structure is different.
• Comparing the fit of different exploratory factor mixture models generally allows for correct identification of categorical and/or continuous latent variables.
• Model selection accuracy is influenced by the degree of class separation and the sample size within each class.

Conclusions:

• Exploratory factor mixture models provide a robust framework for distinguishing between continuous and categorical latent variables.
• Adequate class separation and sufficient within-class sample size are critical for accurate latent variable type identification.
• Careful model selection is necessary to avoid misinterpretations arising from population heterogeneity or unmodeled factor structures.