Finite Mixture Models with Student t Distributions: an Applied Example

Area of Science:

• Statistics
• Psychology
• Prevention Science

Background:

• Finite mixture modeling (FMM) is increasingly used in prevention research to identify latent subgroups.
• A key assumption of standard FMM is within-class normality, which is frequently violated in psychological and prevention data.
• Violating normality assumptions can lead to inaccurate subgroup identification and biased parameter estimates.

Purpose of the Study:

• To introduce prevention researchers to Finite Mixture Modeling (FMM) with Student t distributions for analyzing heavy-tailed data.
• To highlight the limitations of traditional FMM that assumes normal distributions within latent classes.
• To provide practical guidance on applying FMM with Student t distributions in applied research settings.

Main Methods:

• Review of distributional assumptions underlying FMM and limitations of normal distribution-based FMM.
• Introduction and step-by-step application of FMM with Student t distributions using data from a smoking-cessation trial.
• Comparison of results from FMM with normal distributions versus FMM with Student t distributions.

Main Results:

• Fitting FMM with Student t distributions to smoking-cessation trial data revealed differences compared to standard FMM assuming normality.
• The analysis demonstrated the practical application and interpretation of FMM with Student t distributions.
• The study highlighted potential identification of spurious subgroups and biased parameters when normality is violated.

Conclusions:

• Finite Mixture Modeling (FMM) with Student t distributions offers a viable alternative for prevention research with heavy-tailed data.
• Researchers are encouraged to consider FMM with Student t distributions to overcome limitations of the normality assumption.
• Guidelines are provided for implementing FMM with Student t distributions in future prevention research.