Interactions between latent variables in count regression models.

Area of Science:

• Psychology and Social Sciences
• Statistical Modeling

Background:

• Count outcome variables are common in psychology and social sciences.
• Generalized linear models (GLM) for count data often ignore measurement error in predictors, causing attenuation bias.
• Existing methods rarely address interactions involving latent variables in count regression.

Purpose of the Study:

• Introduce a latent variable count regression model (LV-CRM) that incorporates latent predictors and their interactions.
• Evaluate the estimation accuracy and statistical inference of the LV-CRM compared to GLM-based count regression models.
• Demonstrate the practical application of the LV-CRM in clinical psychology.

Main Methods:

• Developed a latent variable count regression model (LV-CRM).
• Conducted three simulation studies to compare LV-CRM with GLM-based count regression models.
• Investigated estimation accuracy and statistical inference under various conditions.

Main Results:

• GLM-based models showed severe bias in regression coefficients, even with high predictor reliability.
• The LV-CRM provided virtually unbiased regression coefficients, even with moderate sample sizes.
• Statistical inference was generally acceptable for LV-CRM, whereas GLM-based models showed mixed results (low coverage, acceptable detection rates).

Conclusions:

• The LV-CRM effectively accounts for measurement error in latent predictors and their interactions in count regression.
• LV-CRM offers a more accurate and reliable alternative to traditional GLM-based approaches for count data analysis.
• The proposed framework is valuable for researchers in psychology and social sciences dealing with complex count data structures.