Local and Overall Deviance R-Squared Measures for Mixtures of Generalized Linear Models

Area of Science:

• Statistical modeling
• Machine learning
• Epidemiology

Background:

• Generalized linear models (GLMs) use deviance for model fit assessment.
• Existing R-squared measures are limited for complex mixture models.
• Maximum Likelihood (ML) via EM algorithm is standard for mixture model parameter estimation.

Purpose of the Study:

• To extend deviance measures and R-squared for mixtures of GLMs.
• To develop local and global fit measures for cluster-level and sample-level analysis.
• To apply these novel measures to COVID-19 spread data.

Main Methods:

• Extending deviance measures to mixtures of GLMs using ML and the EM algorithm.
• Proposing normalized decompositions of local and total deviance.
• Defining local and overall deviance R-squared measures for mixture models.

Main Results:

• Developed novel local and global deviance R-squared measures for GLM mixtures.
• Demonstrated utility through simulations for Gaussian, Poisson, and binomial responses.
• Applied measures to analyze COVID-19 spread clusters in Italy.

Conclusions:

• The proposed deviance R-squared measures effectively assess model fit in GLM mixtures.
• These measures provide interpretable insights into cluster separation and model performance.
• The methodology is applicable to real-world epidemiological data analysis.