A mixed-effect model for positive responses augmented by zeros.

Area of Science:

• Statistics
• Biostatistics
• Regression Modeling

Background:

• Many real-world datasets contain a high proportion of zero values alongside positive continuous measurements.
• Standard regression models often fail to adequately capture the complex distributional characteristics of such data, particularly when skewness and correlation are present.

Purpose of the Study:

• To propose and evaluate a flexible zero-augmented mixture regression model for positive and zero-inflated data.
• To model the mean of positive responses and the probability of observing a zero response simultaneously, accounting for skewness and correlation.

Main Methods:

• Development of a zero-augmented mixture regression framework incorporating fixed and random effects.
• Modeling the mean on a log scale and mixture probability on a logit scale.
• Utilizing a Markov chain Monte Carlo algorithm for Bayesian inference and employing q-divergence based influence diagnostics.

Main Results:

• The proposed model successfully accommodates skewed positive responses and zero-inflation.
• The joint distribution of random effects effectively captures within-subject correlation and between-subject heterogeneity.
• Bayesian diagnostics provide insights into model influence.

Conclusions:

• The zero-augmented mixed regression model offers a robust approach for analyzing complex positive and zero response data.
• The method demonstrates practical utility, as shown in its application to a dietary recall dataset.