A mixed‐effect model for positive responses augmented by zeros

Abstract

In this research article, we propose a class of models for positive and zero responses by means of a zero-augmented mixed regression model. Under this class, we are particularly interested in studying positive responses whose distribution accommodates skewness. At the same time, responses can be zero, and therefore, we justify the use of a zero-augmented mixture model. We model the mean of the positive response in a logarithmic scale and the mixture probability in a logit scale, both as a function of fixed and random effects. Moreover, the random effects link the two random components through their joint distribution and incorporate within-subject correlation because of the repeated measurements and between-subject heterogeneity. A Markov chain Monte Carlo algorithm is tailored to obtain Bayesian posterior distributions of the unknown quantities of interest, and Bayesian case-deletion influence diagnostics based on the q-divergence measure is performed. We apply the proposed method to a dataset from a 24 hour dietary recall study conducted in the city of São Paulo and present a simulation study to evaluate the performance of the proposed methods.

Principal Component Analysis and Factor Analysis: differences and similarities in Nutritional Epidemiology application

“…In food groups with zero augmented distribution, it would be better to treat the data before starting data reduction. Statistical methods to estimate usual intake can be applied to deal with intra-individual variation and zero augmented distribution 12,13 . Another option is the direct analysis of the correlation matrix, using alternative correlation instead of the usual Pearson correlation.…”

Modeling semicontinuous longitudinal data with order constraints

“…Neelon et al presented a recent overview of methods to analyze semicontinuous data. Other practical examples include consumption of fruits and vegetables, biomarker data, and monthly medical cost . Olsen and Schafer proposed to jointly model semicontinuous longitudinal data with a two‐component model, ie, one submodel for the nonzero data and another submodel for the zero values, with covariates in the models used to partially explain the variation in the response data or excessive zeros.…”

A zero‐augmented generalized gamma regression calibration to adjust for covariate measurement error: A case of an episodically consumed dietary intake

“…Recently, Rodrigues‐Motta et al. () proposed a zero‐augmented mixture model to handle excess zeroes and skewness simultaneously without transforming the response. The authors, however, did not extend their model to adjust for exposure measurement error.…”

“…Transforming back to the original scale, however, can be problematic, especially in the presence of large within-person and between-person variations (Souverein et al, 2011). Recently, Rodrigues-Motta et al (2015) proposed a zero-augmented mixture model to handle excess zeroes and skewness simultaneously without transforming the response. The authors, however, did not extend their model to adjust for exposure measurement error.…”

“…For foods not consumed daily (hereafter, episodically consumed), many zeroes are recorded in the 24HR to denote nonconsumption. The distribution of such an episodically consumed food is usually characterized by excess zeroes, right skewness, and with heteroscedastic variance (Tooze et al., ; Kipnis et al., ; Rodrigues‐Motta et al., ). Due to excess zeroes and large within‐individual variability, using 24HR intake to relate episodically consumed food with a health outcome can be problematic (Kipnis et al., ).…”