Variable selection for random effects two-part models

Random effects two-part models have been applied to longitudinal studies for zero-inflated (or semi-continuous) data, characterized by a large portion of zero values and continuous non-zero (positive) values. Examples include monthly medical costs, daily alcohol drinks, relative abundance of microbiome, etc. With the advance of information technology for data collection and storage, the number of variables available to researchers can be rather large in such studies. To avoid curse of dimensionality and facilitate decision making, it is critically important to select covariates that are truly related to the outcome. However, owing to its intricate nature, there is not yet a satisfactory variable selection method available for such sophisticated models. In this paper, we seek a feasible way of conducting variable selection for random effects two-part models on the basis of the recently proposed “minimum information criterion” (MIC) method. We demonstrate that the MIC formulation leads to a reasonable formulation of sparse estimation, which can be conveniently solved with SAS Proc NLMIXED. The performance of our approach is evaluated through simulation, and an application to a longitudinal alcohol dependence study is provided.

On Some Mixture Models for Over-dispersed Binary Data

In this paper, we consider several binomial mixture models for fitting over-dispersed binary data. The models range from the binomial itself, to the beta-binomial (BB), the Kumaraswamy distributions I and II (KPI \& KPII) as well as the McDonald generalized beta-binomial mixed model (McGBB). The models are applied to five data sets that have received attention in various literature. Because of convergence issues, several optimization methods ranging from the Newton-Raphson to the quasi-Newton optimization algorithms were employed with SAS PROC NLMIXED using the Adaptive Gaussian Quadrature as the integral approximation method within PROC NLMIXED. Our results differ from those presented in Li, Huang and Zhao (2011) for the example data sets in that paper but agree with those presented in Manoj, Wijekoon and Yapa (2013). We also applied these models to the case where we have a $k$ vector of covariates $(x_1, x_2, \ldots, x_k)^{'}$. Our results here suggest that the McGBB performs better than the other models in the GLM framework. All computations in this paper employed PROC NLMIXED in SAS. We present in the appendix a sample of the SAS program employed for implementing the McGBB model for one of the examples.

PROC NLMIXED

The PROC NLMIXED procedure in Statistical Analysis System can be used to estimate parameters of item response theory (IRT) models. The data for this procedure are set up in a particular format called the “long format.” The long format takes a substantial amount of time to execute the program. This article describes a format called the “wide format” to estimate parameters of an IRT model more efficiently. The wide format substantially reduces execution time for models with few parameters. But the time savings decline as the number of parameters increases.

Analysis of Synergistic and Antagonistic Effects of Herbicides Using Nonlinear Mixed-Model Methodology

When herbicides are applied in mixture, and infestation by weeds is less than expected compared with when herbicides are applied alone, a synergistic effect is said to exist. The inverse response is described as being antagonistic. However, if the expected response is defined as a multiplicative, nonlinear function of the means for the herbicides when applied alone, then standard linear model methodology for tests of hypotheses does not apply directly. Consequently, nonlinear mixed-model methodology was explored using the nonlinear mixed-model procedure (PROC NLMIXED) of SAS System®. Generality of the methodology is illustrated using data from a randomized block design with repeated measures in time. Nonlinear mixed-model estimates and tests of synergistic and antagonistic effects were more sensitive in detecting significance, and PROC NLMIXED was a versatile tool for implementation.