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Abstract
Taking into account the correlation among responses is important to statistical analysis and inference of multivariate response data. Many variable-selection methods in the literature were developed based on generalized estimating equations (GEE). GEE avoids working with a complex joint likelihood function by using a working correlation matrix, of which the misspecification does not effect the consistency of regression parameter estimates. As a competitor and extension of GEE, weighted score estimating equations (WSEE) were developed based on composite likelihood functions. It relaxes the constraints on correlation parameters of GEE for non-normal variables by applying a “working model,” and extends the application to distributions other than generalized linear model (GLM) marginals. We focus on longitudinal binary responses, and propose variable-selection methods based on GEE and WSEE. Forward-selection processes using score tests based on GEE and WSEE are compared for variable-selection accuracy and computation efficiency. Penalized WSEE using smoothly clipped absolute deviation (SCAD), minimax concave penalty (MCP), and adaptive least absolute shrinkage and selection operator (adaptive LASSO) are proposed and compared to previous variable-selection methods. Asymptotic theories of penalized WSEE estimators are established. Assuming that the within-subject responses are stationary, the average autocorrelation estimated Toeplitz (ACFToep) is proposed as a common correlation matrix in solving correlation considered estimating equations. ACF-Toep reduces the computation in parameter estimation. We study our methods by simulations, and illustrate them on a data example.
