Semi-parametric mixed effects models for longitudinal data with applications in business and economics

Longitudinal data is becoming increasingly common in business, social sciences, and biological sciences due to the advantages it offers over cross-section data in modeling and incorporating heterogeneity among subjects and in being able to make causal inferences from observational data. Parametric models and methods are widely used for analyzing longitudinal data for continuous, discrete, and count data occurring in these disciplines. Some popular models are Gaussian, Logit, and Poisson fixed and random effects models. These models are unreliable in situations in which the link function is nonlinear and the form of nonlinearity is not known with certainty. This paper employs a semiparametric extension of fixed and random effects models called generalized additive mixed models (GAMMs) to analyze several longitudinal data sets. These semi-parametric models are flexible and robust extensions of generalized linear models. Following Wood [19], the GAMMs are represented using penalized regression splines and estimated by penalized regression methods treating the penalized component of each smooth as a random effect term and the unpenalized component as a fixed effect term. The degree of smoothness for the unknown functions in the linear predictor part of the GAMM is estimated as the variance parameter of the term. Applications of GAMMs studied include analysis of anti-social behavior, decision to use a professional tax preparer, and analysis of patent data on manufacturing firms. For each application, several GAMMs are compared with their parametric counterparts.