Abstract
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 semi-parametric 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. Keywords: Generalized Additive Mixed Models (GAMMS), Generalized Linear Mixed Models (GLMMS), Logit Models, Poisson Regression Models, Penalized Regression Splines.
Highlights
Linear regression model is the workhorse of empirical research across many disciplines
This paper presents econometric applications of the generalized additive mixed models (GAMM) extensions of the generalized linear mixed models (GLMMs) for longitudinal data, which includes the conventional random effects models and demonstrates that the GAMMs can overcome a serious weakness of the GLMMs: failing to identify the nonlinearities in the link function
Estimation of GAMMs consists in representing the GAMM as a GLMM with a variance component controlling the amount of smoothing for each additive component
Summary
Linear regression model is the workhorse of empirical research across many disciplines. Generalized linear models (GLMs) extend the linear regression model by allowing for response variables, which are bounded or discrete These models are used for modeling continuous, categorical, count, and ordinal data on the response variable. McCullagh and Nelder [11] provide an authoritative account of GLMs and Cameron and Trivedi [4] and Greene [6] provide econometric applications These models are appropriate for cross-section data and do not account for heterogeneity among subjects. Sapra [14] presented several applications of these models to cross-section data in business and economics and demonstrated that GAMs generally provided a better fit to data than GLMs. This paper presents econometric applications of the generalized additive mixed models (GAMM) extensions of the generalized linear mixed models (GLMMs) for longitudinal data, which includes the conventional random effects models and demonstrates that the GAMMs can overcome a serious weakness of the GLMMs: failing to identify the nonlinearities in the link function.
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