Proceedings of World Business, Finance and Management Conference
14 - 15 December 2015, Rendezvous Grand Hotel, Auckland, New Zealand
ISBN: 978-1-922069-91-7
Semi-parametric Regression Modeling in Business and
Economics1
Sunil K Sapra
The paper presents business and economic applications of econometric
techniques that have grown from regression models in recent years focusing on
generalized additive models (GAMs), a semi-parametric extension of multiple
regression models for modeling the relationship between response and predictor
variables on cross-section and time series data and generalized additive mixed
models (GAMMs), a semi-parametric extension of fixed and random effects
models for modeling in longitudinal data settings. The dependent variable may be
continuous, categorical or count. Our semi-parametric models are flexible and
robust extensions of Gaussian, Logit, Poisson, Negative Binomial and other
generalized linear models. Applications include analysis of wage-education
relationship, brand choice, number of trips to a doctor’s office, analysis of antisocial behavior, decision to use a professional tax-preparer, analysis of multiple
bids as a consequence of target management resistance, and analysis of patent
data on manufacturing firms and data on tort filings. Backfitting and penalized
regression spline approaches are utilized for estimation and inference. The
GAMs are represented using penalized regression splines and are estimated by
penalized regression methods. The degree of smoothness for the unknown
functions in the linear predictor part of the GAM is estimated using cross
validation. These semi-parametric regression models allow us to build a
regression surface as a sum of lower-dimensional nonparametric terms
circumventing the curse of dimensionality: the slow convergence of an estimator
to the true value in high dimensions. For each application studied in the paper,
several GAMs are compared and the best model is selected using AIC, UBRE
score, deviances, and R-sq (adjusted). The econometric techniques utilized in
the paper are widely applicable to the analysis of count, binary response and
duration types of data encountered in business and social sciences.
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Sunil K Sapra, Department of Economics and Statistics, California State University, 5151 State
University Dr., Los Angeles, CA 90032, USA, E-mail: ssapra@calstatela.edu;
sunsapra@gmail.com