Univariate Versus Multivariate Modeling of Panel Data: Model Specification and Goodness-of-Fit Testing

Abstract

Two approaches are commonly in use for analyzing panel data: the univariate, which arranges data in long format and estimates just one regression equation; and the multivariate, which arranges data in wide format, and simultaneously estimates a set of regression equations. Although technical articles relating the two approaches exist, they do not seem to have had an impact in organizational research. This article revisits the connection between the univariate and multivariate approaches, elucidating conditions under which they yield the same—or similar—results, and discusses their complementariness. The article is addressed to applied researchers. For those familiar only with the univariate approach, it contributes with conceptual simplicity on goodness-of-fit testing and a variety of tests for misspecification (Hausman test, heteroscedasticity, autocorrelation, etc.), and simplifies expanding the model to time-varying parameters, dynamics, measurement error, and so on. For all practitioners, the comparative and side-by-side analyses of the two approaches on two data sets— demonstration data and empirical data with missing values—contributes to broadening their perspective of panel data modeling and expanding their tools for analyses. Both univariate and multivariate analyses are performed in Stata and R.