Linear Panel Analysis

Abstract

Linear panel analysis refers to the statistical models and methods appropriate for the analysis of continuous or quantitative outcomes with data collected on multiple units (i.e., individuals, schools, or countries) at more than one point in time. This means that linear panel analysis is concerned with the various ways of analyzing change in continuous variables, in describing different patterns of change for different units, in modeling why some units change more than others and what variables are responsible for these differences. These methods may be distinguished from other kinds of longitudinal analyses, such as loglinear, transition or Markov models for analyzing overtime change in categorical outcomes, event history or duration models for analyzing temporal processes leading to the occurrence of specific events, and time-series methods for the analysis of change in continuous outcomes for a single unit over a relatively long period of time. Hence, what characterizes linear panel analysis is a focus on continuous outcomes for multiple units at multiple points. It is conventional within this general rubric to make one further distinction. In some panel datasets, time is dominant, i.e., relatively few units have been observed for relatively long periods of time. In other data, “N” is dominant, i.e., many units have been observed for relatively few points in time. Although the two kinds of data have the same formal structure, time-dominant data, sometimes referred to as “time-series cross-sectional data,” is typically analyzed with statistical methods rooted in the time-series econometric tradition (see Beck and Katz, 1995; Greene, 2003, see also Worrall, Chapter 15 in this volume). This chapter is concerned with the statistical methods used for the analysis of “N-dominant” panel data, typically with observations on hundreds or possibly thousands of units observed at two or more “waves,” in time. Examples of “panel data” are the National Election Studies (NES) panels that track thousands of the same respondents across multiple presidential and congressional elections in 1956–58–60, 1972–74–76, and 2000–2002–2004, the multiwave US Panel Study of Income Dynamics (PSID), and the German Socio-Economic Panel (SOEP) covering some twenty-one waves of observation since 1986.1 There are several important motivations for analyzing panel versus cross-sectional data. Consider the hypothesis that economic performance contributes to the consolidation or stability of democratic regimes. This hypothesis