A SIMULATION APPROACH TO OPTIMIZING SELECTION OF THE STANDARD ERROR SPECIFICATION IN COUNT DATA MODELING

Quantitative social scientists assume their model fit is appropriate to the data, especially the theoretical distribution of choice. However, researchers spend less time justifying the standard error specification. This step is critical as a misspecification of the standard error can lead to an incorrect interpretation of the independent variables, or parameters, of the model. Because researchers derive further research agendas and policy implications directly from the significance of their results, a misspecification of the standard error has large real world ramifications. This research, therefore, examines the validity of typically applied standard error techniques in Poisson and Negative Binomial regression in a case study framework, such as the observed information matrix, outer product of the gradient, clustering, nonparametric bootstrapping, and the jackknife procedure. A dataset of 2005 to 2011 state-based pro-/neutral and anti-immigration legislation is employed. In order to assess the validity of these standard error techniques I sample from the fitted conditional Poisson or Negative Binomial model to create a Monte Carlo (MC) simulation, which yields an estimate of the ‘true’ standard error. A relative error calculation then compares the commonly utilized standard error techniques to the MC ‘true’ standard error. The results indicate that the observed information matrix performs particularly well for small sample sizes. The jackknife procedure also performs quite well. Results for the nonparametric bootstrap, however, vary tremendously across iterations. Though the conclusions of this research are unlikely to generalize to other datasets, the approach taken may easily be adapted to other situations and other model formulations in which researchers are concerned with which standard error method to use. I include sample Stata code to illustrate the approach