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Does Size Matter ? Exploring the Small Sample Properties of Maximum Likelihood Estimation

The last two decades have witnessed an explosion in the use of computationally intensive methodologies in the social sciences as computer technology has advanced. Among these empirical methods are Maximum Likelihood (ML) procedures. ML estimators possess a variety of desirable qualities, perhaps most prominent of which is the asymptotic efficiency of the standard errors. However, the behavior of the estimators in general, of the estimates of the standard errors in particular, and thus of inferential hypothesis tests are uncertain in small sample analyses. In political science research, small samples are routinely the subject of empirical investigation using ML methods, yet little is known regarding what effect sample size has on a researcher’s ability to draw inferences This paper explores the behavior of ML estimates in probit models across differing sample sizes and with varying numbers of independent variables in Monte Carlo simulations. Our experimental results allow us to conclude that: a) the risk of making Type I errors does not change appreciably as sample size descends; b) the risk of making Type II errors increases dramatically in smaller samples and as the number of regressors increases.