APPLYING BETA MAXIMUM LIKELIHOOD ESTIMATION TO CENSORED PROPORTION DATA.

This paper addresses that the maximum likelihood estimation of censored proportion data such as the voteshare of extremist right-wing parties using the censored beta distribution may provide more accurate and more precise statistical results than OLS or Tobit estimation using the normal distribution During a recent decade, the electoral success of extremist right-wing parties, especially in Western Europe, has been under close scrutiny by many quantitative social scientists such as Jackman and Volpert (1996), Swank and Betz (1996), and Golder (2003). They are faced with methodological problems in modeling their dependent variable, the voteshare of extremist right-wing parties, that is largely left-censored, significantly skewed and a proportion at the same time; these characteristics of the dependent variable violate many of the classical assumptions such as normality and homoskedasticity. However, by relying upon OLS, many existing studies fail to produce unbiased and consistent statistical estimators. Furthermore, more advanced efforts, which introduce the Tobit procedure to this discipline, also do not recognize important aspects of proportion data; as voteshare cannot be negative, and as the distribution of the extreme right-wing party data is significantly skewed, Tobit, which assumes observations smaller than zero, whether observed or not, as zero under the normality assumption, may be inappropriate. In fact, since anyone can theoretically run for election and get at least one vote, the probability should never be zero. To adequately handle these problems, this paper applies beta maximum likelihood estimation (BMLE), which is recently introduced by Paolino (2001) to political scientists. Nevertheless, since the beta distribution does not allow zero, I make it allow left-censored data by using the censored beta distribution; this approach assumes a threshold, below which values were not observed, more than zero and smaller than the smallest nonzero percentage; various values of the threshold are tested to make sure whether the statistical results are robust. Then, I will demonstrate that censored BMLE is a better method than OLS or Tobit in analyzing censored proportion data. [ABSTRACT FROM AUTHOR]