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Paper No. 12-05

Download 12-05

EO Ogundimu and JL Hutton

A General Sample Selection model with Skew-normal distribution

Date: March 2012

Abstract: Scores arising from questionnaires often follow asymmetric distributions, on a fixed range. This can be due to scores clustering at one end of the scale or selective reporting. Sometimes, the scores are further subjected to sample selection resulting in its partial observability. Thus, methods based on complete cases for skew data are inadequate for the analysis of such data and a general sample selection model is required. Heckman (1976) proposed a full maximum likelihood estimation method under the normality assumption for sample selection problems, and parametric and non-parametric extensions have been proposed. We develop a general sample selection model with underlying skew-normal distribution. A link is established between the continuous component of our model log-likelihood function and an extended version of a generalized skew-normal distribution. This link is used to derive the expected value of the model, which extends Heckman's two-stage model. Finite sample performance of the maximum likelihood estimator of the model is studied via Monte-Carlo simulation. The model parameters are more precisely estimated under the new model even in the presence of moderate to extreme skewness than the Heckman selection models. The model is applied to data from a study of neck injuries where the responses are substantially skew. Computational and identification issues are discussed.