Skew-probit measurement error models |
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| Affiliation: | 1. Universidade de São Paulo, Caixa Postal 66281 - CEP 05315 970, São Paulo - S.P., Brazil;2. Bayes Forecast-Brasil - S.P., Brazil;1. Instituto de Estadística, Universidad de Valparaíso, Chile;2. Instituto de Matemática e Estatística, Universidade Federal de Goiás, Brazil;3. Departamento de Estatística, Universidade Federal do Piauí, Brazil;4. Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Chile;1. School of Mathematics and Computer Science, Shanxi Normal University, Linfen, 041000, China;2. Department of Statistics, Kansas State University, Manhattan, KS, 66503, United States;1. School of Business and Economics, Loughborough University, Leics, LE11 3TU, UK;2. Department of Economics, Rice University, Houston, United States;1. School of Mathematical Sciences, University College Dublin, Ireland;2. INSIGHT: The National Centre for Big Data Analytics, University College Dublin, Ireland;3. Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada;4. Department of Statistics, Athens University of Economics and Business, Greece;1. Department of Mathematical Sciences, FO 35, University of Texas at Dallas, Richardson, TX 75083-0688, USA;2. School of Earth & Environmental Sciences, G41a Mawson Laboratories, University of Adelaide, North Terrace, SA 5005, Australia |
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| Abstract: | In this paper we extend the structural probit measurement error model by considering the unobserved covariate to follow a skew-normal distribution. The new model is termed the structural skew-normal probit model. As in the normal case, the likelihood function is obtained analytically, and can be maximized by using existing statistical software. A Bayesian approach using Markov chain Monte Carlo techniques for generating from the posterior distributions is also developed. A simulation study demonstrates the usefulness of the approach in avoiding attenuation which arises with the naive procedure. Moreover, a comparison of predicted and true success probabilities indicates that it seems to be more efficient to use the skew probit model when the distribution of the covariate (predictor) is skew. An application to a real data set is also provided. |
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