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A computational note on maximum likelihood estimation in random effects panel probit model
Communications for Statistical Applications and Methods 2019;26:315-323
Published online May 31, 2019
© 2019 Korean Statistical Society.

Seung-Chun Lee1,a

aDepartment of Applied Statistics, Hanshin University, Korea
Correspondence to: 1Department of Applied Statistics, Hanshin University, 137 Hanshindae-gil, Osan, Gyeonggi-Do 18101, Korea.
E-mail: seung@hs.ac.kr
Received March 9, 2019; Revised April 11, 2019; Accepted April 12, 2019.
 Abstract
Panel data sets have recently been developed in various areas, and many recent studies have analyzed panel, or longitudinal data sets. Often a dichotomous dependent variable occur in survival analysis, biomedical and epidemiological studies that is analyzed by a generalized linear mixed effects model (GLMM). The most common estimation method for the binary panel data may be the maximum likelihood (ML). Many statistical packages provide ML estimates; however, the estimates are computed from numerically approximated likelihood function. For instance, R packages, pglm (Croissant, 2017) approximate the likelihood function by the Gauss–Hermite quadratures, while Rchoice (Sarrias, Journal of Statistical Software, 74, 1–31, 2016) use a Monte Carlo integration method for the approximation. As a result, it can be observed that different packages give different results because of different numerical computation methods. In this note, we discuss the pros and cons of numerical methods compared with the exact computation method.
Keywords : GLMM, panel regression, Gauss–Hermite quadrature, Monte Carlo integration