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Accurate Calculation and Maximization of Log-Likelihood for Mixed Logistic Regression
Accurate Calculation and Maximization of Log-Likelihood for Mixed Logistic Regression
Abstract
For the mixed-effect logistic regression model with a single vector of random effects per stratum, log-likelihood can be effectively and accurately calculated either by the well-known Laplace steepest-descent approach (Breslow and Lin 1995) to calculating likelihood integrals or by a series approximation of Crouch of Spiegelman (1990) based on residue integral expansions. The best accuracy available from such approximations is obtained by the Laplace method for large strata (of size in the hundreds or larger) and the Crouch-Spiegelman method for smaller data. The Crouch-Spiegelman method is also particularly effective for numerical log-likelihood maximization because it simultaneously provides accurate derivatives of the log-likelihood with respect to parameters.
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Page Last Revised - October 8, 2021
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