Fast computing of some generalized linear mixed pseudo-models with temporal autocorrelation

This paper considers ways to increase computational speed in generalized linear mixed pseudo-models for the case of many repeated measurements on subjects. We obtain linearly increasing computing time with number of observations, as opposed to O(n ³) increasing computing time using numerical optimization. We also find a surprising result; that incomplete optimization for covariance parameters within the larger parameter estimation algorithm actually decreases time to convergence. After comparing various computing algorithms and choosing the best one, we fit a generalized linear mixed model to a binary time series data set with over 100 fixed effects, 50 random effects, and approximately 1.5 ×  10⁵ observations.