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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(n3) 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.