Nonparametric estimation of the mixing distribution in logistic regression mixed models with random intercepts and slopes

An algorithm that computes nonparametric maximum likelihood estimates of a mixing distribution for a logistic regression model containing random intercepts and slopes is proposed. The algorithm identifies mixing distribution support points as the maxima of the gradient function using a direct search method. The mixing proportions are then estimated through a quadratically convergent method. Two methods for computing the joint maximum likelihood estimates of the fixed effects parameters and the mixing distribution are compared. A simulation study demonstrates the performance of the algorithms and an example using National Basketball Association data is provided.