Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
`` Direct Search'' Solution of Numerical and Statistical Problems
Journal of the ACM (JACM)
On the Convergence of Pattern Search Algorithms
SIAM Journal on Optimization
Maximum likelihood computation for fitting semiparametric mixture models
Statistics and Computing
Numerical Analysis for Statisticians
Numerical Analysis for Statisticians
Editorial: The 2nd special issue on advances in mixture models
Computational Statistics & Data Analysis
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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.