Computing Gaussian likelihoods and their derivatives for general linear mixed models
SIAM Journal on Scientific Computing
SAS for Mixed Models, Second Edition
SAS for Mixed Models, Second Edition
Mixed Membership Stochastic Blockmodels
The Journal of Machine Learning Research
Computational Statistics & Data Analysis
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The generalized persistence (GP) model, developed in the context of estimating ''value added'' by individual teachers to their students' current and future test scores, is one of the most flexible value-added models in the literature. Although developed in the educational setting, the GP model can potentially be applied to any structure where each sequential response of a lower-level unit may be associated with a different higher-level unit, and the effects of the higher-level units may persist over time. The flexibility of the GP model, however, and its multiple membership random effects structure lead to computational challenges that have limited the model's availability. We develop an EM algorithm to compute maximum likelihood estimates efficiently for the GP model, making use of the sparse structure of the random effects and error covariance matrices. The algorithm is implemented in the package GPvam in R statistical software. We give examples of the computations and illustrate the gains in computational efficiency achieved by our estimation procedure.