Prediction in multilevel generalized linear models

By A. Skrondal, Sophia Rabe-Hesketh. 2009

230 citations recorded by the source corpus.

Summary.  We discuss prediction of random effects and of expected responses in multilevel generalized linear models. Prediction of random effects is useful for instance in small area estimation and disease mapping, effectiveness studies and model diagnostics. Prediction of expected responses is useful for planning, model interpretation and diagnostics. For prediction of random effects, we concentrate on empirical Bayes prediction and discuss three different kinds of standard errors; the posterior standard deviation and the marginal prediction error standard deviation (comparative standard errors) and the marginal sampling standard deviation (diagnostic standard error). Analytical expressions are available only for linear models and are provided in an appendix . For other multilevel generalized linear models we present approximations and suggest using parametric bootstrapping to obtain standard errors. We also discuss prediction of expectations of responses or probabilities for a new unit in a hypothetical cluster, or in a new (randomly sampled) cluster or in an existing cluster. The methods are implemented in gllamm and illustrated by applying them to survey data on reading proficiency of children nested in schools. Simulations are used to assess the performance of various predictions and associated standard errors for logistic random‐intercept models under a range of conditions.

Subfields: Economics and Econometrics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/93a07176704b7679eb27c9459337beb06c3054ae

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1. Danijel Schorlemmer
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Citations in the corpus

• The psychometric and empirical properties of measures of risk preferences (2017, unknown): “Skrondal and Rabe-Hesketh (2009) describe this approach in detail.18 Because we control for covariates in the next step and because we are not presently interested in the effect of covariates on risk attitudes, we obtain the posterior scores without including any covariates x in the model.”
• Empirical Evaluation of Hierarchical Ground‐Motion Models: Score Uncertainty and Model Weighting (2017, methodology): “Skrondal, A., and S. Rabe-Hesketh (2009).”
• Two Multilevel Modeling Techniques for Analyzing Comparative Longitudinal Survey Datasets* (2013, background): “Figure 4 shows that the number of country-waves observed per country strongly influences the risk of a Type 2 error, above all for the coefficient on xtjM but also to a 25 See, for example, Skrondal and Rabe-Hesketh 2009.”
• Exploring pro-environmental food purchasing behaviour: An empirical analysis of Italian consumers (2018, background): “…Bayes (EB) predicted random effects in ascending order together with 95% confidence intervals based on comparative standard errors (see for details Skrondal and Rabe-Hesketh, 2009) and can be used to test whether the random effect of the corresponding region is significantly different from zero,…”