Prediction in Multilevel Models

Afshartous, David; Leeuw, Jan de

doi:10.3102/10769986030002109

Cited by 37 publications

(34 citation statements)

References 29 publications

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“…Contributions from a frequentist stance include Swamy (1970), Rosenberg (1973), Rao (1975), Harville (1976), Ware and Wu (1981), Strenio et al (1983), Kackar and Harville (1984), Reinsel (1984Reinsel ( , 1985, Bondeson (1990), Candel (2004Candel ( , 2007, Afshartous and de Leeuw (2005) and Frees and Kim (2006). References with a Bayesian perspective include Lindley and Smith (1972), Smith (1973), Fearn (1975) and Strenio et al (1983).…”

Section: Introductionmentioning

confidence: 99%

Prediction in Multilevel Generalized Linear Models

Skrondal

Rabe‐Hesketh

2009

Journal of the Royal Statistical Society Series A: Statistics in Society

185

142

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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.

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Section: Introductionmentioning

confidence: 99%

Prediction in Multilevel Generalized Linear Models

Skrondal

Rabe‐Hesketh

2009

Journal of the Royal Statistical Society Series A: Statistics in Society

185

142

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“…This algorithm is similar in nature to that of our previous simulation studies (Afshartous & de Leeuw, 2004) where for each simulated multilevel data set an additional J observations were simulated as future observables. Here-since we no longer have the option of simulating data-we mimic this procedure by repeatedly selecting J observations and, in essence, designating these as future observables.…”

Section: Cross Validationmentioning

confidence: 95%

“…In oder to improve upon the rudimentary and potentially problematic model comparisons above, we apply a predictive approach to these four models very similar to the simulations we employed to assess the performance of various prediction rules (Afshartous & de Leeuw, 2004). Specifically, instead of focusing on coefficient estimates we examine how well these models predict a future observable y * j in the jth group, e.g., a future student in a particular school.…”

Section: Model 2 Versus Modelmentioning

confidence: 99%

“…In an earlier study, we consider the problem of predicting a future observable y * j in the jth group of the framework above (Afshartous & de Leeuw 2004). We examined various prediction rules for predicting y * j and demonstrated several analytical results on the relative performance of these prediction rules.…”

Section: Introductionmentioning

confidence: 99%

“…In an earlier study, we investigated the performance of various prediction rules for predicting a future observable within a hierarchical data set (Afshartous & de Leeuw, 2004). We apply the multilevel prediction approach to the NELS:88 educational data in order to assess the predictive performance on a real data set; four candidate models are considered and predictions are evaluated via both cross-validation and bootstrapping methods.…”

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confidence: 99%

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An Application of Multilevel Model Prediction to NELS:88

Afshartous

Leeuw

2004

Behaviormetrika

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Multilevel modeling is often used in the social sciences for analyzing data that has a hierarchical structure, e.g., students nested within schools. In an earlier study, we investigated the performance of various prediction rules for predicting a future observable within a hierarchical data set (Afshartous & de Leeuw, 2004). We apply the multilevel prediction approach to the NELS:88 educational data in order to assess the predictive performance on a real data set; four candidate models are considered and predictions are evaluated via both cross-validation and bootstrapping methods. The goal is to develop model selection criteria that assess the predictive ability of candidate multilevel models. We also introduce two plots that 1) aid in visualizing the amount to which the multilevel model predictions are "shrunk" or translated from the OLS predictions, and 2) help identify if certain groups exist for which the predictions are particularly good or bad.

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Modeling Online Auctions

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Prediction in Multilevel Models

Abstract: Multilevel modeling is an increasingly

Cited by 37 publications

References 29 publications

Prediction in Multilevel Generalized Linear Models

Prediction in Multilevel Generalized Linear Models

An Application of Multilevel Model Prediction to NELS:88

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