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ERIC Number: EJ922103
Record Type: Journal
Publication Date: 2006-Mar
Pages: 26
Abstractor: As Provided
Reference Count: 34
ISSN: ISSN-0033-3123
Multilevel Model Prediction
Frees, Edward W.; Kim, Jee-Seon
Psychometrika, v71 n1 p79-104 Mar 2006
Multilevel models are proven tools in social research for modeling complex, hierarchical systems. In multilevel modeling, statistical inference is based largely on quantification of random variables. This paper distinguishes among three types of random variables in multilevel modeling--model disturbances, random coefficients, and future response outcomes--and provides a unified procedure for predicting them. These predictors are best linear unbiased and are commonly known via the acronym BLUP; they are optimal in the sense of minimizing mean square error and are Bayesian under a diffuse prior. For parameter estimation purposes, a multilevel model can be written as a linear mixed-effects model. In this way, parameters of the many equations can be estimated simultaneously and hence efficiently. For prediction purposes, we show that it is more convenient to retain the multiple equation feature of multilevel models. In this way, the efficient BLUPs are easy to compute and retain their intuitively appealing recursive form. We also derive explicit equations for standard errors of these different types of predictors. Prediction in multilevel modeling is important in a wide range of applications. To demonstrate the applicability of our results, this paper discusses prediction in the context of a study of school effectiveness.
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Publication Type: Journal Articles; Reports - Research
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A