Mixed Models

Ludwig Fahrmeir (), Thomas Kneib (), Stefan Lang () and Brian D. Marx ()
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Ludwig Fahrmeir: LMU Munich, Institute of Statistics
Thomas Kneib: University of Göttingen, Statistics and Econometrics
Stefan Lang: University of Innsbruck, Department of Statistics
Brian D. Marx: Louisiana State University

Chapter Chapter 7 in Regression, 2021, pp 367-430 from Springer

Abstract: Abstract Mixed models extend the predictor $$\eta = {\boldsymbol{x}}'{\boldsymbol{\beta }}$$ η = x ′ β of linear, generalized linear, and categorical regression models by incorporating random effects in addition to the non-random or “fixed” effects $${\boldsymbol{\beta }}$$ β . Therefore, mixed models are sometimes also called random effects models and have become quite popular for analyzing longitudinal data obtained from repeated observations on individuals or objects in longitudinal studies. A closely related situation is the analysis of clustered data, i.e., when observations are obtained from objects selected by subsampling primary sampling units (clusters or groups of objects) in cross-sectional studies. For example, clusters may be defined by hospitals, schools, or firms, where data from (possibly small) subsamples of patients, students, or clients are collected. Generally, clustering may result from any data generating mechanism that induces a cluster structure. In any case, the data consist of $$n_i$$ n i repeated observations $$(y_{i1},\ldots ,y_{ij},\ldots ,y_{in_i},{\boldsymbol{x}}_{i1},\ldots ,{\boldsymbol{x}}_{ij},\ldots ,{\boldsymbol{x}}_{in_i})$$ ( y i 1 , … , y ij , … , y i n i , x i 1 , … , x ij , … , x i n i ) of responses and covariates for each individual or cluster $$i = 1,\ldots ,m$$ i = 1 , … , m .

Date: 2021
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DOI: 10.1007/978-3-662-63882-8_7

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