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Random Effects

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Springer Handbook of Engineering Statistics

Part of the book series: Springer Handbooks ((SHB))

Abstract

This chapter includes well-known as well as state-of-the-art statistical modeling techniques for drawing inference on correlated data, which occur in a wide variety of studies (during quality control studies of similar products made on different assembly lines, community-based studies on cancer prevention, and familial research of linkage analysis, to name a few).

The first section briefly introduces statistical models that incorporate random effect terms, which are increasingly being applied to the analysis of correlated data. An effect is classified as a random effect when inferences are to be made on an entire population, and the levels of that effect represent only a sample from that population.

The second section introduces the linear mixed model for clustered data, which explicitly models complex covariance structure among observations by adding random terms into the linear predictor part of the linear regression model. The third section discusses its extension – generalized linear mixed models (GLMMs) – for correlated nonnormal data.

The fourth section reviews several common estimating techniques for GLMMs, including the EM and penalized quasi-likelihood approaches, Markov chain Newton-Raphson, the stochastic approximation, and the S-U algorithm. The fifth section focuses on some special topics related to hypothesis tests of random effects, including score tests for various models. The last section is a general discussion of the content of the chapter and some other topics relevant to random effects models.

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Abbreviations

BLUP:

best linear unbiased predictor

GEE:

generalized estimating equation

GLM:

generalized linear model

GLMM:

generalized linear mixed model

MCNR:

Monte Carlo Newton–Raphson

PQL:

penalized quasi-likelihood

SIMEX:

simulation extrapolation

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Author information

Authors and Affiliations

  1. Department of Biostatistics, Harvard University, 44 Binney Street, M232, 02115, Boston, MA, USA

    Yi Li

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  1. Yi Li
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Correspondence to Yi Li .

Editor information

Editors and Affiliations

  1. Department of Industrial and Systems Engineering, Rutgers the State University of New Jersey, 96 Frelinghuysen Road, 08854, Piscataway, NJ, USA

    Hoang Pham Prof.

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© 2006 Springer-Verlag

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Li, Y. (2006). Random Effects. In: Pham, H. (eds) Springer Handbook of Engineering Statistics. Springer Handbooks. Springer, London. https://doi.org/10.1007/978-1-84628-288-1_38

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  • DOI: https://doi.org/10.1007/978-1-84628-288-1_38

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-806-0

  • Online ISBN: 978-1-84628-288-1

  • eBook Packages: EngineeringEngineering (R0)

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