Random effect models

Random effect models are particularly useful for handling groups of either nested (where they are also called multilevel models) or crossed data. An example of the former is classes in schools in regions in countries or patients visiting different clinics. Bickel (2007, p.282) suggests having at least 20 groups (e.g. clinics) each containing 30 observations (e.g. patients) to enable the fitting of multilevel models. An example of crossed data is repeated measurements e.g. exam scores over time where different correlation structures can be fitted to repeated measures. They are useful if you wish to generalise from an observed set of factors, such as a particular set of words (items) having the same stem, to the general population (e.g. of all words having this particular stem) in that they take account of sampling variation measured on a set of subjects. Some authors such as Krystal (2004) recommend using random effects models (of factors and covariates) over repeated measures ANOVA. The repeated measures is actually a special case of a subject OR item random effect which can be modelled using random intercepts (see e.g. Liu, Rovine and Molenarr (2012), p.19). More general random effect models are also able to use incomplete data e.g. over time points where not every participant has completed responses at each time point (Hedeker and Gibbons (1997)).

Advantages from comparing the use of random effect models compared to repeated measures ANOVA is given here. This is reproduced here (if the link is broken).

• Examples of the fitting of these models using MIXED and GLM in SPSS are given in pdf format here. Peugh and Enders (2005) also illustrate the fitting of random effect models using SPSS. An example using SPSS to fit random effects models with repeated measures (e.g. time) nested within subjects are given here.

Baguley (2012) shows repeated measures one-way ANOVA can be expressed as a random effects model with subject, repeated measures factor, time, (within subject) for a given outcome in SPSS.

MIXED outcome BY time
  /CRITERIA=CIN(95) MXITER(100) MXSTEP(10) SCORING(1) SINGULAR(0.000000000001) HCONVERGE(0, 
    ABSOLUTE) LCONVERGE(0, ABSOLUTE) PCONVERGE(0.000001, ABSOLUTE)
  /FIXED=time | SSTYPE(3)
  /METHOD=REML
  /REPEATED=time | SUBJECT(subject) COVTYPE(CS).

• Examples of the fitting of these models using the SAS MIXED procedure are here.

• Information and downloadable multilevel and nlme libraries in R is available from here where this pdf file about fitting multilevel models in R was taken. Links to pdf files giving an excellent comprehensive illustration using lmer and glmer procedures in R by Bates and Rahway are given here. R does not like to give p-values for terms in random effect models but there is a function called pvals.fnc which can be used (details are given here.) A MS Word file with Basic course material on using R for beginners is here.

• An overview (with applications) comparing usage in SPSS, SAS and R is given in this pdf file.

• You can, if from an academic institution, download for free MLwiN software which was developed by researchers at the Institute of Education in London. There are, however, no free manuals available but there is a comprehensive multilevel modeling bibliography. MLwiN can also be run from inside R using a R software interface (see here).

• Formulating as a structural equation model see Curran and Bauer (2007) and Dunn et al(2002).

References

Baayen RH (2008) Analyzing linguistic data. A practical introduction to statistics using R. Cambridge University Press. A PDF copy of this book is available from here. This book is also in the CBSU library.

Baguley T (2012) Serious Stats. A guide to advanced statistics for the behavoral sciences. Palgrave MacMillan:new York. Chapter 18 gives comprehensive coverage and illustrations of random effect models.

Bickel R (2007) Multilevel Analysis for Applied Research: It's Just Regression! (Methodology in the Social Sciences). The Guilford Press:New York. How to do multilevel models using SPSS. [Only £30 in Paperback and in CBU library]. Andy Field's (2009) Discovering Statistics using SPSS. Third Edition. Sage:London covers multilevel models in SPSS in chapter 19.

Curran PJ and Bauer DJ (2007) Building path diagrams for multilevel models. Psychological Methods 12(3) 283-297. (Copy free to download and print out for CBSU users)

Dunn G, Everitt B. and Pickles A. (2002) Modelling covariances and latent variables using EQS. Chapman and Hall/CRC Press:London. pp.124-131

Gelman A and Hill J (2007) Data analysis using regression and multilevel/hierarchical models. Cambridge University Press. (R and BUGS code used in case studies).

Heck RH, Thomas SL and Tabata LN (2010) Multilevel and Longitudinal Modeling with IBM SPSS (Quantitative Methodology Series) (Paperback) Routledge Academic:New York. Further details about this book are given here. There is also now a second edition.

Heck RH, Thomas SL and Tabata LN (2012) Multilevel Modeling of Categorical Outcomes using IBM SPSS (Quantitative Methodology Series) (Paperback) Routledge Academic:New York.

Hedeker D and Gibbons RD (1997). Application of Random-effects Pattern-Mixture Models for Missing Data in Longitudinal Studies. Psychologcal Methods 2(1) 64-78. On-line pdf file of this paper is is here.

Krystal GR (2004) Move over ANOVA: progress in analyzing repeated-measures data and its reflection in papers published in the Archives of General Psychiatry. Archives of General Psychiatry 61(3) 310-317. A copy of the abstract is given here.

Liu S, Rovine MJ and Molenaar PCM (2012) Selecting a linear mixed model for longitudinal data: repeated measures analysis of variance, covariance pattern model, and growth curve approaches. Psychological Methods 17(1) 15-30. (A free copy is available on PSYCNET for CBSU users).

Luke DA (2004) Multilevel Modeling Sage:London. (This is a good primer).

Peugh JL and Enders CK (2005) Using the SPSS mixed procedure to fit cross-sectional and longitudinal multilevel models. Educational and Psychological Measurement 65 714-741.

Wright DB and London K (2009) Multilevel modelling: beyond the basic applications. British Journal of Mathematical and Statistical Psychology 62 439-456. Tutorial featuring examples of using R syntax to fit models. A PDF copy of this article is available from here.