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Introduction to Linear Mixed Models Kevin Paterson

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A problem in psycholinguistics research Research in this area examines psychological aspects of language understanding. Research typically involves exposure to set of linguistic stimuli (i.e., hearing or viewing words, reading sentences). Analysis examines fixed effects (i.e., experimental factors) across a random set of participants from chosen population (e.g., skilled readers). However, neglects that stimuli have also been “randomly” selected from a parent population.

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So what’s the problem? Reanalysis of some published studies by Herb Clark (Clark, 1973) showed that, in some cases, experimental effects were caused by subset of stimuli. Critical question – do the effects generalise across the population to which the stimuli belong? Ways of doing this: Combined F1 and F2 analysis – separate analyses treating participants and stimuli as random variables. Min F prime analysis – combines F1 and F2 values.

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Clark’s solution: minF’ minF’ provides estimate of F-value that generalises across both participants and stimuli. Can use on-line resource to compute this: http://www.pallier.org//ressources/MinF/compminf.htm or JML requires reporting of minF’ in articles.

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Another solution: linear mixed effects modelling ANOVA is at heart multiple regression analysis. Linear mixed effects modelling is an approach to regression that includes random variables, and so can include both participants and stimulus variables. Involves predicting value (e.g., RT) as outcome of (1) participant contribution, (2) stimulus contribution, and (2) manipulated variables.

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LMM in SPSS Select MIXED options. Enter data in format uses for regression (different columns to code, participant, stimulus, IVs, and DV).

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Usefulness of LMM Takes account of multiple random variables, and so gets around the problem encountered in Psycholinguistics research. Also appears to be robust against missing cells, so very useful if you have lots of missing data. Useful too for nested designs, e.g., sample of participants from a sample of hospitals in the region.

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LMM in R Lots of nerdy types prefer to compute LMM in R. R is free-to-use programming environment Available from http://cran.r-project.org To compute LMM install the lme4 package. Arguably better at some estimates than SPSS. See Baayen (2008) for more info (and guidance notes from Brysbaert, 2007).

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Useful reading Baayen, R. H. (2008). Analysing linguistic data. Cambridge: Cambridge University Press. Brysbaert, M. (2007). “The language-as-fixed-effect fallacy”: Some simple SPSS solutions to a complex problem (Version 2.0). Royal Holloway, University of London. Clark, H.H. (1973). The language-as-fixed effect fallacy: A critique of language statistics in psychological research. Journal of Verbal Learning and Verbal Behavior, 12, 335-359. Raaijmakers, J.G.W. (2003). A further look at the “language-as-fixed-effect fallacy’. Canadian Journal of Experimental Psychology, 57, 141-151. Raaijmakers, J.G.W., Schrijnemakers, J.M.C., & Gremmen, F. (1999). How to deal with “the language-as-fixed-effect fallacy”: Common misconceptions and alternative solutions. Journal of Memory and Language, 41, 416-426. SPSS. (2005). Linear Mixed-effects modeling in SPSS: An introduction to the MIXED procedure. SPSS report. Available on the internet (copy the title in google).

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