Introduction to Linear Mixed Models Kevin Paterson

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.

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.

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:  or  JML requires reporting of minF’ in articles.

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.

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

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.

LMM in R  Lots of nerdy types prefer to compute LMM in R.  R is free-to-use programming environment  Available from  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).

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, Raaijmakers, J.G.W. (2003). A further look at the “language-as-fixed-effect fallacy’. Canadian Journal of Experimental Psychology, 57, 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, 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).