Introduction to Linear Mixed Models Kevin Paterson

1. Introduction to Linear Mixed ModelsKevin Paterson

2. 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.

3. 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.

4. 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.

5. 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.

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

7. 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.

8. 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).

9. 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).