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:
 http://www.pallier.org//ressources/MinF/compminf.htm 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 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).
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).