[R-sig-ME] A strange design; impossible to model using mixed models?

Mike Lawrence Mike.Lawrence at dal.ca
Sun Jun 6 03:22:55 CEST 2010

Hi folks,

This is likely a case of an experimentalist (not me!) failing to
consult a statistician before applying an experimental design. I have
data where I'm interested in 3 theoretical variables derived from 2
manipulated variables, all measured within-Ss:

#set up the design
a = expand.grid(
	s = 1:100 #subjects
	, x = 1:4 #one predictor variable
	, y = 1:3 #second predictor variable
a$z = rnorm(nrow(a)) #fake data

#recode predictor variables
a$v1 = ifelse(a$x==1,-.5,ifelse(a$x==2,.5,NA)) #based on x
a$v2 = ifelse(a$x==3,-.5,ifelse(a$x==4,.5,NA)) #based on x
a$v3 = ifelse(a$y==1,-.5,ifelse(a$y==2,.5,NA)) #based on y

Now, obviously with such formulation, it's impossible to compute an
interaction between v1 and v2 because they're non-orthogonal, but it
is possible to compute the interactions between v1 & v3, and between
v2 and v3:

fit1 = lmer(
	z ~ v1 * v3 + ( 1 | s )
	, data = a

fit2 = lmer(
	z ~ v2 * v3 + ( 1 | s )
	, data = a

But I feel like it should be possible to do both above models
simultaneously (gaining accuracy in the estimation of the main effect
of v3), as:

fit = lmer(
	z ~
		v1 +
		v2 +
		v3 +
		v1:v3 +
		v2:v3 +
		( 1 | s )
	, data = a

However, I get the error:
Error in function (fr, FL, start, REML, verbose)  :
  Number of levels of a grouping factor for the random effects
must be less than the number of observations

Is it simply impossible to model the three variables simultaneously?


Mike Lawrence
Graduate Student
Department of Psychology
Dalhousie University

Looking to arrange a meeting? Check my public calendar:

~ Certainty is folly... I think. ~

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