# [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

--
Mike Lawrence