[R-sig-ME] How to include a quadratic term in an lmer model

[Linda Mortensen]

Hi list members,
 
I have recently e-mailed this list asking for some advice on how to use mixed-effects models on ordinal responses (see posts entitled "How to use mixed-effects models on multinomial data"). This query concerns the same data set, but since the topic is a different one, I post the query under a different header. 
Following several list members advice, I'm using a linear mixed-effects model to analyse the data described in the earlier posts, so I'm still working within this model framework. But when trying to decide on the best-fitting model, I have run into a problem: In the data set, there is a curved relationship between one of the explanatory variables (i.e., the serial position of items in a list) and the response variable. A model that includes both a linear and a quadratic term for this variable would most likely describe this relationship better than a model that includes only a linear variable. But when I try to include the quadratic term in the model, using the formula "lmer(y ~ x + I(x^2)", I get the following error message:    
"Error in `contrasts<-`(`*tmp*`, value = "contr.treatment") : 
  contrasts can be applied only to factors with 2 or more levels"
And the following warnings:
"In addition: Warning messages:
1: In Ops.factor(cposition, 2) : ^ not meaningful for factors
2: In Ops.factor(cposition, 2) : ^ not meaningful for factors"

Judging from the error message, the problem seems to be that I have coded the serial position variable using the (default) contrast coding system. The serial position variable has five levels (positions 1 through 5), so I don't understand why R is complaining about the number of levels. - There are 5 levels, so the serial position factor has "2 or more levels". Is it the coding system that is the problem? Can someone explain to me what I'm doing wrong here? Any suggestions are greatly appreciated.
 
Linda 

 
Linda Mortensen
Post-doctoral research fellow
Department of Psychology
University of Copenhagen 
Øster Farimagsgade 2A
1353 Copenhagen K
Denmark
Tel.: +45 3532 4889
E-mail: linda.mortensen at psy.ku.dk