[R-sig-ME] Error in mer_finalize(ans) : Downdated X'X is not positive definite, 9.

[Jukka Corander]

Dear all,

I tried to fit several models with lmer, some of which yield the 
following error message: Error in mer_finalize(ans) : Downdated X'X is 
not positive definite, 9.
The experimental data are as follows:
3 factors: Sexual_orientat (2 values), X_type (4 values), Y_type (4 values)
response lgRT is assumed Gaussian,
each participant has been measured in multiple trials (~190) and there 
are 23 participants in the study.
Design is not balanced, because the cases where X_type and Y_type have 
the same value (Y_type=1&X_type=1 etc) are excluded.
Any model without an interaction term Y_type*X_type can be fitted 
without problems using lmer, but all models with that term (including 
3-way interaction) yield the error message.
For instance,
FittedModel4 <- lmer(lgRT ~ Y_type*Sexual_orientat + 
X_type*Sexual_orientat + (1|Subject),data=arraydata)
works fine, but
FittedModel5 <- lmer(lgRT ~ Y_type*X_type*Sexual_orientat + 
(1|Subject),data=arraydata)
yields the error. If the repeated nature of the measurements is ignored 
and a 3-way interaction model is fitted using ordinary anova, it goes 
through, but, of course, estimates cannot be obtained for all 
interaction terms because they are lacking in the design. Is the error 
due to the inbalanced design, or is there something else I've 
ignored/done wrong? Any insights are highly appreciated!

Cheers, Jukka

-- 
Jukka Corander, Professor, PhD
Department of Mathematics
Åbo Akademi University