[R] lme() - MEEM error (singularity in Backsolve) due to user-specified contrasts amount

[Daniel Preciado]

Hello all, 

I posted this question also in Stackoverflow, but in hindsight I realise it probably fits better here. I am trying to use lme() to fit and compare different models to data from an experiment in a repeated measures design. My dependent variable is response time (RT, in milliseconds); and I have 2 factors: F_A (2 levels) and F_B (3 Levels). For F_B, I have specified the following contrasts:
F_B_C1 <- c(1, -1, 0)      # Contrast prize 1 and 2 levels
F_B_C2 <- c(1, 0, -1)      # Contrast prize 1 with Neutral (no prize)
F_B_C3 <- c(1, 0, -1)      # Contrast prize 2 with Neutral (no prize)
F_B_C4 <- c(1, 1, -2)      # Contrast prize with Neutral
contrasts(Data$F_B, how.many=4) <- cbind(F_B_C1, F_B_C2, F_B_C3, F_B_C4) 
Conditions 1 and 2 are 2 levels of the same manipulation, condition 3 is a neutral control. I am interested in the effect of each level (individually) on RT, and overall in the difference between the experimental manipulation (pooling the first 2 conditions of factor B) and the control condition (final condition of factor B).

I defined the lme() models step-wise, starting with a Baseline model, and then updating that one to include each factor individually, and finally the interaction:
RT_Base <- lme(RT ~ 1, random = ~1|SubjID/F_A/F_B, data=Data, method="ML")  #Baseline model
RT_F_A <- update(RT_Base, .~. + F_A)            #Baseline + F_A
RT_F_B <- update(RT_F_A, .~. + F_B)             #(Baseline+F_A) + F_B
RT_Full <- update(RT_F_B, .~. + F_A:F_B)        #Full model (+ interaction)
However, when I execute the code involving F_B, I get an 
"Error in MEEM (...): Singularity in Backsolve at level 0, block 1). 
I can still inspect the results of the model, but I would like to understand where is this error coming from, what does it mean, and how to avoid it. Furthermore, I realized that if I reduce the amount of contrasts to the default 2, the code runs without any error, so I can only assume that it has something to do with the user-specified comparison pairs. Also, the specified contrasts are not displayed (only the default first 2).

I also read in some answer that the intercept needed to be suppressed in order to prevent this error (by adding RT ~ 0+Factors to the model formulae). I tried that, but it produces the same error. 

I would appreciate any feedback regarding this, Thanks!



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