Troublesome residual plot from linear mixed model

Question

I have fitted the following linear mixed model based on the results of an economic game:

lmer(TotalScore~perOOgivenP+Game+(1|Subject),REML=T,data=mdl1table)->m1

TotalScore is a integer. perOOgivenP is a proportion between 0 and 1 (most of which are 0). Game is numeric and tells us if it is the 1st or 2nd game played by the participant

The qq plot looks good so I am confident the residuals are normally distributed. The fitted vs. residuals plot does not look so good. To me it looks like the residuals are biased. I am not sure what Is causing this or what to do about it?

Could it be caused by the amount of 0's in perOOgivenP (32/46 data points). perOOgivenP is the proportion of times a particular behaviour was made. Would anyone suggest making this binary as in 0 or 1 (actual value not 0).

perOOgivenP is as follows: [1] 0.5000000 1.0000000 0.3333333 0.0000000 0.0000000 0.0000000 NaN 0.1666667 0.2500000 0.8000000 0.1666667 0.0000000 0.3333333 [14] 0.0000000 0.0000000 NaN NaN 0.0000000 0.0000000 0.0000000 NaN 1.0000000 NaN 0.0000000 NaN 0.0000000 [27] 0.0000000 NaN NaN NaN NaN 0.0000000 NaN 0.0000000 0.0000000 0.0000000 NaN NaN NaN [40] 1.0000000 NaN 0.0000000 0.4117647 0.0000000 0.0000000 NaN NaN 0.0000000 0.2000000 0.0000000 NaN 0.0000000 [53] 0.3333333 0.0000000 0.2500000 NaN 0.0000000 NaN NaN NaN 0.0000000 NaN 0.0000000 0.0000000 NaN [66] 0.0000000 NaN NaN NaN 0.0000000 0.0000000 0.0000000 0.0000000 NaN NaN NaN NaN NaN [79] NaN NaN

Answer 1

If perOOgivenP has too many zeroes, it may cause the coefficients fails to NA. It can be a big problem. Even if you get the fitting values, it may not be accurate. You need to show more information about this variable.

It is hard to say whenther this residual plot is biased or not. One obvious thing you can do is to run lm(residuals~c(1:n)), where n is the length or residuals. The coefficients of the fitting line should be close to 0. Also, I suggest use abline(h=0) for residual plot.

Answer 2

By "biased" you presumably mean that there is some non-linear structure left in the residuals. It's by no means obvious to me that this is the case here.

Before leaping to any conclusions - and certainly before losing any information by transforming variables into a less-informative state - I would look at more residual plots. An obvious one would be to give a different colour or shape to the residuals where the suspect variable has a value of zero and see how this impacts on the residuals.