Can I have a categorical variable (similar to the likert scale) on the predictor side of the equation in lme?

Question

My mixed model looks something like this

weight ~ age + sex + fruits + (subject | time)

The predictor fruit has been converted to a categorical scale of High Medium and Low.

Do I have to set labels and levels to the variable Fruit? Before I enter it into the model?

summary(lol$fruittotaldi)
Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
0.000   0.000   1.000   1.107   2.000   2.000       2 


Linear mixed model fit by maximum likelihood  ['lmerMod']
Formula: weight ~ age + sex + treatment + time + treatment * time + factor(fruittotaldi) + (time | code)
Data: lol

AIC      BIC   logLik deviance df.resid 
619.6    652.3   -297.8    595.6      100 

Scaled residuals: 
 Min       1Q   Median       3Q      Max 
-1.99904 -0.35179  0.04656  0.38198  1.33412 

Random effects:
Groups   Name        Variance  Std.Dev. Corr 
code    (Intercept) 151.44427 12.3063       
time                  0.05832  0.2415  -0.55
Residual              0.91735  0.9578       

Number of obs: 112, groups:  code, 38

Fixed effects:
                    Estimate Std. Error t value
(Intercept)             80.05023    5.61314  14.261
age                      0.02017    0.11992   0.168
sexm                     7.18388    5.57894   1.288
treatmentb             -13.43906    4.08158  -3.293
time                    -0.37393    0.06007  -6.225
factor(fruittotaldi).L  -0.67890    0.30987  -2.191
factor(fruittotaldi).Q   0.86437    0.28231   3.062
treatmentb:time          0.28061    0.08786   3.194

Correlation of Fixed Effects:
            (Intr) age    sexm   trtmnt time   fc().L fc().Q
age         -0.865                                          
sexm        -0.027 -0.083                                   
treatmentb  -0.493  0.187 -0.030                            
time        -0.254 -0.004  0.002  0.352                     
fctr(frt).L  0.029 -0.046  0.005  0.007  0.115              
fctr(frt).Q -0.037  0.036  0.021  0.010  0.031 -0.142       
tretmntb:tm  0.176  0.000 -0.004 -0.509 -0.690 -0.120 -0.052

Answer 1

First of all, there is absolutely no reason that your predictor variables need to be Normally distributed in order to use a linear model or one of its extensions; the only assumptions linear models make about the predictors are that they are measured without error (and even this assumption can be relaxed under certain circumstances). (e.g. see here or here).

What's important in numeric predictor variables is whether the expected response is linear, i.e. whether you expect a one-unit change in the predictor to give rise to the same amount of change in the response, regardless of the baseline value of the predictor. If not, you might want to consider transforming the predictor in some way (not because it's not Normal, but because you want to transform it to a scale where a one-unit change will have a constant response).

Binning/categorizing continuous predictors is not generally recommended, because it loses information (e.g. see here). However, if you do decide to do so, you should convert your numeric value to an ordered factor, i.e.

lol$fruittotaldi <- ordered(lol$fruittotaldi, 
                            levels=c(0,1,2),
                            labels=c("low","medium","high"))

This isn't a particularly mixed-model-specific question; ordered (ordinal) predictors are handled similarly across most R packages that fit statistical models. There are a few confusing aspects of factors in R:

• all factors in R have an "order of levels", which determines (1) the baseline level for treatment contrasts; (2) the order in which the levels will be plotted in summaries, shown in graphs, etc..
• the difference between ordered factors and ordinary (non-ordered) factors in R (f <- ordered(f)) is that the default contrasts for ordered factors are polynomial contrasts rather than treatment contrasts; instead of "intercept", "level 2 vs baseline", "level 3 vs baseline", the parameters will refer to "mean", "linear effect", "quadratic effect" ...
• in any case, the overall fit of the model (log-likelihood, AIC, etc. etc.) will be independent of the contrasts/how the factors are defined.

Answer 2

The predictor fruit has been converted to a categorical scale of High Medium and Low.

Not sure about what "has been converted" entails, but if you have used something like fruit <- factor(fruit) and if is.factor(fruit) is indeed true then read on.

R will automatically use the one with the lowest numerical value as your reference group, keeping only the binary indicators of the other two levels in the model. If you wish to change that to some other group, check ?relevel.