# Including ordinal independent variables in a linear mixed effects model (using the lme4 package in R)

I am analyzing data from cohort of 500 calves investigating the impact of disease on growth.

My outcome variables are normally distributed, continuous data. I am using hierarchical models with calf nested within farms and testing for the longer term impacts of disease.

The problem I am having is with how to include disease data. I have variables for the number of weeks a calf had disease and the total score over a validated threshold for diagnosis

As I am inexperienced in uploading images, here are the tabulated results of the data above:

Disease Duration (weeks) 0   1    2   3   4   5   6
Frequency               266 128  50  33   8   5   2


Total Score  0   1   2   3    4   5   6   7   8   9  10  13  14  15
Frequency   266  88  51  30  20  13   2   6   4   5   3   1   2   1


Obviously, this data is far from normal. But there a lot of levels to use a dummy coded categorical variable, and I think an ordinal scale better represents the data. What do you think it the best way to include this data as an independent variable in my LME models? (n.b. I don't include both in the same model just one or the other)

The models do return results without convergence errors or other warnings when I include these variables but it doesn't feel like very good practice and I am unsure of what sort of transformation I could do to make this data better (e.g. log transformation leaves the data looking very odd and plots of the raw data make it look like a linear relationship is the most likely)

Here is an example of what I would like to improve:

(adj_w_63 - calf weight, weeks_brd - weeks with disease (as described above), rid - a normally distributed continuous variable, milksolids_total - a normally distributed continuous variable)

library(lme4)
model1<-lmer(adj_w_63 ~ weeks_brd + rid + milksolids_total + (1|farm_ac),
data=comp)
summary(model1)

Linear mixed model fit by REML ['lmerMod']
Formula: adj_w_63 ~ weeks_brd + rid + milksolids_total + (1 | farm_ac)
Data: comp

REML criterion at convergence: 3247

Scaled residuals:
Min      1Q  Median      3Q     Max
-3.5180 -0.5525 -0.0458  0.5945  6.1674

Random effects:
Groups   Name        Variance Std.Dev.
farm_ac  (Intercept) 30.10    5.487
Residual             83.37    9.131
Number of obs: 443, groups:  farm_ac, 11

Fixed effects:
Estimate Std. Error t value
(Intercept)      68.06279    3.30996  20.563
weeks_brd        -1.00200    0.42089  -2.381
rid               0.11010    0.04981   2.210
milksolids_total  0.19904    0.07679   2.592

Correlation of Fixed Effects:
(Intr) wks_br rid
weeks_brd   -0.174
rid         -0.285  0.141
mlkslds_ttl -0.795  0.038 -0.016


Thank you so much for your help.