# z-scores or raw scores for continuous variables in a mixed-effects model

I am trying to use a mixed-effects model to examine the effects of three teaching approaches on the learning of English past tense measured through language tests at five testing points. The dependent variable of my model is the learners' test score. The fixed-effect variables are group (three treatment group and a control group) and testing time (five testing points including a pre-test and four post-tests). In addition, I also set subjects as the random-effect variable. Pre-test scores are controlled for as a covariate in the model because they are not comparable among the four groups.

My model is:

mod<-lmer(score~pre-test+group*time+(1+pre-test|subject),data=EI,REML=FALSE).


The full mark of the five tests is the same, which is 24. My questions are: Should I use the raw scores or z-scores for the covariate (pre-test) in this model? If yes, should I convert raw scores to z-scores for the dependent variable as well?

• Can you explain why the pre-test scores are not comparable among the groups? Are the scores at the other testing points likewise not comparable? – Darren James Sep 22 '17 at 15:07
• Hi Darren, thank you for your question. The four groups being compared cannot be assumed to be equivalent because there are significant between-group differences on pre-test. If the influence of pre-test scores is not eliminated in the model, it will be confound with the effects of the treatment. That is, learners with high pre-test scores are most likely to achieve high post-test scores in spite of the treatment, which thus causes difficulties in interpreting the significant group differences identified at the other four testing points. – Summer Fu Sep 22 '17 at 22:07
• Thanks for clarifying. Have you considered using gain scores? Doing so would be justified as long as the test scores are on the same scale. It would account for the between-group differences and also produce estimates that are easy to interpret. – Darren James Sep 25 '17 at 17:55