# [R-sig-ME] Question regarding random factor accounting for scores scaled by grade

Ades, James j@de@ @end|ng |rom uc@d@edu
Wed Oct 23 06:33:35 CEST 2019

```Hi all:

I’m looking at SBAC standardized test scores (math in one model and English in the other) for middle schoolers (as the dependent variable) and then executive function task scores and demographic factors as explanatory variables.

So in a simple model looking at the relationship between a stroop task and the SBAC math variable I’d have the model:

model <- lmer(math.score ~ School + Ethnicity + Language.Fluency*attendance + Parent.Ed.Lvl +SpEd + t4.minus + eff.rt.stroop + (t4.minus|pid) + (1|grade) + (1|Teacher), data = ace, na.action = 'na.exclude', control = lmerControl(optimizer = "nloptwrap", calc.derivs = FALSE), REML = FALSE)

where t4.minus is the time in between timepoints (there were four, and they varied from participant to participant), pid is the participant, and eff.rt.stroop is the efficiency stroop score.

Since there are four timepoints over two years, there are ultimately six grades: 3rd graders who then become 4th graders,  fifth graders who then become sixth graders, and seventh graders who then become eighth graders.

My question is whether this random factor of grade would not only account for natural variance between grades (with the random intercept) but would also, in a principled and valid way, account for the fact that SBAC score falls on a continuous scale (between 2000-3000) that increases with each grade, such that an equivalent score of 2381 in 3rd grade would be 2411 in 4th grade. Explained (better?) here: http://www.smarterbalanced.org/assessments/scores/.

Thanks much,

James