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Question regarding random factor accounting for scores scaled by grade

1 message · Phillip Alday

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Hi,

I wouldn't treat grade as a blocking/grouping variable here, because it 
doing so doesn't reflect the systematic differences between grades. 
Grades aren't just random offsets from some ideal mean value and you 
don't want to make statements about some abstract set of grades for 
which you've only observed a few concrete realizations. Instead, you 
want to make statements about the grades you've observed and which show 
a systematic structure. On the numerical end of things, six levels is 
right on the lower edge of what you need to be able to estimate random 
effects.

When moving grades into the fixed effects, you then have a choice. You 
can treat grade as a numerical, linear effect, but I suspect linearity 
is a rather strong assumption here. You could also try using a smoother 
or a polynomial fit. What you could do instead is treat grade as a 
categorical fixed effect. Using sequential difference coding (e.g. with 
MASS::contr.sdif), you would even get the individual estimates for each 
step increase in grade level.

It sounds like the SBAC score is scaled by grade level, i.e. that the 
raw score is converted to an abstract scale that is a statement relative 
to a given grade level. If this is the case, then the statements your 
model makes will be statements about change relative to the grade level 
and not about absolute changes in test score, even without having grade 
as a predictor in the model. I would still keep grade in the model, 
however, because it gives you some indication about whether students are 
able to improve beyond the scaling inherent in SBAC. For example, do 
students who start off behind relative to their current grade level fall 
further behind with each grade advancement or are they able to catch up?

I see you have school as a fixed effect. Unless you have a very small 
number of schools or only interested in making statements about the 
particular schools you observed, I would consider treating schools as a 
blocking variable.

Best,
Phillip
On 23/10/19 6:33 am, Ades, James wrote: