[Rasch] Modeling response time

Stuart Luppescu lupp at uchicago.edu
Wed Feb 1 03:56:11 AEDT 2017

On Tue, 2017-01-31 at 09:13 +0000, Finlayson, Ian wrote:
> Hello Stuart,
> Stepping away from IRT/Rasch, one possibility that jumps out to me
> would be to fit a mixed effect regression to the log-transformed
> response times, using persons and items, and then examine the
> standardised residuals for observations greater than, say, 2.5 SD
> from zero. That should highlight response times which are longer than
> might be expected given the person's average response time and the
> item's average response time.

Hi Ian, That is exactly what I tried first. I included random effects
for the interaction of person and item, but the problem is that it is
an overspecified model, and so it doesn't run. Here's the model:

lmer(log(answer_time) ~ qid + (1|examinee/qid), data=test.DF, REML=FALSE)

When I asked about this on the R-sig-mixed-models list, I received this

in this sample data set, there is a single response per question.  This
will make the qid-with-examinee random effect variance almost
impossible to estimate (strongly confounded with the observation-level
residual variance)

Because of this problem I considered using Rasch analysis.
Stuart Luppescu
Chief Psychometrician (ret.)
UChicago Consortium on School Research

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