[R-sig-ME] psychometric function fitting with lmer?

Doran, Harold HDoran at air.org
Fri Oct 29 20:29:06 CEST 2010

> > In some areas of psychology, we encounter binomial response data that,
> > when aggregated to proportions and plotted against a continuous
> > predictor variable, forms a sigmoid-like function.

Yes, what is called an empirical item characteristic curve (eICC)

> It is typical to
> > use OLS to fit a probit function to this data, yielding measures of
> > bias (mean of the Gaussian) and variability (SD of the Gaussian).

 This is a very odd way to compute bias. First, I don't know how one uses OLS
 to fit a probit model. Probit models are fit using (R)IGLS, not OLS. Second,
 why are you treating the observed data as a parameter estimate? Why don't you
 actually estimate the model parameters (i.e., the item parameters), which are
 asymptotically unbiased under certain estimation conditions. You can do this in a number of
 ways in R, lme4 can do this using lmer as described here:
 Or you can use JML methods for Rasch in the MiscPsycho package or you can use
 MML methods in the LTM package. What you seem to be doing is treating the eICC
 as some kind of parameter for the item; but this is not reasonable I don't
> This
> > fitting is typically done within each individual and condition of
> > interest separately, then the resulting parameters are submitted to 2
> > ANOVAs: one for bias, one for variability. I wonder if this analysis
> > might be achieved more efficiently using a single mixed effects model,
> > but I'm having trouble figuring out how to approach coding this.

 I'm not sure I can help you here as I am unclear on what you are doing
 exactly. Maybe if we elaborate a bit on what you are trying to do above, we
 can do this part next.
> Below
> > is an example of data similar to that collected in this sort of
> > research, where individuals fall into two groups (variable "group"),
> > and are tested under two conditions (variable "cue") across a set of
> > values from a continuous variable (variable "soa"), with each cue*soa
> > combination tested repeatedly within each individual. A model like
> >
> > fit = lmer(
> >     formula = response ~ (1|id) + group*cue*soa
> >     , family = binomial( link='probit' )
> >     , data = a
> > )
> >
> > employs the probit link, but of course yields estimates for the slope
> > and intercept of a linear model on the probit scale, and I'm not sure
> > how (if it's even possible) to convert the conclusions drawn on this
> > scale to conclusions about the bias and variability parameters of
> > interest.
> >
> > Thoughts?
> >

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> > https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models

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