# [Rasch] missing data advice needed

Mark Moulton markhmoulton at gmail.com
Tue Jan 4 11:28:54 EST 2011

```Dear Carolyn,

So far as the Rasch analysis goes, I would leave the data missing, even
though zeros are a reasonable imputation in this case.  However, even if
they are reasonable they could distort the item difficulties in odd ways, so
I would leave them missing.

"Descriptive" statistics always assume complete data, so it is problematic
to leave the missing data in for that.  But it is also a little problematic
to leave the zeros, though less so.  What I would do myself is calculate the
expected values for all the missing cells, round them to zero or one, and
build your descriptive statistics using the resulting complete data matrix.
The resulting descriptives will be about the best you could manage.

Winsteps reports cell level expected values (though maybe not for missing
cells -- I can't remember).  Or you could import the data into Excel, along
with person and item measures, and calculate the expected values using
something like:

Eni = if(Xni <> 9,Xni,round(exp(Bn - Di) / (1 + exp(Bn - Di)),0))

(Translation:  If the observed value is not missing, use that, otherwise
round the expected value (same as probability in this case) calculated using
person logit ability Bn and item logit difficulty Di.)

Mark Moulton

On Mon, Jan 3, 2011 at 2:50 PM, Fidelman, Carolyn
<Carolyn.Fidelman at ed.gov>wrote:

>   Hi All,
>
> I have a burning question about treatment of item-level missing data.
> Imagine a short reading or math screener given to 5 year olds (individual
> administration format, of course) in order to place them on some quick
> proficiency scale.  The 20 items are designed to go from easy to
> hard. Because young children can become easily frustrated and burdened once
> they reach their level, a stop rule is in place in which the administrator
> ceases testing once the child has missed 5 items in a row.
>
> My question: is it legit to impute 0s to the missing values (9s) of a
> record such as
>
> 1110100110000099999
>
> thus making it
>
>  1110100110000000000
>
> where the assumption is that the child would not have correctly answered
>
> I know that for WINSTEPS and Rasch analysis, missing values are not an
> issue.  I'm really thinking in terms of the descriptive statistics that
> precede them in a report. It seems more reasonable for purposes of
> comparison to report for a set of 1000 examinees  that the p value of, say,
> Item 18 is  .09 where n=1000, than to say it is .25 for the 200 examinees
> who were actually presented with the item.
>
> Or should I just have two different datasets, one for the Rasch analysis
> (leaving the 9s) and another for the descriptives (imputing 0s for 9s)?
>
> Your wisdom much appreciated!  (and Happy New Year!)
>
> Carolyn
>
>
>
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