# Re: st: table & chi-square from multiply imputed survey data (-ice-, -mim-) [repost]

 From Stas Kolenikov To statalist@hsphsun2.harvard.edu Subject Re: st: table & chi-square from multiply imputed survey data (-ice-, -mim-) [repost] Date Wed, 4 Feb 2009 15:23:26 -0600

```If there is any specialized literature, it would be no more than two
or three papers; I don't remember coming across any on my relative

What I suggested some while ago (should be in archives) to a multiple
imputation for complex survey question is that one would have to use
far more complex inference methods such as the bootstrap (which itself
is not an easy thing with complex survey data). But frankly I don't
see any straightforward way to apply it to the table situation -- it
is really the method to work out the standard errors. Guessing that
the chi-square from the table should be asymptotically equivalent to
the Wald statistic from mlogit using 5 dummies for the categories of
the other variable, you would then have to do this:

1. take a survey bootstrap sample
2. -ice- it according to your imputation model; produce one single
imputed data set
3. run mlogit
4. repeat say 200 times... at least as many as you have design degrees
of freedom. Why people in missing data world think 5 replications is
enough is beyond me.
5. compute the standard errors, perform Wald test.

If there were a neat way to tuck the resulting covariance matrix into
the results of -svy: tab-, it would probably work and produce a
reasonable test statistic. As far as I understand Rao-Scott
corrections to the table chi-squares, they need generalized design
effect estimates coming from those covariance matrices. Unfortunately,
bootstrap is not among the officially supported routines (and even
more unfortunately, there is no single bootstrap, either, unlike
linearization or jackknife), and I am not aware of any ways to
brute-force the covariance matrices into -svy: tab-. Given all that,
-mlogit- is actually not such a silly idea, in the end.

On 2/4/09, Michael I. Lichter <mlichter@buffalo.edu> wrote:
> (Sorry for the repost, but I initially sent this as part of an unrelated
>
>  I want to know how to generate a survey-adjusted chi-square like that
> available from -svy: tab- using data multiply imputed using -ice- (net sj
> 8-1 st0139).
>
>  I'd also be interested in suggestions about how to tabulate these data.
> (E.g., would anybody complain if I computed a mean imputed value for each
> variable for each case, rounded them off, and reported that?)
>
>  Suppose I have two variables, A & B, each with five categories, each
> measured in survey from a complex design, each with about 10% missing data.
> I want to see a 5x5 table with a chi-square statistic allowing an inference
> about the independence (or not) of A & B. I can impute A & B (and some other
> variables at the same time) using -ice-, but then what do I do?
>
>  As far as I can tell, -mim- doesn't support -tab- or -svy: tab-, and -svy:
> tab- itself doesn't support prefix commands. I can try predicting A from B
> using -mlogit-, but that seems silly. I can manually do a tabulation for
> each imputation and, I guess, average the chi-square statistics, and, I
> dunno, subtract one degree of freedom, perhaps? I don't see anything
> relevant in the list logs. Suggestions or pointers to relevant lit?
>
>  Thanks.
>
>  Michael
>
>  --
>  Michael I. Lichter, Ph.D.
>  Research Assistant Professor & NRSA Fellow
>  UB Department of Family Medicine / Primary Care Research Institute
>  UB Clinical Center, 462 Grider Street, Buffalo, NY 14215
>  Office: CC 125 / Phone: 716-898-4751 / E-Mail: mlichter@buffalo.edu
>
>  *
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>

--
Stas Kolenikov, also found at http://stas.kolenikov.name
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```