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Re: st: RE: Re: Missing values test

From   Richard Williams <[email protected]>
To   [email protected], <[email protected]>
Subject   Re: st: RE: Re: Missing values test
Date   Sun, 02 Dec 2007 12:41:26 -0500

At 12:11 PM 12/2/2007, Nick Cox wrote:
I've not done it myself, and this may well be obvious
to those who know the literature, but surely more can
be said.

Missingness can always be represented by a dummy. So
the structure of missing data can always be explored by
logit regression with missingness on something as response
w.r.t. various predictors, which may well include missingness
on some other things as dummy predictors.
I believe Nick is talking about using the MD dummy as your dependent variable. In addition, there have been proposals about using MD dummies as independent vars, which I'll now comment on since i have given partially incorrect responses in the past!

Cohen and Cohen proposed several years ago that you plug in the mean for missing data and then add a MD dummy variable indicator. Allison discusses this technique in his green Sage book, "Missing Data".

When data exist in reality but their value is unknown (e.g. because of nonresponse), Allison calls this technique "remarkably simple and intuitively appealing." But unfortunately, "the method generally produces biased estimates of the coefficients." He says that listwise deletion is better.

HOWEVER, as Richard Campbell recently pointed out to me, buried in the footnotes of Allison's book is the following:

"While the dummy variable adjustment method is clearly unacceptable when data are truly missing, it may still be appropriate in cases where the unobserved value simply does not exist. For example, married respondents may be asked to rate the quality of their marriage, but that question has no meaning for unmarried respondents. Suppose we assume that there is one linear equation for married couples and another equation for unmarried couples. The married equation is identical to the unmarried equation except that it has (a) a term corresponding to the effect of marital quality on the dependent variable and b) a different intercept. It's easy to show that the dummy variable adjustment method produces optimal estimates in this situation."

Richard Williams, Notre Dame Dept of Sociology
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