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Re: st: RE: Re: Missing values test

From   Maarten buis <[email protected]>
To   [email protected]
Subject   Re: st: RE: Re: Missing values test
Date   Sun, 2 Dec 2007 18:23:04 +0000 (GMT)

--- Richard Williams <[email protected]> wrote:
> 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.

The logic behind the advise against this dummy method is simple:

Say we have one explained variable (y) and two explanatory variables
(x1 and x2) and the following regression equation is correct:

y = b0 + b1 x1 + b2 x2 + e

Now assume some of the values of x2 are missing, and that we applied
this dummy method. So, we replace those missing values with the mean
(m2). Call this new varialbe x2'. We also add a dummy (D) which is 1
when x2 contained missing values. So we get the following regression

y = b0 + b1 x1 + b2 x2' + b3 D + e

This equation looks fine for those individuals without missing values:
y = b0 + b1 x1 + b2 x2 + b3 0 + e
  = b0 + b1 x1 + b2 x2 + e

But for those individuals with missing data the equation looks wrong:

y = b0 + b1 x1 + b2 m + b3 1 + e
  = b0' + b1 x1 + e
(whereby b0' = b0 + b2 m2 + b3 1)

So for these two sets of individuals different regression models are
estimated: one including a control for x2 and one not. Moreover, 
notice that the effect of x1 is constrained to be the same in both
equations. So this effect is some mixture between the effect controlled
for x2 and not controlled for x2. This should in most cases worry you.

> 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."

This footnote can be understood with the logic just laid out.

-- Maarten

Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands

visiting address:
Buitenveldertselaan 3 (Metropolitan), room Z434

+31 20 5986715

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