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RE: st: Little's MCAR test

From   "Hoogendoorn, Adriaan" <>
To   "" <>
Subject   RE: st: Little's MCAR test
Date   Wed, 18 Nov 2009 17:02:14 +0100

Dear Maarten,

Some powerful lines you wrote there (again). Tnx. 

Please note that Little's test (and my question) concern the stronger MCAR assumption. This is obviously easier to test than the MAR assumption.
Still, your suggestion seems to make sense even for this situation. Yet, Little's MCAR test is somewhat more general, since it tests the MCAR assumption over several variables with missing values simultaneously. I've seen the test implemented in other statistical software.

Kind regards, Adriaan

From: [] On Behalf Of Maarten buis []
Sent: Wednesday, November 18, 2009 11:42 AM
Subject: Re: st: Little's MCAR test

--- On Wed, 18/11/09, Hoogendoorn, Adriaan wrote:
> I use Stata's facilities for Multiple Imputation to solve
> my missing data problem.
> I'm motivated to do so, since I "think" that the missing
> data pattern is not Missing Completely At Random (MCAR).
> I'd like to sustain my "thought" by testing MCAR and read
> in the literature about a test for this purpose.
> Do you know of a package to do Little's MCAR test?

I don't know this particular test, but one thing you can do
very easily is test whether the probability of having a
missing value on one of the explanatory variables is
associated with the explained variable. The logic is that
missing values only influence the results if the
probability of missingness is associated with the dependent
variable. A simple proof can be found in footnote 1 of
Allison (2002).

You obiviously cannot test whether the probability of
missingness on the dependent variable depends on its own
unobserved value, but you can perform this test for the
explanatory variables, as is shown in the example below for
a continuous dependent variable (wage) and a dichotomous
dependent variable (collgrad).

*------------ begin example --------------
sysuse nlsw88, clear
gen byte miss = missing(union, tenure)

ttest wage, by(miss)
tab miss collgrad, row chi2
*------------- end example ---------------

Hope this helps,

Allison, Paul D. Missing Data. Quantitative Applications
in the Social Sciences, nr. 136. Thousand Oaks: Sage.

Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen

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