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Re: st: st: Using MVN for Multiple Missing Ordinal Variables

From   maarten buis <>
Subject   Re: st: st: Using MVN for Multiple Missing Ordinal Variables
Date   Mon, 9 May 2011 10:15:25 +0200

On Sun, May 8, 2011 at 10:45 PM, Clifton Chow wrote:
> My goal is to impute the missing values on these items in order to feed them into a program to calculate mean difference effect sizes for a meta-analysis to determine the impact (if any) between randomly assigned treated groups and  controls.  I have poured through Allison and have examined the pattern of missing as best I could.  Unfortunately, there is low correlation between missing and demographic or clinical variables, and very little nesting among missing variables.  I had considered univariate missing approach through MI impute ologit, but that's potentially 450 models across 9 sets of instruments, and with little or no correlation among demographic/clinical variables, it does not seem very useful.

That is not a problem, the point of Multiple Imputation is not to
"recover" or "predict" any missing values, they are considered to be
lost forever. The point is to make the best use of the information
that is available in your data. So the imputation part is only there
to replicate existing patterns in your data on to the observations
with missing data, and the fact that there is little pattern is also a
pattern... The reason for doing so is to be able to use those parts of
your observations that are observed, not to, by some statistical
magic, see things that were not observed. So for the imputation model
we do not care about low predictive power, reverse causality, etc.
etc., we only want to reproduce patterns. Low predictive power will
just mean that you won't be adding much by doing the imputation, but
that is just a fact of live.

Typically Likert items are part of a battery of items, all measuring
the same thing. If that is the case, than I expect that a proper
imputation model for your situation would have very high predictive
power, as at the very least I would include all your items in your
imputation model. If these different items measure the same thing that
they will tend to be highly correlated(*). Imagine what pattern you
are imposing when you leave all items out of your model: In that case
you will impose the constraint for the imputed values that correlation
between the items is 0. Remember that the imputation model has nothing
to do with causality, it is only there to reproduce patterns.

Hope this helps,

(*) Not necessarily as it depends on whether you think that the
observed items are influenced by the latent variable (as is assumed in
models like factor analysis) or whether the observed items influence
the latent variable (as is assumed in models like MIMIC models). For
example, see:

Bollen, Kenneth A. 1984. "Multiple Indicators: Internal Consistency or
No Necessary Relationship" Quality and Quantity 18(4): 377-385.

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

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