Date:         Fri, 9 May 1997 13:19:20 GMT
Reply-To:     David Nichols <nichols@SPSS.COM>
Sender:       "SPSSX(r) Discussion" <SPSSX-L@UGA.CC.UGA.EDU>
From:         David Nichols <nichols@SPSS.COM>
Organization: SPSS, Inc.
Subject:      Re: Empty Cells

In article <336933c8.31946960@news.ilstu.edu>,
Wolfgang Viechtbauer <wviecht@rs6000.cmp.ilstu.edu> wrote:
>I am trying to run a 2x2x2x3 ANOVA, and it is no surprise that there
>are some empty cells. Nevertheless, all factors are important, and
>therefore I am looking for some way to still run the analysis. Is
>there any possibility of handling emtpy cells in a general linear
>model with SPSS (7.0)? In fact, I am not quite sure what to do about
>the situation in general. I probably should collect more data in the
>hope that the cells will fill up ...
>
>Any suggestions or comments?
>
>Wolfgang
 
The GLM procedure offers all the options I've seen anywhere for
dealing with empty cells, but the problems created by them are
complex and require the analyst to understand what is implied
by the lack of data. In general, empty cells result in redundant
columns in the design matrix, and a loss of ability to estimate
interaction effects. In models where you have interactions and
are trying to make statements about confounded or contained lower
order effects, the complications introduced are even more
problematic. I see this as less of an issue than many do, since
I don't try to estimate a single main effect in the presence of
an interaction, since that's willfully ignoring the implications
of the model you've fitted. If you're working in an area where
you have good reason not to bother with certain interactions, the
presence of empty cells may not cause any problems at all.
 
On GLM specifically, I would caution that the EMMEANS results for
contained effects may not be correct in the presence of empty
cells. This has been noted on the group before, and is being
remedied for an update release later in the year. I can show you
how to get correct values out of the GLM or MANOVA procedures for
these cases.
 
Bottom line: think about the model(s) that you want to fit and
the cells that are empty, and what this is going to imply about
what you can and cannot estimate. Milliken and Johnson's book
_Analysis of Messy Data, Vol. 1: Designed Experiments_ is a
good resource, with the irritating exception of the fact that
the arithmetic in some of their examples is incorrect. Searle's
_Linear Models for Unbalanced Data_ is another useful text.
 
--
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David Nichols             Senior Support Statistician              SPSS, Inc.
Phone: (312) 329-3684     Internet:  nichols@spss.com     Fax: (312) 329-3668
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