Organization: K.U.Leuven (Belgium)
Newsgroups: bit.listserv.stat-l
Date:         Tue, 17 Nov 1992 11:14:10 UTC+0100
From:         Vuylsteke Magda <LAAAA02@BLEKUL21.BITNET>
Subject:      Re: factor analysis

> About April Milliken's question:
>
> I agree with Andy Taylor that this looks more like a MANOVA question.
> There are some problems with MANOVA. It assumes equal covariance matrixes
> over time points. Also, it gives you in fact a kind of factor analysis,
> because it gives you that linear combination of dependent variables that
> produces the largest separation between the groups. This linear combination
> may or may not be interpretable in view of the substantive problem.
> If you use factor analysis, you are in fact assuming that the factor structure
> across time points is the same (this assumption is a bit less restrictive than
> the equal covariance matrices in manova). There are Lisrel models for panel
> data that would apply, but I think your canine sample is to small to use Lisre
> A reason to use factor (preferably component-) analysis in stead of manova
> would be that the factors might be more interpretable than what manova gives
> you. If you want to use factor analysis, I would recommend a procedure like
> this:
> 1) if the dependent variables are reasonably normal, use manova or discriminan
>  (in SPSS) to test for equality of coveriance matrixes across time points. If
>  variables have non-normal distributions, don't bother because the Box test
>  used for this is extremely sensitive to non-normality.
> 2) split your variables in group means (aggregate in spss) and individual
>  deviations from the group means (groups defined by different time points).
> 3) the correlations of the individual deviation scores will reflect all that
>  is similar within the groups; do a component analysis on these.
> 4) the correlations of the group means reflect variation between groups; do a
>  component analysis on these too.
> 5) If the results from 4) look very different than the results from 3),
>  the assumption of similar factor structures at the different time points
>  is violated. This means trouble. Strew ash on your hair, go home and mourn.
> 6) If 4) looks reasonably similar to 3), use the results from the within
>  groups analysis in 3). If you can interpret them (f.i., can you interpret
>  some factor as canine well-being), derive a formula to compute factor scores,
>  compute these at all different time poins in the same way (using original
>  variables) and do univariate anovas on these (manove is not really needed
>  because your factor scores will be nearly orthogonal).
> 7) Some statisticians may feel that this analysis is a bit messy. I agree it
>  is, but it may give you more insights than doing a manova straightaway.
> 8) A useful reference is: K. Harnkvist (1978). In Journal of Educational
>  Psychology, 70, 706-16. A more modern approach is an article by B.O. Muthen
>  in Psychometrika, 1989, 54: 557-85. But Muthen uses a latent variable approac
>  assuming large samples.
>
> Hope this sparkles some discussion
>
> Joop Hox
> University of Amsterdam

Is this not  about the same as doing a CANONICAL DISCRIMINANT ANALYSIS
or perhaps is it better to do a CANONICAL CORRELATION ANALYSIS with
dummy variables for groups as one set of variables. Some computer
programs give more output for the last analysis.

Drs. Magda Vuylsteke              Telephone (32)-16-286611 ext2215
Computing Center                  Fax       (32)-16-207168
Center of Statistics
University of Leuven
de Croylaan, 52a
3001 Heverlee                     E-mail:laaaa02@blekul21
Belgium
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