http://spssx-discussion.165.s1.nabble.com/Reference-category-for-dummies-in-factor-analysis-tp1070339p1070343.html
This has been an interesting discussion. I don't know why the FA and
scores would change depending on which category is omitted. Were there
You also said classical FA, but then said PCA. What did you use for
Kooij, A.J. van der wrote:
>>... trouble because any category of each original census question would be an exact linear
>>function of the remaining categories of the question.
>>
>>
>Yes, but this gives trouble in regression, not in PCA, as far as I know.
>
>
>
>>In the indicator matrix, one category will have zeroes on all indicator variables.
>>
>>
>No, and, sorry, I was confused with CA on indicator matrix, but this is "sort of" PCA. See syntax below (object scores=component scores are equal to row scores CA, category quantifications equal to column scores CA).
>Regards,
>Anita.
>
>
>data list free/v1 v2 v3.
>
>begin data.
>
>1 2 3
>
>2 1 3
>
>2 2 2
>
>3 1 1
>
>2 3 4
>
>2 2 2
>
>1 2 4
>
>end data.
>
>
>
>Multiple Correspondence v1 v2 v3
>
> /analysis v1 v2 v3
>
> /dim=2
>
> /critit .0000001
>
> /print discrim quant obj
>
> /plot none.
>
>
>
>catpca v1 v2 v3
>
> /analysis v1 v2 v3 (mnom)
>
> /dim=2
>
> /critit .0000001
>
> /print quant obj
>
> /plot none.
>
>
>
>data list free/v1cat1 v1cat2 v1cat3 v2cat1 v2cat2 v2cat3 v3cat1 v3cat2 v3cat3 v3cat4 .
>
>begin data.
>
>1 0 0 0 1 0 0 0 1 0
>
>0 1 0 1 0 0 0 0 1 0
>
>0 1 0 0 1 0 0 1 0 0
>
>0 0 1 1 0 0 1 0 0 0
>
>0 1 0 0 0 1 0 0 0 1
>
>0 1 0 0 1 0 0 1 0 0
>
>1 0 0 0 1 0 0 0 0 1
>
>end data.
>
>
>
>CORRESPONDENCE
>
> TABLE = all (7,10)
>
> /DIMENSIONS = 2
>
> /NORMALIZATION = cprin
>
> /PRINT = RPOINTS CPOINTS
>
> /PLOT = none .
>
>
>
>________________________________
>
>From: SPSSX(r) Discussion on behalf of Hector Maletta
>Sent: Thu 17/08/2006 19:56
>To:
[hidden email]
>Subject: Re: Reference category for dummies in factor analysis
>
>
>
>Thank you, Anita. I will certainly look into your suggestion about CATCPA.
>However, I suspect some mathematical properties of the scores generated by
>CATPCA are not the ones I hope to have in our scale, because of the
>non-parametric nature of the procedure (too long to explain here, and not
>sure of understanding it myself).
>As for your second idea, I think if you try to apply PCA on dummies not
>omitting any category you'd run into trouble because any category of each
>original census question would be an exact linear function of the remaining
>categories of the question. In the indicator matrix, one category will have
>zeroes on all indicator variables, and that one is the "omitted" category.
>Hector
>
>
>-----Mensaje original-----
>De: SPSSX(r) Discussion [mailto:
[hidden email]] En nombre de
>Kooij, A.J. van der
>Enviado el: Thursday, August 17, 2006 2:37 PM
>Para:
[hidden email]
>Asunto: Re: Reference category for dummies in factor analysis
>
>CATPCA (in Data Reduction menu, under Optimal Scaling) is PCA for
>(ordered//ordinal and unorderd/nominal) categorical variables; no need to
>use dummies then.
>Using PCA on dummies I think you should not omit dummies (for nominal
>variables you can do PCA on an indicator maxtrix (that has columns that can
>be regarded as dummy variables; a column for each category, thus without
>omitting one)).
>
>Regards,
>Anita van der Kooij
>Data Theory Group
>Leiden University.
>
>________________________________
>
>From: SPSSX(r) Discussion on behalf of Hector Maletta
>Sent: Thu 17/08/2006 17:52
>To:
[hidden email]
>Subject: Reference category for dummies in factor analysis
>
>
>
>Dear colleagues,
>
>I am re-posting (slightly re-phrased for added clarity) a question I sent
>the list about a week ago without eliciting any response as yet. I hope some
>factor analysis experts may be able to help.
>
>In a research project on which we work together, a colleague of mine
>constructed a scale based on factor scores obtained through classical factor
>analysis (principal components) of a number of categorical census variables
>all transformed into dummies. The variables concerned the standard of living
>of households and included quality of dwelling and basic services such as
>sanitation, water supply, electricity and the like. (The scale was not
>simply the score for the first factor, but the average score of several
>factors, weighted by their respective contribution to explaining the overall
>variance of observed variables, but this is, I surmise, beside the point.)
>
>Now, he found out that the choice of reference or "omitted" category for
>defining the dummies has an influence on results. He first ran the analysis
>using the first category of all categorical variables as the reference
>category, and then repeated the analysis using the last category as the
>reference or omitted category, whatever they might be. He found that the
>resulting scale varied not only in absolute value but also in the shape of
>its distribution.
>
>I can understand that the absolute value of the factor scores may change and
>even the ranking of the categories of the various variables (in terms of
>their average scores) may also be different, since after all the list of
>dummies used has varied and the categories are tallied each time against a
>different reference category. But the shape of the scale distribution should
>not change, I guess, especially not in a drastic manner. In this case the
>shape of the scale frequency distribution did change. Both distributions
>were roughly normal, with a kind of "hump" on one side, one of them on the
>left and the other on the right, probably due to the change in reference
>categories, but also with changes in the range of the scale and other
>details.
>
>Also, he found that the two scales had not a perfect correlation, and
>moreover, that their correlation was negative. That the correlation was
>negative may be understandable: the first category in such census variables
>is usually a "good" one (for instance, a home with walls made of brick or
>concrete) and the last one is frequently a "bad" one (earthen floor) or a
>residual heterogeneous one including bad options ("other" kinds of roof).
>But since the two scales are just different combinations of the same
>categorical variables based on the same statistical treatment of their given
>covariance matrix, one should expect a closer, indeed a perfect correlation,
>even if a negative one is possible for the reasons stated above. Changing
>the reference category should be like changing the unit of measurement or
>the position of the zero point (like passing from Celsius to Fahrenheit), a
>decision not affecting the correlation coefficient with other variables. In
>this case, instead, the two scales had r = -0.54, implying they shared only
>29% of their variance, even in the extreme case when ALL the possible
>factors (as many as variables) were extracted and all their scores averaged
>into the scale, and therefore the entire variance, common or specific, of
>the whole set of variables was taken into account).
>
>I should add that the dataset was a large sample of census data, and all the
>results were statistically significant.
>
>Any ideas why choosing different reference categories for dummy conversion
>could have such impact on results? I would greatly appreciate your thoughts
>in this regard.
>
>Hector
>
>
>
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