http://spssx-discussion.165.s1.nabble.com/PCA-for-dichotomous-data-tp4564908p4573346.html
dimensionality. It should be possible to fit a Rasch model on binary
SPSS 19. This procedure does not require that you have responses to
at random (MAR). Whether the MAR assumption is tenable for your data
> Thank your Hector, for your answer.
>
> the fact that respondents have only three choices for 12 items produces
> lots of cases with zero as entry. But the respondents did not say No,
> they just said nothing. It's a a sort of logic missing. Nevertheless, in
> a first rush I tried a PCA with the dichotomous variables but the large
> number of zero entries violated the conditions, of course (and killed
> the procedure).
>
> In any case, CATPCA is not a solution as I don't have access to this
> module.
>
> As my ultimate intention is to explain church going (regular church goer
> vs. all the rest) I currently work with a discriminant analysis with the
> original items - without having them factor analysed before.
>
> On 08/07/2011 17:15, Hector Maletta wrote:
>>
>> If the data are dichotomous, conventional PCA (SPSS FACTOR procedure) is
>> exactly the same as categorical PCA (SPSS CATPCA procedure). The latter is
>> required when the original data are multi-categorical variables (either
>> nominal or ordinal), in order to generate (iteratively) optimal scaling
>> values for the categories and a Principal Component Analysis of the
>> resulting (interval level) variables.
>>
>> I wonder whether the fact that each respondent may choose up to three
>> dichotomous variables has any influence on this. It depends, I surmise, on
>> the way you want to treat those data.
>> (a) you may treat each CHOICE as one case. In this fashion, there would be
>> one case (one row in the dataset) for each combination of respondent and
>> choice, with up to three (but not necessarily three) choices per
>> respondent.
>> In this case, my above advice works, although its analysis may require a
>> two-level model to distinguish between intra- and inter- respondent
>> effects.
>> (b) you may treat each RESPONDENT as a case. In this option, you may have
>> different COMBINATIONS of responses per respondent. The maximum number
>> (all
>> combinations of three out of 12) is probably much higher than the number
>> of
>> respondents in your sample, and thus only a small proportion of all
>> combinations will show up. These observed combinations may be treated as a
>> NOMINAL multy-category variable, with many values. For this kind of
>> approach
>> CATPCA would be appropriate, but I caution that the number of distinct
>> combinations observed must not be large (with N respondents and M observed
>> combinations, you have N-M-1 degrees of freedom, which may result in a
>> fairly low number, thus invalidating the results in statistical terms.) If
>> only a few response patterns are observed, and the number of respondents
>> is
>> comparatively very large, you'd be OK, but beware of too many choices and
>> too few subjects.
>>
>> Hector
>>
>> -----Mensaje original-----
>> De: SPSSX(r) Discussion [mailto:
[hidden email]] En nombre de ftr
>> Enviado el: Friday, July 08, 2011 11:13
>> Para:
[hidden email]
>> Asunto: PCA for dichotomous data
>>
>> Hello,
>>
>> Eurobarometer 66.1 provides data on social values which I would like to
>> use, with other influences, to explain church going.
>> The item battery of social values provides 12 questions with yes/no
>> answer alternatives. The respondent can choose up to three variables.
>>
>> What I need is a procedure like a PCA for dichotomous data, but I don't
>> have access to CATPCA. I calculated proximities with the dice algorithm
>> to correct for the high probability that none of two items will be
>> selected. I used PROXIMITIES to calculated the similarity of variables.
>>
>> PROXIMITIES v327 to v338
>> /VIEW=VARIABLE
>> /MEASURE= dice (1,0) .
>>
>> Once PROXIMITIES produces the matrix can you input this as a correlation
>> matrix into FACTOR ? And how to move from this variable-based analysis
>> back to the case-based analysis ?
>>
>> Is there a better alternative for getting a variable structure from
>> dichotomous variables ?
>>
>> TIA,
>> F. Thomas
>>
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