Posted by
Kooij, A.J. van der on
Jan 09, 2007; 10:40pm
URL: http://spssx-discussion.165.s1.nabble.com/Treating-Ordinal-Data-as-Continuous-tp1073024p1073028.html
SPSS Categories offers several data analysis techniques for nominal, ordinal, and interval data:
CATREG: multiple regression (and one-dimensional discrimant analysis); Regression menu, Optimal Scaling.
CATPCA: principal component analysis; Data Reduction menu, Optimal Scaling, One set.
OVERALS: canonical correlation analysis for 2 or more sets of variables (and multi-dimensional discriminant analysis); Data Reduction menu, Optimal Scaling, Multiple sets.
These procedures optimally quantify categorical variables in the context of the analysis method. That is, with CATREG the quantifications are optimal for maximizing the R-squared, with CATPCA the quantifications are optimal for maximizing the VAF, and with OVERALS the quantifications are optimal for maximizing the canonical correlation.
The quantified variables are numeric variables and can be used as input to standard analysis methods.
The researcher chooses an optimal scaling level for each variable, defining how much freedom is allowed in the in the quantifications. For example, with ordinal scaling level, the quantified variable is restriced to have a monotonic (ordinal) relation with the categorical variable (thus, a higher rank number will receive a higher quantified value than a lower rank number).
For interval variables, numeric scaling level can be choosen to analyze them at interval level (the variable is only linearly transformed to standard scores), or one of the other scaling levels to obtain optimal nonlinearly transformed variables.
If you are not sure if ordinal variables can be analyzed as if they are interval variables, you can use one of the above methods with ordinal scaling level (or monotonic spline) for all variables and compare results to the results when treating the variables as interval. For scale construction, usually there is not much difference between results of CATPCA ordinal and standard PCA.
Anita van der Kooij
Data Theory Group
Leiden University
________________________________
From: SPSSX(r) Discussion on behalf of Bob Schacht
Sent: Tue 09/01/2007 20:54
To:
[hidden email]
Subject: Re: Treating Ordinal Data as Continuous
At 07:00 AM 1/9/2007, Swank, Paul R wrote:
>The problem is compounded when one thinks of measurement scales as all
>or none, it's either ordinal or interval. However, win, place, and show
>in a horse race is clearly more ordinal that IQ scores. For IQ scores,
>it is clear that the difference between an IQ of 50 and an IQ of 75 is
>perhaps greater than th difference between 75 and 100. On the other and,
>the difference between an IQ of 100 and 101 is probably pretty similar
>to the difference between 99 and 100. It all relies on the relation
>between the scale values and the underlying construct. I think some
>scales are closer to being interval than ordianl while for others, the
>opposite is true. A lot has to do with how well the scale was
>constructed.
My main concern with this issue comes from satisfaction and importance
scales. It seems to me that we don't have enough tools regarding ordinal
measures. The analytical tool set for interval data is far richer than what
is available for ordinal data. The median can be substituted for the mean,
but there is no analytical equivalent of variance, even though it makes
intuitive sense that an ordinal scale with results congregating at the
extremes ought to be more 'variable' than a scale in which the results
congregate around the median.
Bob Schacht
Robert M. Schacht, Ph.D. <
[hidden email]>
Pacific Basin Rehabilitation Research & Training Center
1268 Young Street, Suite #204
Research Center, University of Hawaii
Honolulu, HI 96814
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