# Optimal scaling level for variables categorized from continuous data

A variable was categorized into 10 equally spaced intervals from a continuous variable which was originally in proportion. Now, we have to use this variable in CATREG procedure. If we choose the optimal scaling level to be 'ordinal' then quantification for the last seven categories are the same. That means the observations that originally had values ranging from 0.31 to 1.00, now receive the same quantified value after optimal scaling. If we use 'numeric' as the quantification level instead then different categories receive different quantification (as it should be).

But is using 'numeric' as the optimal scaling level valid here? Although the variable was numeric originally, but later that was transformed to an equally spaced 10-category variable. Note that, using 'nominal' gives quite different quantification, but some of the category quantification is still the same. I guess keeping in mind the nature of the original variable, different categories should not receive the same quantification. Could someone please clarify this?

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What is the stumbling block there for you, I can't get? If you want to use the original variable, use it. If you somehow discretized your variable and don't need it to be transformed nonlinearly then, stick with numeric level transform, while if you want monotonic transform, use (spline) ordinal, and if you accept nonmonotonic nonlinear transform, do (spline) nominal. –  ttnphns Sep 4 '12 at 8:23
Why did you categorize your variable in the first place? It's almost never a good idea. See The Perils of Categorizing Continuous Variables which I wrote on my blog. @ttnphns makes several good suggestions, as well. –  Peter Flom Sep 4 '12 at 10:47
@PeterFlom Umm...it seems like I am making a lot of mistakes here. Actually I was suggested by one of my seniors to transform the proportion type variables into 10 categories, because these variables range from 0.00 to 1.00 and SPSS categories procedure treats values less than 1 as missing. But it seems like fractional-valued variables can be grouped into seven categories (by default if discretization is unspecified) or differently through discretization. Your write up in the blog was excellent, thank you. –  Blain Waan Sep 4 '12 at 13:34
@Blain, Peter is unlikely to know very technical nuances of SPSS, I presume, and your question seems majorly technical. By the way, if only I remember correcty SPSS optimal scaling procedures treat nonpositive (rather than <1) values as missing. Please check it (right now I can't check it myself, sorry). –  ttnphns Sep 4 '12 at 14:54
@ttnphns is right - I am not an SPSS person (I use SAS and R). But why are you using anything called "categories"? Don't group into 10 categories, don't group into 7 categories, don't group at all! Keep your original variable. I am sure that SPSS can deal with values less than 1. –  Peter Flom Sep 4 '12 at 21:48
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