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I was wondering if I can categorize the factor saved scores by taking their quartiles (or some other measures, I am not sure what should I use!) as cut points and use them as predictors in an ordinal logistic regression.

The reason I am thinking of doing so is that, the number of empty cells increases to a lot extent if I use the factor saved scores as they are (continuous in nature).

I have no particular reason behind choosing quartiles as the cut points. The factor scores were obtained from an optimal scaling of the variables (some variable were continuous, some were ordinal, some were nominal) and then factor analysis of the optimally scaled variables using varimax rotation. I am just thinking if I can categorize the factor scores by some means and try to name them as, probably, "lowest scores", "lower scores", "higher scores" and "highest scores" etc. and use them in an ordinal logistic regression as independent variables so that I can comment on the different levels of scores compared to the reference category ("lowest scores") of that factor.

I am not sure what should be used as the cut points. Even I am not sure if this is a right procedure. Can anyone please suggest?

Thanks in advance for your kind theoretical support.

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Continuous IVs are fine for ordinal logistic regression. True, they create empty covariance pattern cells which makes it problematic to rely on goodness-of-fit measures such as chi-square. But think, do you really need to know goodness-of-fit in your case? Anyway, of course you can categorize factor scores, like any continuous variable. – ttnphns Jan 11 at 1:30
@ttnphns Thank you. I actually ran an ordinal logistic regression with the factor scores as independent variables. But the coefficients are not coming significant although I was hoping them to come significant. As the factors are obtained using a varimax rotation, I can expect that the problem is not multicollinearity. So I thought I better categorize the factor scores and reduce the number of empty cells, hoping that it might give a better result! May I know your thoughts about it? – Blain Waan Jan 11 at 6:28
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Categorizing won't make your coefficients higher or more significant, is unlikely to improve your model. The only beneficial effect of it is that you may now believe the goodness-of-fit measure is computed reliably. – ttnphns Jan 11 at 10:02
Thank you so much for your kind advice. – Blain Waan Jan 11 at 10:06

1 Answer

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In genereal reducing the scale of a variable will reduce the information the variable will provide. Hence if the highest scale of a variable is not significant a lower one wont be too.

Now I see myself in a dilemma, if a continuous variable is considered in the context of ordinal regression. To check the goodness-of-fit measure of the model, if a continuos variable is included, is not advisable since the calculated deviance does not follow a chi-squared distribution.

If I now estimate a model with a scaled down version of the variable I could, depending on the scale, use the goodness-of-fit measure. But to make any decisions about the significance of that variable is dangerous. A not significant influence is maybe caused by the downscaling of the continuous variable and not because theres no real impact. Vice versa a significat scaled down version of that continous variable will probably be usefull since the goodness-of-fit measure can be used and the conclusion that the continuous variable is significant may be justified too.

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