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I'm doing an ordinal regression (cumulative logit model), with a 4-point, self-report health assessment measure as my outcome.

My sample size is 8,070, and so far the model has 15 predictors: 8 binary/categorical and 7 continuous.

A few of the continuous variables however are scores (e.g. psychosocial risk & resilience measures), and can be broken down further into their individual subscales.

I'm wondering then how many variables would be too many for my model? The sample size shouldn't decrease, but currently there are only 169 respondents in the lowest level of the outcome variable.

tl;dr - Is there any rule of thumb that tells you how many predictors you can use in an ordinal regression? Thank you.

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In addition to sample size you also need to look at the number of observations. so-called "rule of 10" . For instance if you have 8, 000 observations. the maximum number of predictors are 80. However, the rule is for linear regression. In Logistic regression it is often said that higher number of predictors bring a better stability. One study suggests that we need to user rule of 25. However, it is most common to use rule of 15. In your case having $8,070 / 15 = 538$ variables afford good stability. You may find this post useful.

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    $\begingroup$ If the 4-point scale has all levels well represented in your data, i.e., no category has fewer than say 0.07 of the subjects, then the 15:1 rule is a good choice. $\endgroup$ – Frank Harrell Oct 27 '16 at 23:12
  • $\begingroup$ That's helpful - thanks for the references @MFR (I should have specified--my original sample-size is ~14,150, but comes in at 8,070 cases that have complete data for all 15 predictors.) I ask because, in addition to the full scores/domains, I'm interested in looking at how the individual components of these contribute to the DV as well. E.g. "Emotional health" is related to the DV--but itself is made up of various subscales, like coping, affect, depression, etc. And I'm wondering if any of those subscales are disproportionately driving the effect of "emotional health." $\endgroup$ – Sgolenbo Oct 28 '16 at 15:54
  • $\begingroup$ From what you are saying though, Dr. Harrell (@FrankHarrell), it sounds like we may be overfitting. Only 2.1% of the subjects are in the lowest category (n=169), and the vast majority (~80%) are in the top two categories. Perhaps we might be better off dichotomizing for a binary logistic model... $\endgroup$ – Sgolenbo Oct 28 '16 at 16:00
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    $\begingroup$ NO! Dichotomizing makes it significantly worse. I would use the 15:1 rule against the frequency of the 2nd most frequent category in this case. $\endgroup$ – Frank Harrell Oct 28 '16 at 19:45
  • $\begingroup$ 15:1 rule it is then, thank you for your help. $\endgroup$ – Sgolenbo Oct 31 '16 at 14:56

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