I'm a bit (actually, totally) confused with SPSS ordinal regression output.

Let say we have dependent variable score=1,2,3,4,5 (higher is better) and one predictor gender=male,female.

We run Ordinal regression and get parameter "Estimate" for male=1. 1 is log-odds, so odds ratio (OR) is 2.7

What does it mean? Being male causes to get 2.7 times HIGHER chance to get higher score compare to being female, or LOWER?

Different resources I found in the internet give opposite interpretation (i.e. OR=EXP(B) or OR=EXP(-B) or I can't correctly interpret them...

  • $\begingroup$ Exp(b) is how much times (i.e. the ratio) the estimated odds in the dependent variable increases when the predictor switches to male (from female). The odds is Prob(code>j)/Prob(code<=j) for any j from 1,2,3,4,5. If you choose to think of the odds as Prob(code<=j)/Prob(code>j) then exp(-b) is the same as the previous. $\endgroup$ – ttnphns Apr 11 '15 at 14:23
  • $\begingroup$ Does "Prob(code>j)" mean "probability of having higher value of dependent variable"? Does it mean that Prob(code<=j)/Prob(code>j) equal to reverse scale (1-best, 5-worst)? $\endgroup$ – Niksr Apr 11 '15 at 15:22
  • $\begingroup$ Probability of having value higher than threshold j (j can be 1,2,3,4, no matter, because the effect on the log is modelled as straight, linear). $\endgroup$ – ttnphns Apr 11 '15 at 15:56

In ordinal regression, the odds ratio tells you the odds of being in the higher levels of the dependent ordinal variable (relative to being in or below a given level) for a one unit change in the predictor variable. In your case a 1-unit change in the predictor variable means being a male. Hence, the interpretation of your result would be "Being a male increases the odds of being in the higher levels of the dependent variable by a factor of 2.7 (or 2.7 times). For additional explanation, you can check http://www.ats.ucla.edu/stat/stata/output/stata_ologit_output.htm.

  • $\begingroup$ Thank you. Could you clarify if the 'higher levels of the dependent variable' is equal to "higher numeric value of the dependent variable"? This "level" is exactly what confuses me. $\endgroup$ – Niksr Apr 11 '15 at 15:25
  • $\begingroup$ The numbers tell the rank of a given level. Higher numbers indicate higher rank (i.e., a higher magnitude of the variable of interest). Therefore, for example, if you are talking about pain severity on a four-point scale ranging from 0-3 such that 0=no pain, 1=mild pain, 2=moderate pain, and 3=severe pain, then a higher level indicates any level above the first (or any other)level. ...(to be cont'd). $\endgroup$ – Ayalew A. Apr 13 '15 at 7:25
  • $\begingroup$ (cont'd)...This means, relative to the level 'no pain', all other level are higher levels; relative to 'mild pain' and lower (i.e., 'no pain'), 'moderate pain' and 'sever pain' are higher levels; and relative to 'moderate pain' and lower levels, 'sever pain' is a higher level. $\endgroup$ – Ayalew A. Apr 13 '15 at 7:28
  • $\begingroup$ Perfect, thank you! Now everything clear. I was confused with "higher" term. Now I understand that "3" is always considered higher then "2", i.e. numeric value defines level, not other staff like direction of dependencies or frequencies. $\endgroup$ – Niksr Apr 14 '15 at 8:17
  • 1
    $\begingroup$ Yes, in the context of ordinal regression, the numbers tell nothing more than the rank of a given level, I think. $\endgroup$ – Ayalew A. Apr 14 '15 at 8:38

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