I received the following email from a reader after sending out the last article: Opposite Results in Ordinal Logistic Regression—Solving a Statistical Mystery.
And I agreed I’d answer it here in case anyone else was confused.
Karen’s explanations always make the bulb light up in my brain, but not this time.
With either output,
The odds of 1 vs > 1 is exp[-2.635] = 0.07 ie unlikely to be 1, much more likely (14.3x) to be >1
The odds of £2 vs > 2 exp[-0.812] =0.44 ie somewhat unlikely to be £2, more likely (2.3x) to be >2SAS – using the usual regression equation
If NAES increases by 1 these odds become
Exp[-2.635 + (-0.281)] = 0.05, even more unlikely to be 1, increased likelihood (now 20x) of being >1
Exp[-0.812 + (-0.281)] = 0.33, even more unlikely to be 2, increased likelihood (now 3x) of being >2
In other words, as X gets bigger, the odds of a lower ordered category (1 or £2) get lower, and the odds of the higher ordered category (>1 or >2) gets higherSPSS – using the SPSS equation
If NAES increases by 1 these odds become
Exp[-2.635 – (+0.281)] = 0.05, even more unlikely to be 1, increased likelihood (now 20x) of being >1
Exp[-0.812 – (+0.281)] = 0.33, even more unlikely to be £2, increased likelihood (now 3x) of being >2I don’t understand what is different because it is still the same result, only there is no instruction in the SPSS output about subtracting the coefficients from thresholds.
As a politician here in Australia once famously said, “Please explain”!
You are absolutely correct: all four packages are giving you identical results. This is always something to celebrate.
The big difference, is, as you noted “there is no instruction in the SPSS output about subtracting the coefficients from thresholds.”
Nor is there anything in the SPSS manuals. At least, I couldn’t find it, even when I’m looking for it.
So they’ve parameterized the model in a very useful, but unexpected, way to make interpretation easier, but not shouted that from the rooftops.
If you, the user, doesn’t know there’s a big minus sign in there, you’ll interpret parameters and calculate predicted values incorrectly.
I don’t remember where we finally found it–probably in the Stata manuals. (Stata has truly excellent manuals). I just tried to find it again in the SPSS manuals. I’m not saying it’s not there, but I still can’t find it, even though I’m looking for it.
(btw, if any SPSS users have found it, please tell me where).
So really, the point is to clarify something that’s not obvious for readers, particularly those without four software packages to check results in.
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the differences in the plus and minus in the equations not reported, and the inherited results, are really confusing as the software manual does not explain how to interpret them correctly.
in spss, the results in (1) simple logistic regression and (2) logistic model in mixed model or GEE are exactly the opposite.