Logistic Regression – Understanding Logistic Regression with Ordinal Independent Variables
logisticordinal-datareferencesregression
I have found this post:
Yes. The coefficient reflects the change in log odds for each increment of change in the ordinal predictor. This (very common) model specification assumes the the predictor has a linear impact across its increments. To test the assumption, you can compare a model in which you use the ordinal variable as a single predictor to one in which you discretize the responses and treat them as multiple predictors (as you would if the variable were nominal); if the latter model doesn't result in a significantly better fit, then treating each increment as having a linear effect is reasonable.
Could you please tell me where can find something published that supports this claim? I am working with data and I would like to use ordinal independent variables in logistic regression.
Best Answer
As @Scortchi notes, you can also use orthogonal polynomials. Here is a quick demonstration in R:
First off, are your two independent variables being adjusted as factors or numerically coded responses and is there an interaction term for the two? The reason I ask is because the test of proportional odds grows very sensitive with small cell counts. For this reason, I often find it justifiable to adjust input variables as their ordinally coded values (1: poor, 2: fair-to-poor, etc.). Doing so allows information to be borrowed across groups, proportionality is assessed so that an associated difference in the odds of a more favorable response comparing units differing by 1 in the predictor are consistent with odds of an even more favorable response (the rough and contrived interpretation of the test of proportional odds).
If your numeric coding still fails to give valid proportionality, it is possible to get consistent cumulative odds ratios estimates by collapsing adjacent categories like the two bottom box responses.
Thirdly, another powered test of association between an ordinal response and two ordinal factors is a plain old linear regression model. Using robust standard errors, you get valid confidence intervals despite the distribution of the errors. This tends to be less powerful that categorical methods, but with fewer pitfalls due to zero cell counts.
Lastly, as a comment, robust standard errors allow consistent estimation of the mean model in most circumstances. I'm not sure if these are implemented in SPSS, but R and SAS use these frequently. As with the proportional hazards assumption in the Cox model, when this "model based assumption check" fails, it does not mean the model results are entirely invalid, it's just that the effect estimates are "averaged" over their inconsistent proportionality. For instance, if proportional odds model has excessive numbers of respondents giving top box responses, and a predictor shows a large association for the top box response but smaller association for other cumulative measures, then you'll find that the cumulative odds ratio is a weighted combination of the several thresholded odds ratios, with a higher weight placed upon the top box OR.
Best Answer
As @Scortchi notes, you can also use orthogonal polynomials. Here is a quick demonstration in R: