Hi, I am examining whether it is possible to predict distance travelled when a person goes missing (levels - eg 0-5km, 6-10km, 11-20km etc) from a categorical IV (risk assessment - high, medium, low, or no apparent risk). Using an ordinal regression, I have a significant model but none of the beta values for high, medium, low compared with no apparent risk are significant. Does anyone know how to interpret this? I've been asked to further explain what this means by a reviewer but other than 'the model is a significant fit but...' I don't know what else to say.
Thanks in advance.
How do you know the model is significant in the first place? What test did you use? The attached reference does not mention such a test. Prediction success is usually measured by a cross validation experiment.See the second screenshot for a standard reference.
Best wishes, David Booth
I'm assuming that the model with risk assessment added is superior to that for an intercept only model e.g., by a likelihood ratio test. If so then I think the issue is that the predictor is ordinal but you are adding it as three unordered dummies. This isn't wrong but it is an inefficient test of the hypothesis that increasing risk is associated with greater distance. You get the same issue with ANOVA and linear contrasts.
1) If you have continuous risk scores then use those as 1 df predictor (potentially also. I'd also use a model with actual distance rather than categorised distance if possible.
2) Treat the ordered risk variable as continuous by coding it 0,1,2,3. This will be be more efficient and is effectively fitting a linear contrast.
3) Treat the risk category as a monotonic predictor (though I don't know software other than brms in R that supports this). See https://cran.r-project.org/web/packages/brms/vignettes/brms_monotonic.html. I think is a more principled approach than 2) as it doesn't fix the intervals.
If you have only one predictor I'd also suggest just running an appropriate ordinal correlation such as the gamma correlation or Kendall's tau. The ordinal logistic regression doesn't add much unless you are looking at the model predictions (e.g., plotting them) or there are other predictors.
Interpretation of ordered regression is not straightforward because of its proportional odds assumption. For example, the proportion between '0-5km' and '6-10km' pair, proportion between '0-5km' and '11-20km' pair, and ''6-10km' and '11-20km' pair may not be the same. Moreover, you would need to manipulate your outcome a bit more to make your result more meaningful (predicted probability scale) for the reviewers. This is one of many reasons I encourage students to keep their outcome as a continuous variable. If you use a simple logistic regression, then you can back-transform your logit transformed outcome into linear; however, that's not easy for ordered regression.
I encourage you to look into the UCLA website for interpretation of ordered regression. https://stats.idre.ucla.edu/other/mult-pkg/faq/ologit/
There may be a correlation/dependency between the two input variables. There may be significant differences between cells, but the effect may be neither linear nor the two variables independent.
I always take the first step of just looking at the data, and see if any pairs are significantly different from the overall average / standard deviations. Rather similar to a Chi Square contingency table, but since in this case you have measurement results rather than counts you need to incorporate the standard deviations. You may also want to calculate a co-variance matrix.
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