# R: Interpretation ordinal regression with clm

I have a question regarding the interpretation of an ordinal regression in R with the clm function.

I am new to this and used this formula:

RegADHD <- clm(ADHD$$Score ~ ADHD$$Group)


Score is a ordered factor from 0-3 (0= no symptoms, 3= maximal symptoms)

Group is a group variable with 3 categories (no exposure, less exposure, severe exposure).

With summary I get this:

Coefficients:
Estimate Std. Error z value Pr(>|z|)
ADHD$Group3 1.0422 0.4647 2.242 0.0249 * --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Threshold coefficients: Estimate Std. Error z value 0|1 1.3612 0.3720 3.659 1|2 2.5735 0.4465 5.764 2|3 3.3582 0.5367 6.258 (2 observations deleted due to missingness)  But I don´t really understand what is the interpretation of this coefficient? More specifically, I struggle because I get only one value (for group 3). These are the contrasts of group:  2 3 1 0 0 2 1 0 3 0 1  To get the odds I did: round(exp(RegADHD$beta), 3)


This is 2.835

with(RegADHD, table(ADHD$$Score, ADHD$$Group))


leads to

   1   2   3
0  0   34  30
1  0   7  11
2  0   1   5
3  0   1   5


Does this mean that the probability of having a higher score (in ADHD) increases 2.835 times with being in the severe exposure group, compared with no exposure? But then I don´t know anything about less exposure... I don´t understand why I get only one coefficient!

I hope anyone can help me, I am thankful for every advice!

## migrated from stackoverflow.comOct 7 '18 at 8:23

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• As noted by @mdewey , there appears to be something wrong with the Group variable. It looks like it has only two levels. I also suspect you want some output other than that given by summary. To get an anova-like table, try library(car); library(RVAideMemoire); Anova.clm(RegADHD). To get differences between groups, try library(emmeans); emmeans(RegADHD, ~ Group); pairs(emmeans(RegADHD, ~ Group)) – Sal Mangiafico Oct 7 '18 at 15:22
• Looking at the output from with(RegADHD, table(ADHD$Score, ADHD$Group), you have no observations for the first Group. – Sal Mangiafico Oct 7 '18 at 16:44
• Ohh you´re right, I detected my mistake in the configuration of the data frame.. fixed it now, so I have observations for every group and 2 coefficients as I expected. But the question remains: How can I interpret the output from this function? And if we assume I´ll do another with one additional and want to compare both... I can use an anova then I guess? But do I have to be careful with SS or contrasts then? Any advices? – LotteLi Oct 7 '18 at 18:44
• For me, I would tend to look at the output from Anova.clm and emmeans, probably along with the group medians. That's the way I would look at this, like I would a typical anova with post-hoc. But the information from summary may be more meaningful for you. ... When you say do another one and compare both, not sure what you would intend to compare. – Sal Mangiafico Oct 7 '18 at 19:05
• Thanks, what I want to know is: I used treatment contrasts (group 1 is reference). I think this is ok for what I want to know, because group 1 is somewhat like a Baseline. Now in the next step I want to add 4 other variables (all metric) to see if they change the interaction. To compare both models I want to run a Anova then. Can I do this with treatment contrasts? And can I just use anova(model1, model2)? Or is it problematic because of Type I SS (I know this is problematic with unbalanced groups in classical Anova, but does it also hold here?) – LotteLi Oct 8 '18 at 6:48

## 1 Answer

The odds ratio you have calculated is correct but your interpretation of it is not quite right. You did not tell R that Group was a factor so it has assumed it is a continuous variable with values 0, 1, 2. So the OR you have is for a unit change in Group, from 0 to 1, or from 1 to 2. I suspect that what you want to do is to change the class of Group and re-run. If you do and you still have problems then edit the new information into your question and see if someone can explain further.

With the new information we see that in fact there was nobody in the lowest Group (no exposure) so the coefficient is comparing severe with less, not with no. With that change your interpretation is correct.

• Thank you for your answer! But Group is a factor variable (not just numeric)... – LotteLi Oct 7 '18 at 12:11
• In that case why do you only get one coefficient for it? – mdewey Oct 7 '18 at 12:49
• Yes this is what I am also wondered about! I don´t understand it, but I do only get this one, even though group is a factor. – LotteLi Oct 7 '18 at 14:44
• Perhaps edit the question to paste the whole output of summary(RegADHD). – mdewey Oct 7 '18 at 15:02
• And perhaps also paste in the output of with(RegADHA, table(Score, Group)). – mdewey Oct 7 '18 at 15:03