I have a ordinal dependendent variable, easiness, that ranges from 1 (not easy) to 5 (very easy). Increases in the values of the independent factors are associated with an increased easiness rating.

Two of my independent variables (condA and condB) are categorical, each with 2 levels, and 2 (abilityA, abilityB) are continuous.

I'm using the ordinal package in R, where it uses what I believe to be

$$\text{logit}(p(Y \leqslant g)) = \ln \frac{p(Y \leqslant g)}{p(Y > g)} = \beta_{0_g} - (\beta_{1} X_{1} + \dots + \beta_{p} X_{p}) \quad(g = 1, \ldots, k-1)$$
(from @caracal's answer here)

I've been learning this independently and would appreciate any help possible as I'm still struggling with it. In addition to the tutorials accompanying the ordinal package, I've also found the following to be helpful:

But I'm trying to interpret the results, and put the different resources together and am getting stuck.

  1. I've read many different explanations, both abstract and applied, but am still having a hard time wrapping my mind around what it means to say:

    With a 1 unit increase in condB (i.e., changing from one level to the next of the categorical predictor), the predicted odds of observing Y = 5 versus Y = 1 to 4 (as well as the predicted odds of observed Y = 4 versus Y = 1 to 3) change by a factor of exp(beta) which, for diagram, is exp(0.457) = 1.58.

    a. Is this different for the categorical vs. continuous independent variables?
    b. Part of my difficulty may be with the cumulative odds idea and those comparisons. ... Is it fair to say that going from condA = absent (reference level) to condA = present is 1.58 times more likely to be rated at a higher level of easiness? I'm pretty sure that is NOT correct, but I'm not sure how to correctly state it.

1. Implementing the code in this post, I'm confused as to why the resulting 'probability' values are so large.
2. The graph of p (Y = g) in this post makes the most sense to me ... with an interpretation of the probability of observing a particular category of Y at a particular value of X. The reason I am trying to get the graph in the first place is to get a better understanding of the results overall.

Here's the output from my model:

m1c2 <- clmm (easiness ~ condA + condB + abilityA + abilityB + (1|content) + (1|ID), 
              data = d, na.action = na.omit)
Cumulative Link Mixed Model fitted with the Laplace approximation

easiness ~ illus2 + dx2 + abilEM_obli + valueEM_obli + (1 | content) +  (1 | ID)
data:    d

link  threshold nobs logLik  AIC    niter     max.grad
logit flexible  366  -468.44 956.88 729(3615) 4.36e-04

Random effects:
 Groups  Name        Variance Std.Dev.
 ID      (Intercept) 2.90     1.70    
 content  (Intercept) 0.24     0.49    
Number of groups:  ID 92,  content 4 

                Estimate Std. Error z value Pr(>|z|)    
condA              0.681      0.213    3.20   0.0014 ** 
condB              0.457      0.211    2.17   0.0303 *  
abilityA           1.148      0.255    4.51  6.5e-06 ***
abilityB           0.577      0.247    2.34   0.0195 *  

Threshold coefficients:
    Estimate Std. Error z value
1|2   -3.500      0.438   -7.99
2|3   -1.545      0.378   -4.08
3|4    0.193      0.366    0.53
4|5    2.121      0.385    5.50

1 Answer 1


My Regression Modeling Strategies course notes has two chapters on ordinal regression that may help. See also this tutorial.

The course notes go into detail about what model assumptions mean, how they are checked, and how to interpret the fitted model.

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    $\begingroup$ Done - thanks for the alert $\endgroup$ Dec 21, 2019 at 14:35
  • 2
    $\begingroup$ While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. - From Review $\endgroup$ Apr 23, 2022 at 13:43
  • $\begingroup$ Sorry, no. That would require too much repetition and greatly reduce the number of questions I have time to answer. And I work hard to keep links current. For example this week I edited 20 old posts to update links. $\endgroup$ Apr 23, 2022 at 14:37
  • 1
    $\begingroup$ @FrankHarell - this question was in a "low quality posts" review list. When the answer is only found in an external link the requirement for the reviewers is to press "link only answer", and then the text in the comment you see here is generated and posted automatically. I wasn't the one that flagged the answer, just ended up reviewing it, and I think the vote I took in the review is fair. If my memory is correct the typical recommendation for link-only answers is to post them as comments instead. $\endgroup$ Apr 23, 2022 at 16:42
  • $\begingroup$ That doesn't make sense, if someone has gone to a lot of trouble to create an answer in a permanent external location. And the answer may get better over time in that location. $\endgroup$ Apr 23, 2022 at 19:15

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