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Despite having read the documentation of the rms::orm() R package for fitting ordinal cumulative probability models, I am unclear on what models are being compared in the model likelihood ratio test that appears in the output. Is this comparing the proportional odds model to an analogous generalized logit non-proportional odds model?

An example of the relevant part of the output of a model of the form orm(y ~ x1 + x2, data = d) appears below for reference.

                        Model Likelihood               Discrimination    Rank Discrim.    
                              Ratio Test                      Indexes          Indexes    
 Obs          1463    LR chi2     354.50    R2                  0.216    rho     0.471    
 Distinct Y     19    d.f.             4    g                   1.049                     
 Median Y        8    Pr(> chi2) <0.0001    gr                  2.856                     
 max |deriv| 1e-08    Score chi2  357.09    |Pr(Y>=median)-0.5| 0.182                     
                      Pr(> chi2) <0.0001
Gabriel
  • 743

1 Answers1

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The test is comparing a proportional odds model with the specified covariates to a proportional odds model with only an intercept.

Evidence

  1. The degrees of freedom are right for that but not for the test comparing to a generalized logit model. I can't show this in your example, because you've cut off that part of the output, but in examples from the help page the df of the test is the number of regression (non-intercept) coefficients.

  2. orm allows arbitrarily many levels of the outcome variable, so there is no simple test against a non-proportional-odds model (in contrast to lrm, where this would make sense)

  3. The documentation says about the proportional-odds assumption "This can be checked by plotting the inverse cumulative probability function of one minus the empirical distribution function, stratified by X, and assessing parallelism.", which would be a strange thing to say if the standard output included a formal test.

  4. Looking at the source code, the test statistic is the difference between the null-model value computed at line 90 and the alternative-model value at line 267. The null value is for a model with no predictors and the alternative is for a proportion-odds model with the specified predictors

Thomas Lumley
  • 38,062