With the new estat parallel command, you can easily test the proportional odds (parallel lines) assumption for ordered logit models. This feature is a part of StataNow™.

The proportional odds model (ordered logit model) fit by ologit employs the proportional odds assumption, also called the parallel lines assumption, which states that the cumulative probability curves for each outcome category plotted against a predictor should be parallel. This assumption allows the effect of each predictor variable to be expressed as a single coefficient. Stata's new estat parallel command tests the proportional odds assumption after fitting a model with ologit.

Let's see it work

Let's use fictional data on daily cigarette consumption. The codebook command shows us the four levels of tobacco consumption and the two categories of religion in the dataset.

. webuse tobacco, clear
(Fictional tobacco consumption data)

. codebook tobacco religion



tobacco                                                            Tobacco usage


                  Type: Numeric (byte)
                 Label: tobaclbl

                 Range: [0,3]                         Units: 1
         Unique values: 4                         Missing .: 0/15,000

            Tabulation: Freq.   Numeric  Label
                        9,469         0  0 cigarettes
                        3,806         1  1–7 cigarettes/day
                        1,050         2  8–12 cigarettes/day
                          675         3  >12 cigarettes/day
			                                      

religion                                              Religion prohibits smoking


                  Type: Numeric (byte)
                 Label: religlbl

                 Range: [0,1]                         Units: 1
         Unique values: 2                         Missing .: 0/15,000

            Tabulation: Freq.   Numeric  Label
                       13,504         0  Indifferent
                        1,496         1  Discourages smoking

We want to investigate the effect of religion on tobacco consumption. The outcome variable is ordinal, so we use ologit to fit an ordered logit model. We specify the nolog option to suppress the iteration log and the or option to display the effect of religion as an odds ratio rather than a coefficient.

. ologit tobacco i.religion, nolog or

Ordered logistic regression                             Number of obs = 15,000
                                                        LR chi2(1)    =  27.03
                                                        Prob > chi2   = 0.0000
Log likelihood = -14447.759                             Pseudo R2     = 0.0009



      tobacco 
 
 Odds ratio   Std. err.      z    P>|z|     [95% conf. interval]
 
 
 
     religion 
 
                                                                
Discourage..  
 
   .7453873   .0428261    -5.11   0.000     .6660032    .8342335
 
 
 
        /cut1 
 
   .5091016   .0177491                       .474314    .5438892
        /cut2 
 
   2.013823   .0260681                      1.962731    2.064916
        /cut3 
 
   3.028884   .0396792                      2.951114    3.106654

Note: Estimates are transformed only in the first equation to odds ratios.

Members of antitobacco religions have lower odds of increased cigarette consumption compared with individuals that do not belong to antitobacco religions: the odds ratio of 0.745 indicates a 25.5% decrease in odds. The proportional odds model estimates a single coefficient for the effect of religion, which means that the odds ratio for religion does not depend on the outcome category. Is this an oversimplification? We use the estat parallel command to test the proportional odds assumption.

. estat parallel

Tests of proportional odds assumption

Number of obs            = 15,000
Number of predictors     =      1
Number of outcome levels =      4
Degrees of freedom       =      2


             Test 
 
      chi2  P>chi2
 
 
 
            Brant 
 
   4.28838   0.117
 Likelihood-ratio 
 
   4.58904   0.101
            Score 
 
   4.29863   0.117
             Wald 
 
   4.28838   0.117
      Wolfe–Gould 
 
   5.20475   0.074

estat parallel performs five tests of the proportional odds assumption, and the null hypothesis for each of these tests is that the assumption holds. Examining the output, we see that none of the five tests shows strong evidence that our assumption was violated. If we had encountered a departure from proportional odds, one recourse would be to fit a model that does not impose this assumption, such as the stereotype logistic regression model.