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Multilevel ordered logistic models


Stata’s new meologit command allows you to fit multilevel mixed-effects ordered logistic models. A multilevel mixed-effects ordered logistic model is an example of a multilevel mixed-effects generalized linear model (GLM). You can fit the latter in Stata using the new meglm command.

Here we replicate the three-level multilevel model example using the meologit command.

We have student-level data, where students are nested in classes, and classes are nested in schools. Our dependent variable thk is an ordered categorical variable that takes on the values 1, 2, 3, or 4; and we have three explanatory variables: prethk, cc, and tv. We will treat prethk as continuous. cc and tv are binary, and we want to include their interaction in the model. Let's fit an ordered logistic model:

. webuse tvsfpors . meologit thk prethk cc##tv || school: || class: Fitting fixed-effects model: Iteration 0: log likelihood = -2212.775 Iteration 1: log likelihood = -2125.509 Iteration 2: log likelihood = -2125.1034 Iteration 3: log likelihood = -2125.1032 Refining starting values: Grid node 0: log likelihood = -2152.1514 Fitting full model: Iteration 0: log likelihood = -2152.1514 (not concave) Iteration 1: log likelihood = -2125.9213 (not concave) Iteration 2: log likelihood = -2120.1861 Iteration 3: log likelihood = -2115.6177 Iteration 4: log likelihood = -2114.5896 Iteration 5: log likelihood = -2114.5881 Iteration 6: log likelihood = -2114.5881 Mixed-effects ologit regression Number of obs = 1600
No. of Observations per Group
Group Variable Groups Minimum Average Maximum
school 28 18 57.1 137
class 135 1 11.9 28
Integration method: mvaghermite Integration points = 7 Wald chi2(4) = 124.39 Log likelihood = -2114.5881 Prob > chi2 = 0.0000
thk Coef. Std. Err. z P>|z| [95% Conf. Interval]
prethk .4085273 .039616 10.31 0.000 .3308814 .4861731
1.cc .8844369 .2099124 4.21 0.000 .4730161 1.295858
1.tv .236448 .2049065 1.15 0.249 -.1651614 .6380575
cc#tv
1 1 -.3717699 .2958887 -1.26 0.209 -.951701 .2081612
/cut1 -.0959459 .1688988 -0.57 0.570 -.4269815 .2350896
/cut2 1.177478 .1704946 6.91 0.000 .8433151 1.511642
/cut3 2.383672 .1786736 13.34 0.000 2.033478 2.733865
school
var(_cons) .0448735 .0425387 .0069997 .2876749
school>class
var(_cons) .1482157 .0637521 .063792 .3443674
LR test vs. ologit regression: chi2(2) = 21.03 Prob > chi2 = 0.0000 Note: LR test is conservative and provided only for reference.

Our model has two random-effects equations, separated by ||. Our first is a random intercept at the school level, and the second is a random intercept at the class level. The order we listed them matters: class comes after school, meaning that classes are nested within schools. Using the same logic, we could include more levels of nesting.

The output table includes the fixed-effect portion of our model, the estimated cutpoints (because this is an ordered logistic model), and the estimated variance components.

Also watch A tour of multilevel GLMs.

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