Modeling Likert scale outcomes with trend-proportional odds with and without cluster data

Likert scales are commonly used in epidemiological studies employing surveys. In this tutorial we demonstrate how the proportional odds model and the trend odds model can be applied simultaneously to data measured in Likert scales, allowing for random cluster effects. We use two datasets as examples: an epidemiological study on aging and cognition among community-dwelling Black persons, and a clustered large survey data from 28,882 students in 81 middle schools. The first example models the Likert outcome from the question: "People act as if they think you are dishonest". The trend-proportional odds model indicates that Black men have higher odds than Black women of reporting being perceived dishonest. The second example models the Likert outcome from the question: "How often have you been beaten up at school?". The trend-proportional odds model indicates that children with disability have a higher odds of severe violence than other children. For both examples, the cumulative odds ratio increases by more than 60% at the higher Likert levels.