Dear Statalisters,

I'm using Stata 15.1. I have a Likert scale from 1 to 5 as outcome, and I'm performing two regressions:

1) a stereotype logit regression (command slogit) on original observations (after finding the Brant test for proportional odds was highly significant),

2) a logistic quantile regression (more precisely, since I'm using the median, a logistic median regression, using the user-written command lqreg; Orsini and Bottai, 2011) on the observations at the weekly level (since I have 3 observations per day, it's the mean among 21 observations).

I know both approaches are questionable (and I'm using two approaches precisely because the nature of the outcome makes the method to choose controversial), but my question is not related to this.

The point is: I'm using in both regressions the lagged value of the outcome as a covariate (in the one on original observations, even lag 3, corresponding to the same observation the day before). Thus, I need to test for nonstationarity first.

A) Stereotype logit regression: I have no idea how to do, since only 5 values (that are ordered) are possible, thus observations may take the maximum or the minimum value of the outcome.

B) Logistic quantile regression: here, exploiting the fact that no observation takes the maximum or the minimum outcome value, I would use the same transformation adopted by the lqreg command (Bottai et al, 2010), that would allow me to have a variable ranging across all real numbers, that would also be the one used in my regression.

Could you help me with A, and tell me whether my approch with B is correct (and how to modify it in case it isn't)?

Bottai, M., B. Cai, and R. E. McKeown. 2010. Logistic quantile regression for bounded outcomes. Statistics in Medicine 29: 309–317.

Orsini N, Bottai M: Logistic quantile regression in Stata. Stata J 2011, 11: 327–344.