Regression with clustering at true zero, middle value and maximum value.

[Adam Shier]

Hello,
I am looking to understand what influences the hours individuals will commit to a certain task. The item collecting my dv (Hours) had a lower limit of 0 and an upper limit of 40.
As you can see from the histogram below, the most common response was 0, followed by 20, followed by 40. I would really appreciate advice on the type of analysis to run.
I had seen suggestions for the tobit model, with correct assumption that the upper limit of 40 is censored, however, with my zeros being actual zeros, I fear this would be misguided.
Best,
Adam

[Maxence Morlet]

These are the options I would recommend:

- Poisson PML

- Heckman two-step model if you believe that individuals non-randomly self-select into accomplishing these tasks (you need an instrument to identify the effect and a plausible selection equation as well).

- Do you believe that there are two "different" populations in the 0 cluster? In this case, you may want to check zero-inflated Poisson.

Would the latent variable actually be equal to values superior to 40? But you only observe it up to 40, is that the case?

[Adam Shier]

Thank you for your response, Maxence. Essentially the data is based on vignette analysis wherein participants were asked to indicate how many hours of their own time they would be willing to dedicate to a 40 hour program. My intuition behind the values being superior to 40 is that, were the upper bound of 40 not present in another, similar scenario, some indicating 40 would in fact indicate more time.