I have the following linear model in
model <- lm(response ~ v1*v2 + v3*v2 + v4, data=df)
v2 is number of hours spent sleeping
v4 is ordinal (7 pt likert) measuring subject rating of sleep quality
v3 are 3 level factors measuring time spent on different activities (0-10mins, 11-20, 20+)
response is a count variable ranging from 1-6. This measures number of correct items on a 6 item quiz
I'm wondering what criteria is used to decide whether poisson regression should be used instead. I've considered the following:
I've read that in a poisson model the mean and variance of the
responseshould be equal, which is not true in this case (mean = 5, variance = 1.1, mode = 6).
The distribution is negatively skewed, which works in favour of using a poisson model. What types of transformations are possible if I wanted to use OLS?
The range of the variable is 1-6. I believe one reason to use a poisson is due to the bounding at 0, however, I dont have any 0 values and the majority of the values are in the upper range (6)
Does poisson regression require a larger sample size than OLS to gain sufficient power? My N is ~120
I've tried running
ncvTest()to check for heteroscedasticity and the test results are in favour of using OLS (no assumption violation)
Many say that poisson regression should be used to count data no matter what, but OLS doesn't seem unreasonable given some of the points above. What should my primary considerations be and how should I weigh the points outlined above? Is there anything that could be used to argue against the use of a poisson model in this case (maybe sample size?)?
To address the duplicate post concern: I don't believe the other post is asking the same thing (or at least the answer provided there doesn't really help in this case):
The other post is dealing with extensive variables, but in this case we have intensive
Given intensive variables, the other post suggests a linear model is OK but doesn't explain why
The response variable in the other post is unbounded at the upper end (i.e. number of patents). In this case, the response measures number of correct items on an exam. Given there is a maximum value to that (i.e. the value cant be greater than the number of items on the exam), the response here is bounded at both ends, with no respondents touching the lower bound of 0
So my question here is really asking about how to correctly handle positive integer (discrete) response values that are bounded at both ends