I have trouble selecting the correct regression model for my data.
Let's call my dependent variable Y. It can take values from 0 to 5 depending on how many corresponding documents have been published. A value of 0 means none of the five documents were published, and that is really bad. On the other hand, 5 means that all of the possible five documents have been published,and that's really great.
Also I have 4 independent variables. Three of them (let's call them $X_1$, $X_2$ and $X_3$) are continuous and one of them (let's call it X4) is binary variable.
The main task is to find the effects of each independent variable on dependent variable Y. Maybe, I will use more independent variables, or build two regression models or similar,I'm not sure about that for now. But first I need to decide exactly which type of regression to choose.
My sample size is 127.
This is a barplot of relative frequencies of Y:
It was suggested to me to use Poisson regression or negative binomial regression (Y was recognized as a count variable). I used R, but the fitted values are not similar to my original dependent/response variable:
My main goal is to find statistically significant variables and not to predict anything, but these fitted values/predictions should've been at least somewhat logical?
Also, what about ordinal logistic regression, or if you could suggest to me some other regression model which will correspond to my data?