Dependent Variable takes on the values 0, 1, 2, 3 - What is the right (logistic) regression model to use? I am looking for help to analyze the data from my online experiment.
For my master thesis I conducted an online experiment where participants had to conduct a shopping task where they were provided with a local and a non-local product three times in a row. So for three times, they had to choose between either the local or the non-local product. The result of the shopping task is my dependent variable "Green Shopping Behavior".
Every time someone chose the local product, they got a "1" and if they chose the non-local product they got a "0". In the end i added everything up, so for each observation the dependent variable can take the values 0, 1, 2 and 3. So from my understanding i have a metrically scaled variable that can be considered count data.
I have two metric/continuous independent variables I want to use to predict if participants chose 0/1/2/3 local products, as well as control variables.
Since the structure of my dependent variable is not fitted for a linear regression I looked into other regression models and landed on different logistic models but am heavily confused about what the right approach is. I understand that a classic logistic regression is not suitable, because my dependent variable ist not binary, I further looked into multinomial and ordered logistic regression analysis from which I think that the ordered regression is most suitable given the structure of my dependent variable. Could you give me some insights into what is the right analysis, if i am on the right track or if i am heavily mistaken and if you would propose a completely different strategy?
Your help is highly appreciated!
edit: I use STATA

Although ordinal regression is a generally useful choice for ordered outcomes, in this particular case a binary regression could also be considered.
In each of the 3 trials per individual there is a binary choice: local versus non-local. In R you can model this situation with binary regression, coding the outcomes in a two-column integer matrix of c(successes, failures) with a row for each individual. That would also allow for individuals who didn't finish all 3 trials. See the Details of the R help page for family. I suspect that STATA allows for similar coding.
My impression is that would provide the same result as ordinal logistic regression here, but I haven't thought that through carefully. A potential advantage of using binary regression is that it's (perhaps unfortunately) more likely to be familiar to your audience than ordinal regression and thus easier to explain.
A binary regression could also be used to evaluate changes in outcome probabilities as a function of trial number, although it might be unlikely in this study. You could separate out each trial with a 0/1 outcome and annotation of the individual and trial number, treat the individuals as random effects in a mixed model, and include trial number as a covariate.
