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

If you stick really close to the data generating process, these are repeated binary decisions. I.e. each participants makes three decisions of choosing the local product or not (each time a 1/0 outcome).
It's not count data, because the counts cannot reach any arbitrary number. Arguably, it could be truncated (at 3) count data or ordinal data, but that's not exactly how the data arose. That does not mean that you could not create a useful model by considering it that way, especially an ordinal model may indeed be useful. However, an ordinal model ignores that participants are asked to make a very similar choices - possibly with some known differences between questions - each time.
If one goes down the repeated binary route, then it matters what we wish to assume/what detailed data we have on each decision. E.g. when asked about the products, the product might sometimes have been a vegetables, exotic fruit, or clothes. People might tend to prefer buying vegetables locally, think that exotic fruits are so much better from further away and be more mixed about clothes. Or perhaps you think people might change their answer based on something else (e.g. is it the first question they get asked, participant's age, favorability rating 0-100 for globalization etc.). In that case modeling each binary choice (with explanatory variables like type of choice, participant age etc. as a fixed effect) and accounting for decisions being by the same participant (e.g. participant random effect) would be an option. Or, perhaps the choices were really all the same, in which one can reduce this to a binomial outcome (i.e. number of yes answers out of 3 with the same probability applying to all of them). Thus, I'm arguing for the use of (random effects) logistic regression (which is well supported e.g. in R using the lme4 or brms packages).
