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

Yes, ordinal logistic regression (also referred to as the proportional odds model) is your best choice. If your outcome were to have 7+ ordered categories, linear regression may also be used, though because you have few ordered categories (i.e., 4) I would use ordinal logistic regression as suggested in the comments by @mkt. The article cited below (Bauer & Sterba, 2011) is a good introduction to ordinal regression.
References
Bauer, D. J., & Sterba, S. K. (2011). Fitting multilevel models with ordinal outcomes: performance of alternative specifications and methods of estimation. Psychological methods, 16(4), 373.
