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

Beware of adding difficult-to-compare indicators
Treating your variable as an ordinal assumes both that each decision has equal weight (local apple is equivalent to local grape even if the latter is 4 times the price and the former has 2 times the reduction in environmental impact by purchasing locally) and yet that the difference between 3 local choices and 2 is not comparable to the difference between 2 local choices and 1. This is a strange combination.
Use metrics and weight your data
I would suggest determining variables that matches what you really want to study - some function of (differences in) price or environmental impact for instance - and making use of those variables. This will give the decisions made by your participants the appropriate weight and scale appropriately to future tasks. If you have very few items and they are offered to all participants then  modelling them separately as suggested by Björn will make the most of your data.
Alternative approach which may be more informative to your research question - pivot to decision-level rather than participant-level modelling
I guess your research question is about whether people choose to purchase greener versions of products. You're looking at this from a 'person' perspective - would you be better served by analysing from a 'decision' perspective?
I suggest a more informative model here might be price of local item, environmental impact of local item, price of remote item, environmental impact of remote item (other item characteristics as you present to the participant) and participant characteristics predicting whether the choice is made to take a local item or not. That gives you a binary variable for which you could use logistic regression.
The resulting model has much higher generalisability to other items, which you could test through offering other people other shopping tasks.
