Is MNL the right model to use when the choice options vary across observations? - multinomial

Question

In a survey of 100 people, I am asking each person to choose between product A and product B. I ask each person this question 3 times, but each time I present a different set of products. Say, first time, Person 1 is asked to choose between 'Phone 1' and 'Phone 2', given certain attributes of each phone. The second time the choice is again 'Phone 1' vs. 'Phone 2', but a different set of attributes for each phone.
A person is presented three attributes associated with the two phone alternatives every time the question is asked. So, each time between Phone 1 and Phone 2, the attributes of the phone such as cost, memory and camera pixels are presented so that user can choose which set of attributes is most attractive, Phone 1's or Phone 2's.
Overall, 3*100 = 300 responses; 3 responses per person. Each time the attributes cost, memory and camera pixels presented and user asked to choose the feature set they prefer.
My goal is to analyze how users value features of a phone vs. cost of the phone.
In this scenario, can I use a MNL - even though each time I asked the person a question, I only presented two choices ? My understanding is that MNL is sued when (a) there are multiple choices and (b) the choice options do not change across observations, i.e. each person is asked to choose between multiple products, say A, B, C and A, B, C do not change across observations.
In the scenario described above, the two choices varied across the three times the same person was asked the question ? If not MNL, should I rather create a binary logit model given that user only had to choose between two options when the question was asked (even though he was asked the question three times)? If I can use binary logit, should I be concerned that the choice set of products change across observations ? or should I let the attributes defined in each of the rows address the differences in product choices across observations.
I have setup the data as follows (thinking I can do MNL but may be I should set it up differently and use another modeling approach?):

Answer 1

I am working on designing and analyzing similar survey but mine is related to transportation. I am at the beginning level and I am still new to the whole concept, however I will give you an advice and reference maybe it is helpful.
First point: I have come cross 3 models as following from a useful video on YouTube:
MNL refers to Multinomial Logit Model. MNL is used with
alternative-invariant regressors (for example salary of participant
in the survey, or his/her gender …).
Conditional logit model is used with alternative-invariant (gender,
salary, education level …) and alternative-variant regressors (cost
of the product, memory, camera pixel …)
Mixed logit model which uses random parameters. It is also used with
alternative-invariant (gender, salary, education level …) and
alternative-variant regressors (cost of the product, memory, camera
pixel …)
Note regarding alternative-invariant and alternative-variant regressors:
The gender of person participating in the survey will NOT vary between Product A or Product P, so it is alternative-invariant regressor. While price of product could vary between Product A and Product B so it is called alternative-variant regressors.
Based on above I assume you need to use conditional logit model or mixed logit model.
For me I couldn’t find a special function in R for the conditional logit model or mixed logit model. The same mlogit function is used, refer to the examples below for the help of mlogit package:
a pure "multinomial model"
summary(mlogit(mode ~ 0 | income, data = Fish))
a pure "conditional" model
summary(mlogit(mode ~ price + catch, data = Fish))
a "mixed" model
m <- mlogit(mode ~ price+ catch | income, data = Fish)
summary(m)
same model with charter as the reference level
m <- mlogit(mode ~ price+ catch | income, data = Fish, reflevel = "charter")
From the examples above, I think (but NOT sure) that in the Manual of mlogit package, they refer to mixed logit when you used both alternative-invariant and alternative-variant regressors. While conditional model when you have only alternative-variant regressors. On the other hand, multinomial model when you have only multinomial alternative-invariant regressors.
Second point: There is something called “panel data” when you are asking the same person to choose one product for each choice-set. Same person here means that in your model you are taking into consideration, the gender, the salary, the education level … which they will stay the same for the same person. Check this: https://en.wikipedia.org/wiki/Panel_data
To use panel techniques please refer to help in mlogit package in R. I am quoting from it the following:
“panel only relevant if rpar is not NULL and if the data are repeated observations of the same unit ; if TRUE, the mixed-logit model is estimated using panel techniques”
So in my understanding, if you want to use the panel techniques you have to use random draws because panel will be true and rpar will not be NULL.
Moreover, for example about using the panel data, please refer to the below example from “Estimation of multinomial logit models in R : The mlogit Packages” by Yves Croissant
data("Train", package = "mlogit")
Tr <- mlogit.data(Train, shape = "wide", varying = 4:11, choice = "choice", sep = "_", opposite = c("price", "time", "change", "comfort"), alt.levels=c("A", "B"), id.var ="id")
Train.ml <- mlogit(choice ~ price + time + change + comfort, Tr)
Train.mxlc <- mlogit(choice ~ price + time + change + comfort, Tr, panel = TRUE, rpar = c(time = "cn", change = "n", comfort = "ln"), correlation = TRUE, R = 100, halton = NA)
Train.mxlu <- update(Train.mxlc, correlation = FALSE)
I hope that is useful to you.