This does not seem like a Cox regression problem. The Cox model is used to examine influences of variables on the time is takes for an event to happen. The time variable in your data seems to be 1 for the choice that was made and 2 for the choices that weren't made in each presentation/trial. It's not clear to me how Cox analysis with such a "time" variable would accomplish your goal, although if you have some reference to how it does so I would be glad to learn from it.
What you have is a set of trials involving a forced choice of 1 among 3 objects. Typically this would be analyzed as a multinomial logistic regression, and SPSS does have tools for that type of analysis. This examines how the probability of making a particular choice depends on predictor variables (in your case, price, price range, their interaction, and size) at each trial.
Complicating matters in this design is that over the entire study there were multiple SKU involved but only 3 were available in each trial. So the probability of choosing an SKU that wasn't presented is 0. Evidently the size of each SKU was fixed but the price was varied among trials. This type of design gets a bit beyond my personal expertise, but I will propose one way to proceed.
To analyze this as a multinomial regression, which seems most appropriate, it seems that you will have to include an additional predictor variable that indicates whether or not the SKU was available in a particular trial. That way, at least formally, all the SKU are included in the model for each trial. Then you proceed as follows, with one data line for each trial:
The output variable for each presentation is the SKU that was chosen.
The price, price_range, some type of interaction term between them, and the size are included as predictor variables. It's not clear that including the Respondent ID will help much, as each Respondent only saw 2 of the 12 different types of presentation, but include that if you think it is important (it may be difficult to interpret, however).
A set of variables indicating whether a particular SKU was available for choice at that trial is added as predictors. The "stratum" per se is then no longer needed as a predictor.
You should not just ignore the range_price variable as a possible predictor. It's hard to interpret interaction terms without also knowing the main effects.
There are a few dangers here whose importance may be affected by the details of your design. One is that although you have prices in numbers you only have a limited set of prices and price ranges, so it might be difficult to interpret your data directly in terms of change of odds per change in price. This may be a particular issue with your interaction term. A second is that the particular combinations of sizes, prices, and price ranges you used might have some internal relations that then pose problems like those that arose when your price_range and strata ended up being just two ways of presenting the same variable.
If this answer doesn't help, you might want to pose a new question based more directly on your experimental design, such as "multinomial regression with different choices among trials." If possible, if you do pose a new question present the choices available in each of your 12 "strata".
Best Answer
Linear regression does not predict the 100th percentile. Linear regression is more akin to predicting a mean, which doesn't translate into "percentiles".
And I just played around with the
rq()function in R (in thequantregpackage). It does indeed allow you to use interaction effects. Try something like: