I am trying to build a hierarchical linear model based on data structured like this dataset below. The model form I am looking to build is

Purchased ~ f(price + color + more item attributes + age + gender + other person attributes)

Betaprice ~ f(age + gender + other person attributes)

Does anyone know a good approach for this?

 person item purchased age  gender  Color   Price
    1   1    1         23   F     Blue      20
    1   2    0         23   F     Red       15
    1   3    1         23   F     Green     18
    2   1    0         34   M     Blue      20
    2   2    1         34   M     Red       15
    2   3    0         34   M     Green     18
    3   1    1         19   M     Blue      20
    3   2    1         19   M     Red       15
    3   3    0         19   M     Green     18

I'm not really sure if I understand the question correctly but since I'm not able to comment due to my less reputation I'll post an answer:

I assume this can be done via a linear mixed model, where the persons are random samples. But to answer your question: What is your goal? Do you want to know which persons buy something? Or do you want to know which persons buy something special? Or a special color? I assume you are interested in the total purchase of one person, so in R maybe something like

fit<- lmer(Price ~ person + (1 | item/color/purchased) + (1 | gender) + (1 | age) + (1 + person | item)..)
  • $\begingroup$ My goal is to predict how sensitive a member is to price based on attributes about that individual. In the end, I want to be able to compute kind of like a price elasticity at the individual level. $\endgroup$ – user295944 Nov 4 '17 at 17:56
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    $\begingroup$ Interesting. How many individuals do you have? And in which way shall the model be hierarchically? $\endgroup$ – Ben Nov 4 '17 at 18:07
  • $\begingroup$ In my sample now, I have about 5k individuals and 5 items. I can get more though. I am not sure how the hierarchy is structures, which is why I'm on here ;) . I know I would like to predict probability of purchase for each item and the beta on price be a function of attributes about individuals. $\endgroup$ – user295944 Nov 6 '17 at 16:37
  • $\begingroup$ I guess what you are looking for are so-called logistic-functions/models. But I only stumbled over them and it looks appropriate to me because you are having a boolean factor (purchased yes/no). But I'm not sure since the predicted probability won't be a boolean, of course. I will think about it. $\endgroup$ – Ben Nov 7 '17 at 17:21
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    $\begingroup$ right now I'm just trying a logistic regression with purchased~color + attribute2 + attribute3+...+ price + price:age + ... then after I can obtain the price coefficients and build a formula like 1(price coef)+age(price:age coef)+... $\endgroup$ – user295944 Nov 8 '17 at 18:09

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