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Let's say I conducted an experiment in which I measured if customers bought a particular product and also measured customer satisfaction with the shop and familiarity with that product.

The dependent variable is the outcome (Out) which is binary ("bought" or "not bought") and the IVs are customer satisfaction (CusSat) and familiarity with product (FamPro). Both IVs are continuous variables.

I predict that the higher the satisfaction and familiarity with a product the more probable it is that customers will buy it. I'm not interested in the effect of either familiarity or satisfaction alone. I'm really interested in knowing if, in the case that both familiarity and satisfaction are high increases the chances of buying a product.

I think this problem requires a binary logistic regression, but I'm not sure how to test the prediction above. Because I measure these variables for two products (Prod) I have a repeated measures design, so need to use glmer I believe.

> df <- data.frame(Prod=c(1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2), Cus=c(1,1,2,2,3,3,4,4,5,5,,6,7,7,8,8), Out=c(0,0,1,0,1,1,1,0,1,0,1,1,0,0,1,0), CusSat=c(130,80,103,100,140,100,90,99,140,80,90,111,130,100,70,90), FamPro=c(7,3,20,10,5,13,8,9,10,13,12,12,9,6,9,18))
> mod <- glmer(Out ~ scale(CusSat)*scale(FamPro) + (1|Cus), data=df, family=binomial())

Is the model set up correctly? How can I test the prediction above from this?

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