I've got a dataset that I'd like to model, and it seems like the best model would be of the form:
$y = (\beta_1 x_1 + \beta_2 x_2 + \beta_3 x_3) \cdot (\beta_4 x_4 + \beta_5 x_5 + \beta_6 x_6) + \epsilon$.
The $\beta_4$ through $\beta_6$ are independent of each other and have a linear effect on $y$ once modulated by the $\beta_1$ through $\beta_3$, which are independent of each other but scale the effect of the other predictors. I would expect the residuals of the above model to be fairly normal. If I want to fit this model in R, I can use a nonlinear model fitting routine such as
nls(), it seems. But is there a better approach? This looks like the sort of model that might be a special case with a name and an optimized fitting approach. Is it?