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I have data set with 3 indepdent variables and 1 dependent variable. They are related to each other in the following way.

y* = a q^{1/3} + b q R C_{NS} + c

where a, b, and, c are coefficients, q, R, and, C_{NS} are independent variables. Depending on the values of y*, I have another binary random variable of interest.

y = 1 if y* > thresholdvalue
y = 0 if y* < thresholdvalue

I have data set containing values of y, q, R, and, C_{NS}. I want to find a nonlinear regression model that would be appropriate fit for this. I have only dealt with linear models. What would be an appropriate model in this case?

Khushal
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    This is a linear regression model and can be fit with standard multiple regression techniques and algorithms. But why do you wish to dichotomize $y$ in this way? Why not fit it directly? – whuber Nov 25 '23 at 17:28
  • I don't understand the linearity in this situation. Clearly the equation of y* is not a linear function of 3 variables. It has interaction and fractional powers. y* denotes a quantity that can be used to predict the occurrence of an event based on its value. If its value crosses the threshold, then the event occurs and not otherwise. – Khushal Nov 25 '23 at 17:32
  • Clearly the equation is linear in the variables you are solving for: namely, $a,$ $b,$ and $c.$ That's what matters. See https://stats.stackexchange.com/questions/148638 for further explanation. – whuber Nov 25 '23 at 17:38
  • I didn't realize that we should be looking at model parameters. Does that mean we can use a generalized linear model (glm) in R to fit such data and include such an interaction in the linear model? – Khushal Nov 25 '23 at 17:52
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    Yes, it does. Your formulation suggests using a logistic regression using a logit or probit link as a first resort. – whuber Nov 25 '23 at 17:55

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