Question

In a logit or logistic regression, to convey the influence of an explanatory variable ? on the probability of observing a one for the dependent variable, best practice is to report the average of the slope coefficient estimates for ? over all observations in the sample.

Answer 1

Consider the given problem here “Yi” be the dependent variable and “Xi” be the explanatory variable, where “Yi” is a binary variable takes “1” and “0”, where “”, => presence of the event and “0” be the absence of the event. Now, “Pi” be the probability that “Yi” will take “1”. So, the log odd in favor of the events is given by.

=> Li = ln(Pi/1-Pi) = b1 + b2*Xi, where we have to estimate the unknown parameters “b1” and “b2” with the help of the given sample. So, once we estimate the parameters the estimated “Pi” is given by.

=> Pi = 1/[1+e^-(b1+b2*Xi)] = e^( b1+b2*Xi)/[1+e^(b1+b2*Xi)], which is non-linear to “Xi”, => the partial effect of “X” on “P” is not constant. So, the influence of “X” on “P” is not the estimated value of the slope coefficient.