Question

Lecture 9 we examined robust, regression-based Lagrange Multiplier test statistics for testing the functional form of a conditional mean where

H0 : m(xi, θ) = m(xiβ)

HA : m(xi, θ) = m(xiβ + δ1(xiβ)2 + δ2(xiβ)3)

Suppose that we want to perform a similar test for the functional form of a probit model, i.e.,

H0 : G(xiθ) = Φ(xiβ)

HA : G(xiθ) = Φ(xiβ + δ1(xiβ)2 + δ2(xiβ)3)

Using the method from Lecture 9, explain which regression you would run to perform this test. (Hint: for a standard normal, ∂ Φ(xβ) = φ(xβ)x.)

∂β

Answer 1

Probit model is a type of regression where thr dependent variable can take two values like Yes or No,The purpose of the model is to estimate the probability that an observation with particular characteristics will fall into a specific one of the categories; moreover, classifying observations based on their predicted probabilities is a type of binary classification model.

A probit model is a popular specification for an ordinal or a binary response model. As such it treats the same set of problems as does logistic regression using similar techniques. The probit model, which employs a probit link function, is most often estimated using the standard maximum likelihood procedure, such an estimation being called a probit regression.