![]() ![]() ![]() This can also be expressed as Φ -1( p) = X β + ε where X = is a 1 × k+1 row vector of random variables (with x 1 = 1) and β = is a k+1 × 1 column vector of parameters (the regression coefficients). Where the residual random variable has a standard normal distribution, i.e. The probit regression model takes the form We will also use the notation for the standard normal pdf, φ( z) = NORM.S.DIST( z, FALSE). The inverse function Φ -1( p) = NORM.S.INV( p) is called the probit function (probit = probability unit) and plays a role similar to the logit function in probit regression. Then in Excel, Φ( z) = NORM.S.DIST( z, TRUE). Let Φ( z) represent the standard normal cumulative distribution function. The inverse standard normal distribution function is another link function and is the basis for a regression approach similar to logistic regression, called probit regression. A function with this property is called a link function. The logit function maps a probability, which takes discrete values of 0 or 1, into a continuous value between -∞ and ∞. ![]()
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