Methods and formulas for Predict for Binary Logistic

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Fitted and predicted values

To calculate the prediction, invert the link function for the model, which is the logit link function. The formula is: Notation

TermDescription
exp(·) the exponential function
X' the transpose of the vector of points to predict for the vector of estimated coefficients

Standard error of fitted values and predictions

Notation

TermDescription
Φ1, for the binomial and Poisson models
xhthe vector of a new design point the transpose of xh
Xthe design matrix
Wthe weight matrix the first derivative of the link function evaluated at  the predicted mean response

Confidence limits for fits and predictions

The confidence limits use the Wald approximation method. This is the formula for a 100(1 − α)% two-sided confidence interval:

Notation

TermDescription the inverse of the link function evaluated at x   the transpose of the vector of the predictors the vector of estimated coefficients the value of the inverse cumulative distribution function for the normal distribution evaluated at αthe significance level  Xthe design matrix
Wthe weight matrix 1, for binomial and Poisson models
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