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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