Methods and formulas for event predictions in Fit Poisson Model

Select the method or formula of your choice.

Fitted and predicted values

Different models have different link functions. To calculate the prediction, invert the link function for the model. The inverse functions are in this table.

Model Link Function Formula for Prediction
Binomial Logit
Binomial Normit
Binomial Gompit
Poisson Natural log
Poisson Square root
Poisson Identity

Notation

TermDescription
exp(·) the exponential function
Φ(·) the cumulative distribution function of the normal distribution
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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