expected {DGLMExtPois}

Expected Probabilities and Frequencies for the hyper-Poisson and COM-Poisson Model

Description

The hP_expected and CMP_expected functions calculate the probability distribution of the count response variable Y for each observation and obtain the corresponding expected frequencies. It is an informal way of assessing the fit of the hP or CMP model by comparing the predicted distribution of counts with the observed distribution.

Usage

hP_expected(object)

CMP_expected(object)

Arguments

object

a fitted object of class inheriting from "glm_hP" or "glm_CMP".

Details

The average expected probabilities are computed as

\bar(Pr)(y=k) = \frac{1}{n} \sum_{i=1}^n \widehat{Pr}(y_i = k | x_i)

The expected frequencies are obtained by multiplying by n.

Two measures are offered for summarizing the comparison between expected and observed frequencies: the sum of the absolute value of differences and the sum of the square of differences (similar to the Pearson statistic of goodness of fit).

Value

A list containing the following components:

frequencies

the expected counts for the hP or CMP fit.

observed_freq

the observed distribution.

probabilities

the expected distribution for the hP or CMP fit.

dif

sum of the absolute value of differences between frequencies and observed_freq.

chi2

sum of the square of differences between frequencies and observed_freq.

References

J. M. Hilbe (2011). Negative Binomial Regression. (2nd ed.). Cambridge University Press.

M. Scott Long and Jeremy Freese (2014). Regression Models for Categorical Dependent Variables using STATA. (3rd ed.). Stata Press.

Examples

## Fit a hyper-Poisson model

Bids$size.sq <- Bids$size ^ 2
hP.fit <- glm.hP(formula.mu = numbids ~ leglrest + rearest + finrest +
                 whtknght + bidprem + insthold + size + size.sq + regulatn,
                 formula.gamma = numbids ~ 1, data = Bids)

## Compute the expected probabilities and the frequencies

hP_expected(hP.fit)
## Estimate a COM-Poisson model

Bids$size.sq <- Bids$size ^ 2
CMP.fit <- glm.CMP(formula.mu = numbids ~ leglrest + rearest + finrest +
                   whtknght + bidprem + insthold + size + size.sq + regulatn,
                   formula.nu = numbids ~ 1, data = Bids)

## Compute the expected probabilities and the frequencies

CMP_expected(CMP.fit)