Pearson dispersion estimator ( $ϕ$ )

For a generalized linear model with variance function

V

, the Pearson estimator is

ϕ = \frac{1}{n - p} \sum_{i} \frac{( Y _{i} - μ _{i} ) ^{2}}{V ( μ _{i} )} .

Table of contents
- Pearson residual Pearson dispersion estimator
- Pearson chi-squared statistic Pearson dispersion estimator

Pearson residual ( $r_{i}^{P}$ )

The Pearson residual is

r_{i}^{P} = (Y_{i} - μ_{i}) / ϕ V (μ_{i})

.

Pearson chi-squared statistic ( $X_{P}^{2}$ )

The Pearson chi-squared statistic for a generalized linear model is

X_{P}^{2} = \sum_{i} \frac{( Y _{i} - μ _{i} ) ^{2}}{V ( μ _{i} )} .

Dividing it by the residual degrees of freedom estimates the dispersion parameter.

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