Description Usage Arguments Details Value Author(s) References See Also Examples

The function fits the log linear model (“Procedure II”) proposed by Breslow (1984) accounting for
overdispersion in counts *y*.

1 |

`formula` |
A formula for the fixed effects. The left-hand side of the formula must be the counts |

`data` |
A data frame containing the response ( |

`phi` |
When |

`tol` |
A positive scalar (default to 0.001). The algorithm stops at iteration |

For a given count *y*, the model is:

*y | λ ~ Poisson(λ)*

with *λ* a random variable of mean *E[λ] = μ*
and variance *Var[λ] = φ * μ^2*.

The marginal mean and variance are:

*E[y] = μ*

*Var[y] = μ + φ * μ^2*

The function uses the function `glm`

and the parameterization: *μ = exp(X b) = exp(η)*, where *X*
is a design-matrix, *b* is a vector of fixed effects and *η = X b* is the linear predictor.

The estimate of *b* maximizes the quasi log-likelihood of the marginal model.
The parameter *φ* is estimated with the moment method or can be set to a constant
(a regular *glim* is fitted when *φ* is set to 0). The literature recommends to estimate *φ*
with the saturated model. Several explanatory variables are allowed in *b*. None is allowed in *φ*.

An offset can be specified in the argument `formula`

to model rates *y/T* (see examples). The offset and the
marginal mean are *log(T)* and *μ = exp(log(T) + η)*, respectively.

An object of formal class “glimQL”: see `glimQL-class`

for details.

Matthieu Lesnoff [email protected], Renaud Lancelot [email protected]

Breslow, N.E., 1984. *Extra-Poisson variation in log-linear models*. Appl. Statist. 33, 38-44.

Moore, D.F., Tsiatis, A., 1991. *Robust estimation of the variance in moment methods for extra-binomial
and extra-poisson variation*. Biometrics 47, 383-401.

`glm`

, `negative.binomial`

in the recommended package MASS,
`geese`

in the contributed package geepack,
`glm.poisson.disp`

in the contributed package dispmod.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 | ```
# without offset
data(salmonella)
quasipois(y ~ log(dose + 10) + dose,
data = salmonella)
quasipois(y ~ log(dose + 10) + dose,
data = salmonella, phi = 0.07180449)
summary(glm(y ~ log(dose + 10) + dose,
family = poisson, data = salmonella))
quasipois(y ~ log(dose + 10) + dose,
data = salmonella, phi = 0)
# with offset
data(cohorts)
i <- cohorts$age ; levels(i) <- 1:7
j <- cohorts$period ; levels(j) <- 1:7
i <- as.numeric(i); j <- as.numeric(j)
cohorts$cohort <- j + max(i) - i
cohorts$cohort <- as.factor(1850 + 5 * cohorts$cohort)
fm1 <- quasipois(y ~ age + period + cohort + offset(log(n)),
data = cohorts)
fm1
quasipois(y ~ age + cohort + offset(log(n)),
data = cohorts, phi = fm1@phi)
``` |

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