logpoisson {glmmAK}R Documentation

Poisson log-linear regression model

Description

Fits the poisson log-linear regression model using the maximum-likelihood. The log-likelihood is maximized using the Newton-Raphson algorithm (the same as Fisher scoring in this case). The function returns the inverse of the observed and expected information matrix.

Usage

logpoisson(y, x, offset=0, epsilon=1e-08, maxit=25, trace=FALSE)

## S3 method for class 'logpoisson':
print(x, ...)

## S3 method for class 'logpoisson':
summary(object, ...)

Arguments

y response vector taking integer values or zero.
x matrix or data.frame with covarites.
Intercept is included by default in the model and should not be included in x.
offset possible offset term. It is assumed to be equal to zero if not specified.
epsilon positive convergence tolerance epsilon. The iterations converge when

abs((l[new] - l[old])/l[new]) <= epsilon,

where l denotes the value of the log-likelihood.

maxit integer giving the maximal number of iterations.
trace logical indicating if output should be produced for each iteration.
object an object of class "logpoisson".
... other arguments passed to print or summary.

Value

An object of class "logpoisson". This has components

coefficients the coefficients of the linear predictor.
loglik the value of the log-likelihood.
score the score vector.
vcov the inverse of the information matrix.
linear.predictors the values of the linear predictor for each observation.
fitted.values the values of fitted counts for each observation.
converged logical indicating whether the optimization routine converged.
iter number of iterations performed
y
x

Author(s)

Arnošt Komárek arnost.komarek[AT]mff.cuni.cz

References

Agresti, A. (2002). Categorical Data Analysis. Second edition. Hoboken: John Wiley & Sons. Section 7.2.

See Also

glm.

Examples

set.seed(1977)
n <- 100
x1 <- rbinom(n, 1, 0.4)
x2 <- runif(n, 0, 1)
eta <- 5 + 0.1*x1 -0.2*x2
mu <-  exp(eta)
y <- rpois(n, mu)

### Fit the model using poisson
Xmat <- data.frame(x1=x1, x2=x2)
fit <- logpoisson(y=y, x=Xmat)
summary(fit)

### Fit the model using standard glm
fit0 <- glm(y~x1+x2, family=poisson(link="log"))
summary(fit0)

[Package glmmAK version 1.2 Index]