summary.cozigam {COZIGAM}R Documentation

Summary for a COZIGAM fit

Description

Takes a fitted cozigam object produced by cozigam() and produces various useful summaries from it.

Usage

## S3 method for class 'cozigam':
summary(object, dispersion = NULL, ...)

## S3 method for class 'summary.cozigam':
print(x,digits = max(3, getOption("digits") - 3),
                  signif.stars = getOption("show.signif.stars"), ...)

Arguments

object a fitted cozigam object as produced by cozigam().
dispersion a known dispersion parameter. NULL to use estimate or default (e.g. 1 for Poisson).
x a summary.cozigam object produced by summary.cozigam().
digits the number of significant digits to use when printing.
signif.stars logical. If TRUE, ``significance stars" are printed for each coefficient.
... other arguments.

Details

print.summary.cozigam tries to be smart about formatting the coefficients, standard errors, etc. and additionally gives ``significance stars" if signif.stars is TRUE.

Value

summary.cozigam produces a list of summary information for a fitted cozigam object.

p.coeff an array of estimates of the strictly parametric model coefficients, including the linear constraints parameters.
p.t an array of the p.coeff's divided by their standard errors.
p.pv an array of p-values for the null hypothesis that the corresponding parameter is zero. Calculated with reference to the t distribution with the estimated residual degrees of freedom for the model fit if the dispersion parameter has been estimated, and the standard normal if not.
m the number of smooth terms in the model.
chi.sq an array of test statistics for assessing the significance of model smooth terms. If b_i is the parameter vector for the ith smooth term, and this term has estimated covariance matrix V_i then the statistic is b_i'V_i^{k-}b_i, where V_i^{k-} is the rank k pseudo-inverse of V_i, and k is estimated rank of V_i.
s.pv an array of approximate p-values for the null hypotheses that each smooth term is zero. Be warned, these are only approximate. In the case of known dispersion parameter, they are obtained by comparing the chi.sq statistic given above to the chi-squared distribution with k degrees of freedom, where k is the estimated rank of V_i. If the dispersion parameter is unknown (in which case it will have been estimated) the statistic is compared to an F distribution with k upper d.f. and lower d.f. given by the residual degrees of freedom for the model.Typically the p-values will be somewhat too low, because they are conditional on the smoothing parameters, which are usually uncertain, but note that the statistic can also have low power if the rank, k, is too high relative to the EDF of the term.
se array of standard error estimates for all parameter estimates.
edf array of estimated degrees of freedom for the model terms.
residual.df estimated residual degrees of freedom.
n number of data.
family the family used.
formula the original GAM formula.
dispersion estimated (or given) scale parameter.
cov.unscaled the estimated covariance matrix of the parameters, divided by scale parameter.
cov.scaled the estimated covariance matrix of the parameters.
p.table significance table for parameters.
s.table significance table for smooths.

Author(s)

Hai Liu and Kung-Sik Chan

See Also

cozigam, predict.cozigam

Examples

set.seed(1)
n <- 600
x1 <- runif(n, 0, 1)
x2 <- runif(n, 0, 1)
x3 <- runif(n, 0, 1)

f <- test(x1, x2)*2 + f0(x3)/5
eta0 <- f/1.1
mu0 <- exp(eta0)  

eta.p10 <- (test(x1,x2) - mean(test(x1,x2)))*2/1.1
eta.p20 <- (f0(x3) - mean(f0(x3)))/5/1.1

alpha0 <- 0.5
delta10 <- 1
delta20 <- 0
eta.p0 <- delta10*eta.p10 + delta20*eta.p20 
p0 <- .Call("logit_linkinv", alpha0 + eta.p0, PACKAGE = "stats")

z <- rbinom(rep(1,n), 1, p0)
y <- rpois(rep(1,n), mu0)
y[z==0] <- 0; rm(z)

res <- cozigam(y~s(x1,x2)+s(x3), constraint="component", zero.delta=c(NA, 0), family=poisson)
summary(res)


[Package COZIGAM version 2.0-1 Index]