VGAM (version 0.7-5)

VGAM-package: Vector Generalized Linear and Additive Models

Description

VGAM provides functions for fitting vector generalized linear and additive models (VGLMs and VGAMs), and associated models (Reduced-Rank VGLMs, Quadratic RR-VGLMs, Reduced-Rank VGAMs). This package fits many models and distributions by maximum likelihood estimation (MLE) or penalized MLE. Also fits constrained ordination models in ecology such as constrained quadratic ordination (CQO).

Details

This package centers on the iteratively reweighted least squares (IRLS) algorithm. Other key words include Fisher scoring, additive models, penalized likelihood, reduced-rank regression and constrained ordination. The central modelling functions are vglm, vgam, rrvglm, cqo, cao. For detailed control of fitting, each of these has its own control function, e.g., vglm.control. The package uses S4 (see methods-package).

The classes of GLMs and GAMs are special cases of VGLMs and VGAMs. The VGLM/VGAM framework is intended to be very general so that it encompasses as many distributions and models as possible. VGLMs are limited only by the assumption that the regression coefficients enter through a set of linear predictors. The VGLM class is very large and encompasses a wide range of multivariate response types and models, e.g., it includes univariate and multivariate distributions, categorical data analysis, time series, survival analysis, generalized estimating equations, extreme values, correlated binary data, bioassay data and nonlinear least-squares problems.

VGAMs are to VGLMs what GAMs are to GLMs. Vector smoothing (see vsmooth.spline) allows several additive predictors to be estimated as a sum of smooth functions of the covariates.

For a complete list of this package, use library(help="VGAM"). New VGAM family functions are continually being written and added to the package. A monograph about VGLM and VGAMs etc. is in the making but unfortunately won't be finished for a while.

References

Yee, T. W. and Hastie, T. J. (2003) Reduced-rank vector generalized linear models. Statistical Modelling, 3, 15--41.

Yee, T. W. and Stephenson, A. G. (2007) Vector generalized linear and additive extreme value models. Extremes, 10, 1--19.

Yee, T. W. and Wild, C. J. (1996) Vector generalized additive models. Journal of the Royal Statistical Society, Series B, Methodological, 58, 481--493.

Yee, T. W. (2004) A new technique for maximum-likelihood canonical Gaussian ordination. Ecological Monographs, 74, 685--701.

Yee, T. W. (2006) Constrained additive ordination. Ecology, 87, 203--213.

Documentation accompanying the VGAM package at http://www.stat.auckland.ac.nz/~yee/VGAM contains further information and examples.

See Also

TypicalVGAMfamilyFunction, CommonVGAMffArguments.

Examples

# Example 1
# Fit the proportional odds model, p.179, in McCullagh and Nelder (1989)
data(pneumo)
pneumo = transform(pneumo, let=log(exposure.time))
(fit = vglm(cbind(normal, mild, severe) ~ let,
            cumulative(parallel=TRUE, reverse=TRUE), pneumo))
fit@y   # Sample proportions
weights(fit, type="prior")   # Number of observations
coef(fit, matrix=TRUE)
constraints(fit)   # Constraint matrices


# Example 2
# Zero-inflated Poisson model
x = runif(n <- 2000)
phi = logit(-0.5 + 1*x, inverse=TRUE)
lambda = loge(0.5 + 2*x, inverse=TRUE)
y = rzipois(n, lambda, phi)
table(y)
fit = vglm(y ~ x, zipoisson, trace=TRUE)
coef(fit, matrix=TRUE)  # These should agree with the above values


# Example 3
# Fit a two species GAM simultaneously
data(hunua)
fit2 = vgam(cbind(agaaus, kniexc) ~ s(altitude, df=c(2,3)),
            binomialff(mv=TRUE), hunua)
coef(fit2, mat=TRUE)   # Not really interpretable
plot(fit2, se=TRUE, overlay=TRUE, lcol=1:2, scol=1:2)
attach(hunua)
o = order(altitude)
matplot(altitude[o], fitted(fit2)[o,], type="l", lwd=2, las=1,
    xlab="Altitude (m)", ylab="Probability of presence",
    main="Two plant species' response curves", ylim=c(0,.8))
rug(altitude)
detach(hunua)


# Example 4
# LMS quantile regression
data(bminz)
fit = vgam(BMI ~ s(age, df=c(4,2)), fam=lms.bcn(zero=1), data=bminz, tr=TRUE)
predict(fit)[1:3,]
fitted(fit)[1:3,]
bminz[1:3,]
# Person 1 is near the lower quartile of BMI amongst people his age
cdf(fit)[1:3]

# Quantile plot
par(mfrow=c(1,1), bty="l", mar=c(5,4,4,3)+0.1, xpd=TRUE)
qtplot(fit, percentiles=c(5,50,90,99), main="Quantiles",
       xlim=c(15,90), las=1, ylab="BMI", lwd=2, lcol=4)

# Density plot
ygrid = seq(15, 43, len=100)  # BMI ranges
par(mfrow=c(1,1), lwd=2)
a = deplot(fit, x0=20, y=ygrid, xlab="BMI", col="black",
    main="Density functions at Age = 20 (black), 42 (red) and 55 (blue)")
a
a = deplot(fit, x0=42, y=ygrid, add=TRUE, llty=2, col="red")
a = deplot(fit, x0=55, y=ygrid, add=TRUE, llty=4, col="blue", Attach=TRUE)
a@post$deplot  # Contains density function values


# Example 5
# GEV distribution for extremes
data(oxtemp)
(fit = vglm(maxtemp ~ 1, egev, data=oxtemp, trace=TRUE))
fitted(fit)[1:3,]
coef(fit, mat=TRUE)
Coef(fit)
vcov(fit)
vcov(fit, untransform=TRUE)
sqrt(diag(vcov(fit)))   # Approximate standard errors
rlplot(fit)