MarginPlots {SGB}

Histograms, quantile and probability plots for the z(u)-transforms of parts

Description

These functions draw a plot for each part in the dataset.

Usage

hzbeta(u, obj, weight = rep(1,dim(u)[1]) )
qzbeta(u, obj, weight = rep(1,dim(u)[1]) )
pzbeta(u, obj, weight = rep(1,dim(u)[1]) )

Arguments

u

data matrix of compositions (independent variables) $(N \times D)$; $D$: number of parts

obj

list, result of regSGB. See regSGB.

weight

vector of length $n$; positive observation weights, default rep(1,n).

Details

Let $U$ follow a $SGB(shape1,scale,shape2)$ distribution. Then the composition

$Z=C[(U/scale)^{shape1}]$

is called the $z(u)$-transform of $U$.
$Z$ follows a $Dirichlet(shape2)$ distribution and each part $Z_i, i=1,...,D$ is Beta-distributed with parameters (shape2[i],sum(shape2)-shape2[i]).
Goodness of fit plots are produced for the parts of the $z(u)$-transforms against the Beta distribution. Each function creates $D$ plots, where $D$ is the number of parts.
hzbeta: histograms and the corresponding Beta-densities,
qzbeta: marginal quantile plots,
pzbeta: marginal probability plots.
If weight is specified, weighted histgrams, quantile and probability plots are drawn.

Value

$D$ plots are produced comparing the marginal distribution of the parts of the $z(u)$ compositions with the theoretical Beta distribution.

Examples

## Arctic lake data
data(arc)
# Compositions
ua <- arc[,1:3]

# SGB regression
data(oilr)

# plot
par(mfrow=c(3,3))
hzbeta(ua,oilr)
qzbeta(ua,oilr)
pzbeta(ua,oilr)