SGButil {SGB}

Computation of scales and z-vectors

Description

bval computes the scale for each observed composition from the parameters and auxiliary variables for that observation.
zval computes the z-vector for each observed composition, i.e. the transform that is Dirichlet distributed under the SGB model for the observed composition.

Usage

bval(D, x, d, V)
zval(u, x, d, V)

Arguments

D

number of parts

x

vector of parameters (shape1,coefi,shape2) where shape1 is the overall shape, coefi is the vector of regression coefficients (see initpar.SGB) and shape2 the vector of D Dirichlet shape parameters

d

(n \times m) - data matrix of explanatory variables (variables corresponding to coefi); n: sample size, m: number of auxiliary variables

u

(n \times D) - data matrix of compositions (independent variables); D: number of parts

V

D \times (D-1) - matrix specifying the full rank transformation of log(parts) into log-ratios

Details

See Graf (2017), Equation (8), or the vignette "SGB regression", Equation (1).

Value

transformed composition of length D.

References

Graf, M. (2017). A distribution on the simplex of the Generalized Beta type. In J. A. Martin-Fernandez (Ed.), Proceedings CoDaWork 2017, University of Girona (Spain), 71-90.

Examples

## Example with 2 compositions
u <- matrix(c(0.2,0.4,0.5,0.5,0.3,0.2),nrow=2,byrow=TRUE)
u
D <- NCOL(u)  # number of parts

## auxiliary variable
d <- matrix(c(3.2,4.6),ncol=1)

## log-ratio transformation
V <- matrix(c(c(1,-1,0)/sqrt(2),c(1,1,-2)/sqrt(6)),ncol=2)

## vector of parameters:
shape1 <- 2.00
coefi <- c(-0.78,  0.06,  0.96, -0.11)
shape2 <- c(1.80,  3.10,  4.00) 
x <-c(shape1, coefi, shape2)
bval(D,x,d,V)
zval(u,x,d,V)