SGB (version 1.0.1.1)

InequalityConstr: Inequality constraints and jacobian

Description

Setting of inequality constraints on shape parameters.
hin.SGB sets inequality constraints on the shape parameters in a SGB regression.
hin.SGB.jac defines the corresponding Jacobian.

Usage

hin.SGB(x, d, u, bound, ...)
hin.SGB.jac(x, d, u, ...)

Value

hin.SGB : vector of length \(D+1\) with the current value of c(shape1-0.1,shape1*shape2-bound). It should be non-negative at convergence of the regression algorithm.

hin.SGB.jac : corresponding jacobian matrix of dimensions \((D+1) \times\)

length(x).

Arguments

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

data matrix of explanatory variables (without constant vector) \((N \times m)\); \(N\): sample size, \(m\): number of auxiliary variables.

u

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

bound

the estimates of shapes are constrained by shape1*shape2[i] > bound, i=1,...,D. By default bound = 2.1.

...

not used.

Details

These functions are invoked internally by regSGB with bound specified by the user.
shape1 is constrained to be larger than 0.1, in order to avoid numerical problems and shape2 must be positive.
Moments of ratios of parts only exist up to bound. Thus bound = 2.1 guarantees the existence of variances of ratios of parts.

Examples

## Parameter vector for a 3 parts composition with one explanatory variable (+ intercept):
x <- c(1,3.2,0.04,0.05,6,7:9)
bound <- 2.1
u <- t(c(0.1,0.5,0.4))  # only used to compute the number of parts.
hin.SGB(x, d, u, bound)
# = c(shape1-0.1, shape1*shape2-bound,shape2)
# all must be positive.