EqualityConstr: Equality constraints for overall shape and/or regression parameters and jacobian

Description

Setting of equality constraints on parameters.
heqa.SGB sets the overall shape parameter to shape1.
heqb.SGB sets specified regression parameters to 0.
heqab.SGB is a combination of both.
heqa.SGB.jac, heqb.SGB.jac, heqab.SGB.jac compute the corresponding Jacobians.

Usage

heqa.SGB(x, d, u, bound, shape1, ...)
heqa.SGB.jac(x, ...)
heqb.SGB(x, d, u, bound, shape1, index, ...)
heqb.SGB.jac(x, d, u, bound, shape1, index, ...)
heqab.SGB(x, d, u, bound, shape1, index, ...)
heqab.SGB.jac(x, d, u, bound, shape1, index, ...)

Value

heqa.SGB, heqb.SGB, heqab.SGB: vector of the same length as index specifying the current value of x[index] or x[1]-shape1, where x is the current vector of parameters. It should be near zero at convergence of the regression algorithm.

heqa.SGB.jac, heqb.SGB.jac, heqab.SGB.jac: the corresponding jacobian matrices of dimensions \(length(index) \times length(x)\).

Arguments

x: current 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 explanatory variables.
u: data matrix of compositions (independent variables) \((N \times D)\); \(D\): number of parts.
bound: not used.
shape1: chosen fixed value of the overall shape parameter.
Default shape1 = 1 for heqa.SGB and heqab.SGB.
shape1 is not fixed in heqb.SGB.
index: vector of length equal to the number of fixed parameters; specifies the indices of the fixed components in the vector of parameters x, such that for
heqa.SGB, heqa.SGB.jac: index=1. The fixed value of the overall shape parameter is shape1 (by default 1).
heqb.SGB, heqb.SGB.jac: index= c(...) with ... the indices of regression parameters to be set to 0.
heqab.SGB, heqab.SGB.jac: index=c(1,...); shape1 is the fixed value of the overall shape parameter, and ... the indices of the regression parameters to be set to 0.
...: not used.

Details

These functions are invoked by regSGB through the specification of the function name, shape1 and/or index.

Examples

Run this code

## parameter vector for a 3 parts composition with one explanatory variable (+ intercept):
x <- c(1,3.2,0.04,0.05,6,7:9)

## shape1 fixed to 1.5:
heqa.SGB(x,d,u,bound,1.5)
heqa.SGB.jac(x)

## Parameters 3 (first slope) and 4 (second intercept) fixed to 0:
heqb.SGB(x,d,u,bound,shape1,c(3,4))
heqb.SGB.jac(x,d,u,bound,shape1,c(3,4))

## Parameters 1, 3, 4 fixed to 1.5, 0, 0 respectively:
heqab.SGB(x,d,u,bound,1.5,c(1,3,4))
heqab.SGB.jac(x,d,u,bound,1.5,c(1,3,4))