# EqualityConstr: Equality constraints for overall shape and/or regression... In SGB: Simplicial Generalized Beta Regression

## 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

 1 2 3 4 5 6 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, ...) 

## 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.

## 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).

regSGB, summary.regSGB
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 ## 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))