stepSGB: Stepwise backward elimination for SGB regression
In SGB: Simplicial Generalized Beta Regression

Description Usage Arguments Details Value References See Also Examples

Stepwise elimination of the non significant regression parameters. Possibility to assign a fixed value shape1 to the overall shape parameter.

stepSGB(obj0, d, u,  weight = rep(1, dim(d)[1]), shape10 = obj0[["par"]][1],
  bound = 2.1, shape1 = NULL, Mean2 = TRUE, maxiter = 10, 
  control.optim = list(fnscale = -1), 
  control.outer = list(itmax = 1000, ilack.max = 200, trace = TRUE,
   kkt2.check = TRUE, method = "BFGS") )

`obj0`	object of class regSGB, see `regSGB`.
`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.
`weight`	vector of length n; positive observation weights, default `rep(1,n)`. Should be scaled to sum to n.
`shape10`	positive number, initial value of the overall shape parameter, default obj0[["par"]][1].
`bound`	inequality constraints on the estimates of shapes: `shape1*shape2[i] > bound, i=1,...,D.` By default `bound = 2.1`, see `InequalityConstr`.
`shape1`	fixed value of the overall shape parameter. Default is NULL (no fixed value).
`Mean2`	logical, if TRUE (default), the initial shape2 parameters are each replaced by their average. See `initpar.SGB`.
`maxiter`	maximum number of iterations, i.e. attempts to set a parameter to 0.
`control.optim`	list of control parameters for optim, see `optim`. Default is from `auglag`, except `list(fnscale = -1)`. Always specify `fnscale = -1`.
`control.outer`	list of control parameters to be used by the outer loop in constrOptim.nl, see `auglag`. Default is from `auglag`, except `list(itmax = 1000, ilack.max = 200)`.

This is an experimental procedure for searching a set of non-significant parameters that will be set to zero. The shape parameters are excluded from the elimination procedure. The algorithm starts with obj0, output of regSGB. The p-values for the regression parameters in summary(obj0) are taken in decreasing order. The parameter with the largest p-value is set to zero and regSGB computes the regression with this constraint. If the AIC value is smaller than the AIC in obj0, the parameter with the next largest p-value in obj0 is set to zero and the regression with the two constraints is computed. The process iterates until either a larger AIC is found or maxiter is attained.
The initial value of the overall shape parameter is set to the estimated value in the full model obj0. The other initial values are computed as in regSGB.
There is the possibility to fix the value of the overvall shape parameter, if shape1 is given a positive number a_0 (default NULL, no fixed value).
If regSGB was called without Formula, the data-frame with auxiliary variables for stepSGB follows the same rules as for the initial regSGB object, see Example 1 in regSGB.

A list of class 'stepSGB' with the following 5 components:

reg

A list with the following components:
full Object of class regSGB, same as obj0, see regSGB.
iter1 Object of class regSGB obtained at iteration 1.
...
iterk Object of class regSGB obtained at iteration k.

`Formula`	The original formula, or NULL
`iter`	Value of k, the last iteration.
`tab`	Data frame with `k+1` columns, overall results and `k` iterations. The rows are `value` Log-likelihood `n.par` Total number of parameters (including the shape2 param.) `n.par.fixed` Number of fixed parameters. `AIC` Value of the AIC criterion. `convergence` 0 if converged. `kkt1` 1 if first Karush-Kuhn-Tucker criterion fulfilled, zero otherwise. `kkt2` 1 if second Karush-Kuhn-Tucker criterion fulfilled, zero otherwise. `counts.function` Number of times the objective function (the log-likelihood) was evaluated. `counts.gradient` Number of times the gradient was evaluated. \
`call`	Arguments for calling `stepSGB`.

vignette("SGB regression", package = "SGB")

regSGB, initpar.SGB, auglag.

data(carseg)
## Extract the compositions
uc <- as.matrix(carseg[,(1:5)])
## Initial regression
data(ocar)

step_ocar <- stepSGB(ocar, carseg, uc, bound=2.1, control.outer=list(trace=FALSE))

summary(step_ocar[["reg"]][["full"]])
summary(step_ocar[["reg"]][["iter4"]])
step_ocar[["tab"]]