getDerivativeDS: Partial Derivatives Computation of beta's.

In paularaissa/distStatsServer: Distributed Statistical Computing - Server Side Package

Description

Computes the matrix of second derivatives (Hessian) of the log'likelihood function H=XWX^T, and the equation X(y-P_i) that composes the formula to compute the estimated β's.

Usage

getDerivativeDS(formula, beta, family)

Arguments

formula	a string character to be transformed as an object of class formula.
beta	is a list of regression coefficients (estimated beta's).
family	a string character with the name of the error distribution and link function to be used in the analysis. If family is set to 'binomial', it defines the link function as logit and likelihood as binomial. If family is set to 'poisson', it defines the link function as log and likelihood as poisson.

Details

The Hessian (matrix of second derivatives) of the log-likelihood is

H = XWX^T

where W (computed by findW) is a diagonal matrix of the derivatives P_i (computed by findPi), and X is the matrix of observations (computed by getVarbyFormula). The solutions for δ is

δ_k = (XW_kX^T)^-1 X(y-P_i)

and for the partial derivatives computation, it was divided in two equations

W = (XW_kX^T)

Y = X(y-P_i)

where W is the current matrix of derivatives, y is the vector of observed responses and P_i is the vector of probabilities.

Value

A list with components:

xtxw	a data matrix, the Hessian matrix.
xtyp	a data matrix, the Y matrix that represents a partial computation of derivatives.

Dependencies

getVarbyFormula, findPi, findW

Author(s)

Paula R. Costa e Silva

paularaissa/distStatsServer documentation built on June 19, 2019, 12:43 a.m.