saws: Small sample Adjustments for Wald-type tests using Sandwich...

In saws: Small-Sample Adjustments for Wald Tests Using Sandwich Estimators

Small sample Adjustments for Wald-type tests using Sandwich estimator of variance

Description

This function takes an object from a regression function and gives confidence intervals and p-values using the sandwich estimator of variance corrected for small samples.

Usage

saws(x,test = diag(p), beta0 = matrix(0, p, 1), 
    conf.level = 0.95, method = c("d3", "d5", "d1", "d2", "d4", "dm"),bound=.75)

Arguments

x	a list containing three elements: coefficients, u, omega (see details)
test	either a numeric vector giving elements of coefficient to test, or an r by p matrix of constants for testing (see details)
beta0	null parameters for testing (see details)
conf.level	level for confidence intervals
method	one of "d3", "d5", "d1", "d2", "d4", or "dm" (see details)
bound	bound for bias correction, denoted b in Fay and Graubard, 2001

Details

Typically, the x object is created in a specialized function. Currently there are three such functions, link{lmfitSaws},geeUOmega and clogistCalc. The function lmfitSaws is a simple linear model function that creates all the output needed. The function geeUOmega takes output from the gee function of the gee package and creates the 'u' matrix and the 'omega' array. The 'coefficients' is a vector with p parameter estimates, and is a standard output from the regression. The matrix 'u' is K by p with u[i,] the ith estimating equation, where there are K approximately independent estimating equations. The array 'omega' is K by p by p where omega[i,,] is a p by p matrix estimating - du/dbeta (here beta=coefficients). See Fay and Graubard (2001) for details.

Suppose that the coefficient vector from the regression is beta. Then we test r hypotheses, based on the the matrix product, TEST (beta-beta0)=0, where TEST is an r by p matrix. If the argument 'test' is an r by p matrix (where r is arbitrary), then TEST=test. If 'test' is a vector, then each element of test corresponds to testing that row of beta is 0, i.e., TEST<-diag(p)[test,], where p is the length of the coefficient vector. For example, test<-c(2,5), tests that beta[2]-beta0[2]=0 and that beta[5]-beta0[5]=0. The alternatives are always two-sided.

There are several methods available. They are all discussed in Fay and Graubard (2001). The naming of the methods follows that paper (see for example Table 1, where deltam corresponds to dm, etc.):

dm

the usual model based method which does not use the sandwich, uses a chi squared distribution

d1

the standard sandwich method which makes no corrections for small samples

d2

sandwich method, no bias correction, uses F distribution with df=dhat (see paper)

d3

(default method:sandwich method, no bias correction, uses F distribution with df=dtilde (see paper)

d4

sandwich method, with bias correction, uses F distribution with df=dhatH (see paper)

d5

sandwich method, with bias correction, uses F distribution with df=dtildeH (see paper)

Value

An object of class 'saws'. A list with elements:

originalCall	call from the original object
method	method used (see details)
test	test matrix (see details)
beta0	beta0 vector (see details)
coefficients	estimated coefficients
df	a vector of estimated degrees of freedom. This will have as many elements as there are coefficients
V	variance-covariance matrix
se	vector of standard errors of the coefficients
t.value	a vector of t-values: test (coef - beta0)/se
p.value	a vector of two-sided p-values
conf.int	p by 2 matrix of confidence intervals

Note

For versions prior to 0.9-7.0, when there was an offset in the formula, the results where incorrect. See the NEWS file.

Author(s)

M.P. Fay

References

Fay and Graubard (2001). Small-Sample Adjustments for Wald-Type Tests Using Sandwich Estimators. Biometrics 57: 1198-1206. (for copy see /inst/doc/ directory)

See Also

For examples, see geeUOmega and clogistCalc. See also print.saws

saws documentation built on June 24, 2022, 1:07 a.m.