Compute the Chi-square approximations to a weighted sum of Chi-square(1) random variables.

Returns an approximate quantile for a weighted sum of independent \(\chi^2(1)\) random variables.

dr.pvalue(coef,f,chi2approx=c("bx","wood"),...)

bentlerxie.pvalue(coef, f)

wood.pvalue(coef, f, tol=0.0, print=FALSE)

Arguments

coef

a vector of nonnegative weights

f

Observed value of the statistic

chi2approx

Which approximation should be used?

tol

tolerance for Wood's method.

print

Printed output for Wood's method

...

Arguments passed from dr.pvalue to wood.pvalue.

Details

For Bentler-Xie, we approximate \(f\) by \(c \chi^2(d)\) for values of \(c\) and \(d\) computed by the function. The Wood approximation is more complicated.

Value

Returns a data.frame with four named components:

test

The input argument f.

test.adj

For Bentler-Xie, returns \(cf\); for Wood, returns NA.

df.adj

For Bentler-Xie, returns \(d\); for Wood, returns NA.

pval.adj

Approximate p.value.

References

Peter M. Bentler and Jun Xie (2000), Corrections to test statistics in principal Hessian directions. Statistics and Probability Letters, 47, 381-389.

Wood, Andrew T. A. (1989) An \(F\) approximation to the distribution of a linear combination of chi-squared variables. Communications in Statistics: Simulation and Computation, 18, 1439-1456.

Author

Sanford Weisberg <sandy@stat.umn.edu>