# waldTest: Wald Chi-Square Test In groupTesting: Simulating and Modeling Group (Pooled) Testing Data

## Description

This function implements the Wald chi-square test on a Kx1 parameter vector theta. The test assumes that thetaHat, a consistent estimator of theta such as MLE, is asymptotically normal with mean theta and covariance matrix Sigma. The function can implement 1 test on theta as well as multiple, Q, tests jointly on theta.

## Usage

 `1` ```waldTest(R, thetaHat, Sigma, r = 0, L = NULL) ```

## Arguments

 `R` A QxK matrix of known coefficients depending on how the test is to be carried out. `thetaHat` An estimate of theta. `Sigma` An estimated covariance matrix for `thetaHat`. `r` A Qx1 matrix of hypothesized values. `L` A character string to be used as a name of the test. When NULL, "L" will be used.

## Details

Suppose that Q tests are to be performed jointly on the K by 1 parameter vector theta. Let R be a QxK matrix of known coefficients such as 0, 1, and -1, and r be a Qx1 matrix of hypothesized values. The hypotheses are H0: Rθ = r vs. H1: Rθ != r. The test statistic has a chi-square distribution with Q degrees of freedom (Buse, 1982; Agresti, 2002).

## Value

A data.frame object of the Wald test results.

## References

Agresti A. (2002). Categorical Data Analysis (2nd ed.). Wiley. ISBN 0471360937.

Buse A. (1982). The Likelihood Ratio, Wald, and Lagrange Multiplier Tests: An Expository Note. The American Statistician, 36:153-157.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37``` ```## Example 1 # Parameter: p (proportion) MLE <- 0.42 Var <- 0.016 # (a) Test H0: p = 0.50 vs. H1: p != 0.50 R <- matrix(1, nrow=1, ncol=1) p0 <- 0.50 waldTest( R=R, thetaHat=MLE, r=p0, Sigma=Var ) ## Example 2 # Parameter: beta = (beta1, beta2), regression coefficients MLE <- c(1.09, 2.95) Cov <- rbind(c(0.21, -0.27), c(-0.27, 0.66)) # (a) Test H0: beta1 = beta2 vs. H1: beta1 != beta2 R <- rbind(c(1,-1)) waldTest( R=R, thetaHat=MLE, r=0, Sigma=Cov, L="1 vs 2" ) # (b) Test H0: beta1 = 0 vs. H1: beta1 != 0 R <- rbind(c(1,0)) waldTest( R=R, thetaHat=MLE, r=0, Sigma=Cov ) ## Example 3 # Parameter: beta = (beta0, beta1, beta2) MLE <- c(-3.05, 1.99, 0.93) Cov <- rbind(c( 0.045, -0.022, -0.034), c(-0.022, 0.032, 0.008), c(-0.034, 0.008, 0.048)) # Performing simultaneous test: # H0: beta0 = -3, H0: beta1 = 2, H0: beta2 = 1 # H1: beta0 != -3, H1: beta1 != 2, H1: beta2 != 1 R <- rbind(c(1,0,0), c(0,1,0), c(0,0,1)) r <- matrix( c(-3,2,1), nrow=3 ) waldTest( R=R, thetaHat=MLE, r=r, Sigma=Cov) ```

groupTesting documentation built on Nov. 22, 2021, 9:09 a.m.