# testcoef.pois.env: Hypothesis test of the coefficients of the envelope model In Renvlp: Computing Envelope Estimators

 testcoef.pois.env R Documentation

## Hypothesis test of the coefficients of the envelope model

### Description

This function tests the null hypothesis L * beta = A versus the alternative hypothesis L * beta ~= A, where beta is estimated under the envelope model in poisson regression.

### Usage

```testcoef.pois.env(m, L, A)
```

### Arguments

 `m` A list containing estimators and other statistics inherited from pois.env. `L` The matrix multiplied to beta on the left. It is a d1 by p matrix, while d1 is less than or equal to p. `A` The matrix on the right hand side of the equation. It is a d1 by 1 matrix.

Note that inputs `L` and `A` must be matrices, if not, use `as.matrix` to convert them.

### Details

This function tests for hypothesis H0: L beta = A, versus Ha: L beta != A. The beta is estimated by the envelope model in predictor space. If L = Ip and A = 0, then the test is equivalent to the standard F test on if beta = 0. The test statistic used is vec(L beta - A) hatSigma^-1 vec(L beta - A)^T, where beta is the envelope estimator and hatSigma is the estimated asymptotic covariance of vec(L beta - A). The reference distribution is chi-squared distribution with degrees of freedom d1.

### Value

The output is a list that contains following components.

 `chisqStatistic` The test statistic. `dof` The degrees of freedom of the reference chi-squared distribution. `pValue` p-value of the test. `covMatrix` The covariance matrix of vec(L beta).

### Examples

```data(horseshoecrab)
X1 <- as.numeric(horseshoecrab[ , 1] == 2)
X2 <- as.numeric(horseshoecrab[ , 1] == 3)
X3 <- as.numeric(horseshoecrab[ , 1] == 4)
X4 <- as.numeric(horseshoecrab[ , 2] == 2)
X5 <- as.numeric(horseshoecrab[ , 2] == 3)
X6 <- horseshoecrab[ , 3]
X7 <- horseshoecrab[ , 5]
X <- cbind(X1, X2, X3, X4, X5, X6, X7)
Y <- horseshoecrab[ , 4]

m <- pois.env(X, Y, 1)

L <- diag(7)
A <- matrix(0, 7, 1)

test.res <- testcoef.pois.env(m, L, A)
test.res
```

Renvlp documentation built on Aug. 8, 2022, 1:06 a.m.