# homogeneity.test: Test of variance homogeneity of correlated variances In MVT: Estimation and Testing for the Multivariate t-Distribution

## Description

Performs several test for testing equality of p ≥ 2 correlated variables. Likelihood ratio test, score, Wald and gradient can be used as a test statistic.

## Usage

 `1` ```homogeneity.test(object, test = "LRT", type = "scale") ```

## Arguments

 `object` object of class `'studentFit'` representing the fitted model. `test` test statistic to be used. One of "LRT" (default), "Wald", "score" or "gradient". `type` one of `"scale"` (default) or `"both"` indicating the type of the hypothesis to test homogeneity of variances or variances and means, respectively.

## Value

A list of class 'homogeneity.test' with the following elements:

 `statistic` value of the statistic, i.e. the value of either Likelihood ratio test, Wald, score or gradient test. `parameter` the degrees of freedom for the test statistic, which is chi-square distributed. `p.value` the p-value for the test. `estimate` the estimated covariance matrix. `null.value` the hypothesized value for the covariance matrix. `method` a character string indicating what type of test was performed. `null.fit` a list representing the fitted model under the null hypothesis. `data` name of the data used in the test.

## References

Harris, P. (1985). Testing the variance homogeneity of correlated variables. Biometrika 72, 103-107.

Modarres, R. (1993). Testing the equality of dependent variables. Biometrical Journal 7, 785-790.

Osorio, F., and Galea, M. (2015). Statistical inference in multivariate analysis using the t-distribution. Unpublished manuscript.

## Examples

 ```1 2 3 4 5 6``` ```data(examScor) fit <- studentFit(examScor, family = Student(eta = .25)) fit z <- homogeneity.test(fit, test = "LRT") z ```

### Example output

```Call:
studentFit(x = examScor, family = Student(eta = 0.01841))
Converged in 97 iterations

Center:
mechanics    vectors    algebra   analysis statistics
39.2459    50.8419    50.7489    46.9611    42.2372

Scatter matrix estimate:
mechanics vectors   algebra   analysis  statistics
mechanics  301.46055
vectors    124.32688 171.39077
algebra    100.37281  84.71008 111.29784
analysis   106.76788  95.03320 110.48892 218.19315
statistics 116.68248  99.19755 120.82291 154.34480 297.81509

Number of Observations: 88

Likelihood ratio test for equality of variances

data: examScor
LRT statistic = 51.538, df = 4, p-value = 0
alternative hypothesis: true variances are not equal.

sample estimate:
mechanics vectors   algebra   analysis  statistics
mechanics  301.46055
vectors    124.32688 171.39077
algebra    100.37281  84.71008 111.29784
analysis   106.76788  95.03320 110.48892 218.19315
statistics 116.68248  99.19755 120.82291 154.34480 297.81509
```

MVT documentation built on May 1, 2019, 10:16 p.m.