diagL1 (version 1.0.0)

HV_test: Homogeneity of Variance Tests for Linear L1 Models

Description

Homogeneity of Variance Tests for Linear L1 Models

Usage

HV_test(y, x, groups, alpha = 0.05, tolerance = 0.001, max_iteration = 2000)

Value

A list with results from 3 homogeneity of variance tests

alpha

alpha argument.

asymptotic_critical_value

asymptotic alpha-based test critical value.

HV_LRT

LF1 statistic value using MLE (Maximum Likelihood Estimator).

HV_max_lambda_ratio

p-value of LF1 statistic using MLE.

HV_max_log_lambda_ratio

LF1 statistic value using ROS (Residuals Order Statistics).

number_of_groups

number of groups.

N

overall sample size.

lambda_heteroscedastic

heteroscedastic estimation of the scaling parameters.

lambda_homocedastic

homoscedastic estimation of the scale parameter.

Arguments

y

A vector with response variables.

x

A matrix with a single explanatory variable.

groups

Vector containing the group index to which the observation belongs.

alpha

Significance level of the test, must be between 0 and 1.

tolerance

threshold that determines when the iterative algorithm should stop (for regL1_het).

max_iteration

maximum number of iterations (for regL1_het).

Details

The 3 statistics to test homogeneity of variance are discussed in Rodrigues (2024), for more details see this reference. In practice, use the HV_LRT statistic results. If possible, use the HV_LRT statistic with a critical value obtained via bootstrap simulation.

References

Rodrigues, K. A. S. (2024). Analysis of the adjustment of the L1 regression model. Phd dissertation, University of São Paulo, BR.

Examples

# \donttest{
set.seed(123)
x1 = matrix(rnorm(20), ncol = 1)
y1 = x1 + rlaplace(20, 0, 1)
x2 = matrix(rnorm(20), ncol = 1)
y2 = x2 + rlaplace(20, 0, 1.5)
x3 = matrix(rnorm(20), ncol = 1)
y3 = x3 + rlaplace(20, 0, 2)
x4 = matrix(rnorm(20), ncol = 1)
y4 = x4 + rlaplace(20, 0, 2.5)
x5 = matrix(rnorm(20), ncol = 1)
y5 = x5 + rlaplace(20, 0, 3)

y = c(y1, y2, y3, y4, y5)
x = rbind(x1, x2, x3, x4, x5)
group_index = c(rep(1,20),rep(2,20),rep(3,20),rep(4,20),rep(5,20))

# Application of the homogeneity of variance test
test_result = HV_test(y, x, group_index)
test_result
# }