diagL1 (version 1.0.0)

LF_test: Lack of Fit Tests for Linear L1 Models

Description

Lack of Fit Tests for Linear L1 Models

Usage

LF_test(y, x, groups, alpha = 0.05)

Value

A list with results from 3 lack of fit tests

alpha

alpha argument.

critical_value

alpha-based test critical value.

LF1_MLE

LF1 statistic value using MLE (Maximum Likelihood Estimator).

LF1_MLE

p-value of LF1 statistic using MLE.

LF1_ROS

LF1 statistic value using ROS (Residuals Order Statistics).

LF2

LF2 statistic value.

modelo_H0

model fitted under H0.

modelo_Ha

model fitted under Ha.

MLE

estimation of the scale parameter of the estimator model via MLE.

ROS

estimation of the scale parameter of the estimator model via ROS.

SAE_H0

SAE (Sum of Absolute Errors) of the adjusted model under H0.

SAE_Ha

SAE (Sum of Absolute Errors) of the adjusted model under Ha.

matrix_mean_x

average of the explanatory variable per group of observations.

number_of_groups

number of groups.

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.

Details

The 3 statistics to test lack of fit are discussed in Rodrigues (2024), for more details see this reference. In practice, use the LF1_MLE statistic results. These tests were developed with just one explanatory variable in mind, which is why we include an error if there is more than one explanatory variable.

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, 5)
x2 = matrix(rnorm(20), ncol = 1)
y2 = x2 + rlaplace(20, 1, 5)
x3 = matrix(rnorm(20), ncol = 1)
y3 = x3 + rlaplace(20, 2, 5)
x4 = matrix(rnorm(20), ncol = 1)
y4 = x4 + rlaplace(20, 3, 5)
x5 = matrix(rnorm(20), ncol = 1)
y5 = x5 + rlaplace(20, 4, 5)

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 lack of fit test
test_result = LF_test(y, x, group_index)
test_result
# }