SLRMss {SLRMss}R Documentation

Symmetric Linear Regression Models for small samples

Description

Computes Wald, Likelihood Ratio, Score, or Gradient statistics for symmetric linear regression models. Also computes modified versions of the Likelihood Ratio, Score, and Gradient tests for small sample sizes.

Usage

SLRMss(formula, family, xi, statistic, testingbeta, data)

Arguments

formula

An object of class formula (or one that can be coerced to that class): a symbolic description of the model to be fitted.

family

A description of the error distribution to be used in the model. There are four supported families, Normal, t-Student, Power Exponential and Logistic ("Normal", "Student", "Powerexp" and "Logistic", respectively)

xi

An extra parameter of some specified error distribution. For t-Student is a positive value and for Power Exponential is a real number between -1 and 1/3.

statistic

The statistic which will be used. It includes "Wald", "LR", "Score" or "Gradient".

testingbeta

A vector containing the names of the variables to be testing.

data

An optional data frame containing the variables in the model.

Value

A list with the following components

beta.coefficients

A matrix with the estimated position parameters under alternative hypothesis.

phi

A numeric value with the estimated precision paramater under alternative hypothesis.

beta.coefficients.h0

A matrix with the estimated position parameters under null hypothesis.

phi.h0

A numeric value with the estimated precision paramater under null hypothesis.

y.fitted

A vector with the fitted values of the model.

null.hypothesis

The description of the null hypothesis.

statistics

A matrix with the selected statistics and theirs p-values. The corrected statistic is marked with an asterisk.

statistic.distribution

The name of the statistics' distribution used to test null hypothesis. It always return "Chi-Squared".

df

The degrees of freedom of the statistics' distribution. It's the length of the testingbeta vector.

residuals

The difference among the real y values and the fitted y.

std.residuals

The residuals divided by the precision parameter

AICc

The corrected Akaike Information Criterion for small samples.

BIC

The Bayesian Information Criterion.

References

Medeiros, F. M. C and Ferrari, S. L. P. (2017). Small-sample testing inference in symmetric and log-symmetric linear regression models, Statistica Neerlandica. doi:10.1111/stan.12107.

Examples

data(orange)
fit1 <- SLRMss(emulsion ~ arabicgum + xanthangum + orangeoil, family="Student", 
xi=3, testingbeta="xanthangum", statistic="LR", data=orange)
print(fit1)

data(cheese)
fit2 <- SLRMss(cohe ~ fat + xangum + sodcase, family="Normal", 
testingbeta=c("xangum","sodcase"), statistic="Gradient", data=cheese)
print(fit2)

[Package SLRMss version 1.0.0 Index]