npregfast (version 1.2.0)

globaltest: Testing the equality of the M curves specific to each level

Description

This function can be used to test the equality of the $M$ curves specific to each level.

Usage

globaltest(formula, data = data, der, weights = NULL, nboot = 500,
  h0 = -1, h = -1, nh = 30, kernel = "epanech", p = 3, kbin = 100,
  seed = NULL)

Arguments

formula

An object of class formula: a sympbolic description of the model to be fitted.

data

A data frame or matrix containing the model response variable and covariates required by the formula.

der

Number which determines any inference process. By default der is NULL. If this term is 0, the testing procedures is applied for the estimate. If it is 1 or 2, it is designed for the first

weights

Prior weights on the data.

nboot

Number of bootstrap repeats.

h0

The kernel bandwidth smoothing parameter for the global effect (see references for more details at the estimation). Large values of the bandwidth lead to smoothed estimates; smaller values of the bandwidth lead lo undersmoothed estimates. By default, cro

h

The kernel bandwidth smoothing parameter for the partial effects.

nh

Integer number of equally-spaced bandwidth on which the h is discretised, to speed up computation.

kernel

A character string specifying the desired kernel. Defaults to kernel = "epanech", where the Epanechnikov density function kernel will be used. Also, several types of kernel funcitons can be used: triangular and Gaussian density function,

p

Degree of polynomial to be used. Its value must be the value of derivative + 1. The default value is 3 due to the function returns the estimation, first and second derivative.

kbin

Number of binning nodes over which the function is to be estimated.

seed

Seed to be used in the bootstrap procedure.

Value

• The $T$ value and the $p$-value are returned. Additionally, it is shown the decision, accepted or rejected, of the global test. The null hypothesis is rejected if the $p$-value$< 0.05$.

Details

globaltest can be used to test the equality of the $M$ curves specific to each level. This bootstrap based test assumes the following null hypothesis:

$$H_0^r: m_1^r(\cdot) = \ldots = m_M^r(\cdot)$$

versus the general alternative

$$H_1^r: m_i^r (\cdot) \ne m_j^r (\cdot) \quad \rm{for} \quad \rm{some} \quad \emph{i}, \emph{j} \in { 1, \ldots, M}.$$

Note that, if $H_0$ is not rejected, then the equality of critical points will also accepted.

To test the null hypothesis, it is used a test statistic, $T$, based on direct nonparametric estimates of the curves.

If the null hypothesis is true, the $T$ value should be close to zero but is generally greater. The test rule based on $T$ consists of rejecting the null hypothesis if $T > T^{1- \alpha}$, where $T^p$ is the empirical $p$-percentile of $T$ under the null hypothesis. To obtain this percentile, we have used bootstrap techniques. See details in references.

References

Sestelo, M. (2013). Development and computational implementation of estimation and inference methods in flexible regression models. Applications in Biology, Engineering and Environment. PhD Thesis, Department of Statistics and O.R. University of Vigo.

Examples

library(npregfast)
data(barnacle)
globaltest(DW ~ RC : F, data = barnacle, der = 1, seed = 130853, nboot = 100)