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
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Arguments
formula 
An object of class 
data 
A data frame or matrix containing the model response variable
and covariates required by the 
na.action 
A function which indicates what should happen when the data contain 'NA's. The default is 'na.omit'. 
der 
Number which determines any inference process.
By default 
smooth 
Type smoother used: 
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, cross validation is used to obtain the bandwidth. 
h 
The kernel bandwidth smoothing parameter for the partial effects. 
nh 
Integer number of equallyspaced bandwidth on which the

kernel 
A character string specifying the desired kernel.
Defaults to 
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. 
cluster 
A logical value. If 
ncores 
An integer value specifying the number of cores to be used
in the parallelized procedure. If 
... 
Other options. 
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) = … = 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, …, 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 α}, where T^p is the empirical ppercentile of T under the null hypothesis. To obtain this percentile, we have used bootstrap techniques. See details in references.
Note that the models fitted by globaltest
function are specified
in a compact symbolic form. The \~ operator is basic in the formation
of such models. An expression of the form y ~ model
is interpreted as
a specification that the response y
is modelled by a predictor
specified symbolically by model
. The possible terms consist of a
variable name or a variable name and a factor name separated by : operator.
Such a term is interpreted as the interaction of the continuous variable and
the factor. However, if smooth = "splines"
, the formula is based on the function
formula.gam of the mgcv package.
Value
The T value and the pvalue are returned. Additionally, it is shown the decision, accepted or rejected, of the global test. The null hypothesis is rejected if the pvalue< 0.05.
Author(s)
Marta Sestelo, Nora M. Villanueva and Javier RocaPardinas.
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
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