Bootstrap based test for testing an allometric model

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Description

Bootstrap-based procedure that tests whether the data can be modelled by an allometric model.

Usage

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allotest(formula, data = data, na.action = "na.omit", nboot = 500,
  kbin = 200, seed = NULL)

Arguments

formula

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

data

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

na.action

A function which indicates what should happen when the data contain 'NA's. The default is 'na.omit'.

nboot

Number of bootstrap repeats.

kbin

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

seed

Seed to be used in the bootstrap procedure.

Details

In order to facilitate the choice of a model appropriate to the data while at the same time endeavouring to minimise the loss of information, a bootstrap-based procedure, that test whether the data can be modelled by an allometric model, was developed. Therefore, allotest tests the null hypothesis of an allometric model taking into account the logarithm of the original variable (X^* = log(X) and Y^* = log(Y)).

Based on a general model of the type

Y^*=m(X^*)+\varepsilon

the aim here is to test the null hypothesis of an allometric model

H_0 = m(x^*) = a^*+ b^* x^*

vs. the general hypothesis H_1, with m being an unknown nonparametric function; or analogously,

H_1: m(x^*)= a^*+ b^* x^* + g(x^*)

with g(x^*) being an unknown function not equal to zero.

To implement this test we have used the wild bootstrap.

Value

An object is returned with the following elements:

statistic

the value of the test statistic.

value

the p-value of the test.

Author(s)

Marta Sestelo, Nora M. Villanueva and Javier Roca-Pardinas.

References

Sestelo, M. and Roca-Pardinas, J. (2011). A new approach to estimation of length-weight relationship of Pollicipes pollicipes (Gmelin, 1789) on the Atlantic coast of Galicia (Northwest Spain): some aspects of its biology and management. Journal of Shellfish Research, 30 (3), 939–948.

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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library(npregfast)
data(barnacle)
allotest(DW ~ RC, data = barnacle, nboot = 50, seed = 130853)