Bootstrap-based procedure that tests whether the data can be modelled by an allometric model.
Usage
allotest(
formula,
data,
na.action = "na.omit",
nboot = 500,
seed = NULL,
cluster = TRUE,
ncores = NULL,
test = "res",
...
)Arguments
- formula
An object of class
formula: a sympbolic description of the model to be fitted.- data
An optional data frame, matrix or list required by the formula. If not found in data, the variables are taken from
environment(formula), typically the environment from whichallotestis called.- 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.
- seed
Seed to be used in the bootstrap procedure.
- cluster
A logical value. If
TRUE(default), the bootstrap procedure is parallelized (only forsmooth = "splines"). Note that there are cases (e.g., a low number of bootstrap repetitions) that R will gain in performance through serial computation. R takes time to distribute tasks across the processors also it will need time for binding them all together later on. Therefore, if the time for distributing and gathering pieces together is greater than the time need for single-thread computing, it does not worth parallelize.- ncores
An integer value specifying the number of cores to be used in the parallelized procedure. If
NULL(default), the number of cores to be used is equal to the number of cores of the machine - 1.- test
Statistic test to be used, based on residuals on the null model (
res) or based on the likelihood ratio test using rss0 and rss1lrt.- ...
Other options.
Value
An object is returned with the following elements:
- statistic
the value of the test statistic.
- value
the p-value of the test.
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.
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.