This function allows to select the optimal dimension number
for correspondence biplot, given the set of possible dimension combination
of the original data. It determines the models that are located on the boundary of the convex hull
and selects an optimal model by means of the scree test values (st).
For exploring, it is also possible to check the optimal model dimension by using
boostrap samples which have the same marginal proportions and the total number
of the original table. When the input parameter boots = T, it does bootstrap sampling.
There are three kinds of possible bootstrap sampling.
When boottype = "bootnp" it performs a non parametric bootstrap sampling.
When boottype = "bootpsimple" it performs a parametric simple bootstrap sampling.
When boottype = "bootpstrat", it performs a parametric stratified bootstrap sampling.
In particular in case of parametric bootstrap types,
when resamptype=1 it considers a multinomial distribution, and when resamptype = 2
it considers a poisson distribution.
tunelocal(Xdata, ca3type = "CA3", resp = "row", norder = 3, digits = 3, boots = FALSE,
nboots = 0, boottype= "bootpsimple", resamptype = 1, PercentageFit = 0.01)
Chi-square criterion and df of models on the convex hull.
It gives the criterion values of the models that are located on the boundary of the convex hull
and selects the optimal model by means of the scree test values (st).
When using boots = FALSE, it gives the set of possible dimension combination
of the original data using only the original data array.
When using boots = TRUE, it gives the set of possible dimension combination
of the original data using bootstrapped data arrays.
The three-way data. It can be a R object array or raw data (n individuals by three categorical variables, for an example,
see museum data).
When a three-way non-symmetrical variant is performed, by default, the response variable is the row variable when an array is given, or
the first of three columns when a raw data set is given.
For changing, consider the parameter resp = "col" or resp = "tube".
The specification of the analysis to be performed.
If ca3type = "CA3", then a three-way (symmetrical) correspondence analysis will be performed
(default analysis).
If ca3type = "NSCA3", then three-way non-symmetrical correspondence analysis will be performed.
If ca3type = "OCA3", then ordered three-way symmetrical correspondence analysis will be performed.
If ca3type = "ONSCA3", then ordered three-way non-symmetrical correspondence analysis will be performed.
The input parameter for specifying in non-symmetrical three-way correspondence analysis variants (ca3type = "NSCA3"
and ca3type = "ONSCA3") what is the response variable (logically antecendent to the others).
By default resp = "row", but it could be the column variable resp = "col" or the tube
variable resp = "tube".
The input parameter for specifying the number of ordered variable when ca3type = "OCA3" or ca3type = "ONSCA3".
The input parameter specifying the digital number. By default, digits = 3.
The flag parameter to perform the search of optimal dimensions using
bootstrap samples. By defaults, boots = FALSE.
The number of bootstrap samples to generate when boots = TRUE. Note that when boots = FALSE,
by default nboots = 0, but when boots = TRUE, by default nboots = 100.
The specification of the kind of bootstrap sampling to be performed.
If boottype = "bootpsimple", then a parametric bootstrap using a simple sampling scheme will
be performed (default sampling).
If boottype = "bootpstrat", then a parametric bootstrap using a stratified sampling scheme will
be performed.
If boottype = "bootnp", then a non-parametric bootstrap using a simple sampling scheme will
be performed.
When the kind of bootstrap is parametric you can set the data distribution using
the input parameter resamptype according to two distribution: resamptype=1 corresponds
to multinomial distribution and resamptype=2 to Poisson distribution.
Required proportion of increase in fit of a more complex model. By default,
PercentageFit = 0.01.
Rosaria Lombardo, Michel van de Velden, Eric J Beh.
Wilderjans T F, Ceulemans E, and Meers K (2013) CHull: A generic convex hull based model
selection method. Behavior Research Methods, 45, 1-15.
Ceulemans E, and Kiers H A L (2006) Selecting among three-mode principal component models
of different types and complexities: A numerical convex hull based method. British Journal of
Mathematical & Statistical Psychology, 59, 133-150.
tunelocal(Xdata = happy, ca3type = "CA3")
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