Prepares the fixed and random P-spline basis matrices, and associated
information, that are needed for fitting of Tensor Product P-splines (TPPS)
as described by Rodriguez-Alvarez et al. (2018). This function is called
internally by addSpatialModelOnIC.asrtests,
addSpatialModelOnIC.asrtests and
chooseSpatialModelOnIC.asrtests when fitting TPPS models
for local spatial variation. There are two methods available, controlled by
asreml.option for creating and storing the basis functions.
This function is most likely to be called directly when mbf has been used
in creating an asreml.object and it is desired to use the object in a
session subsequent to the session in which the object was created.
# S3 method for data.frame
makeTPPSplineMats(data, sections = NULL,
row.covar, col.covar,
nsegs = NULL, nestorder = c(1,1),
degree = c(3,3), difforder = c(2,2),
rotateX = FALSE, theta = c(0,0),
asreml.option = "grp", mbf.env = sys.frame(),
...)A list of length equal to the number of sections is produced. Each of
these components is a list with 8 or 9 components. The component
named data.plus, being the input data.frame to which has been added
the columns required to fit the TPPS model (the data.frame stored
in the data component holds only the covariates from data).
List of length 8 or 9 (according to the asreml.option).
data = the input data frame augmented with structures required
to fit tensor product splines in asreml-R. This data frame can be used
to fit the TPS model.
Added columns:
TP.col, TP.row = column and row coordinates
TP.CxR = combined index for use with smooth x smooth term
TP.C.n for n=1:diff.c = X parts of column spline for use
in random model (where diff.c is the order of column differencing)
TP.R.n for n=1:diff.r = X parts of row spline for use in
random model (where diff.r is the order of row differencing)
TP.CR.n for n=1:(diff.c*diff.r) = interaction between the
two X parts for use in fixed model. The first variate is
a constant term which should be omitted from the model when the constant
(1) is present. If all elements are included in the model then the
constant term should be omitted,eg.
y ~ -1 + TP.CR.1 + TP.CR.2 + TP.CR.3 + TP.CR.4 + other terms...
when asreml="grp" or "sepgrp", the spline basis
functions are also added into the data frame. Column numbers for each
term are given in the grp list structure.
mbflist = list that can be used in call to asreml (so long as Z
matrix data frames extracted with right names, eg BcZ<stub>.df)
BcZ.df = mbf data frame mapping onto smooth part of column
spline, last column (labelled TP.col) gives column index
BrZ.df = mbf data frame mapping onto smooth part of row spline,
last column (labelled TP.row) gives row index
BcrZ.df = mbf data frame mapping onto smooth x smooth term, last
column (labelled TP.CxR) maps onto col x row combined index
dim = list structure, holding dimension values relating to the
model:
"diff.c" = order of differencing used in column dimension
"nbc" = number of random basis functions in column dimension
"nbcn" = number of nested random basis functions in column dimension
used in smooth x smooth term
"diff.r" = order of differencing used in column dimension
"nbr" = number of random basis functions in column dimension
"nbrn" = number of nested random basis functions in column dimension
used in smooth x smooth term
trace = list of trace values for ZGZ' for the random TPspline
terms, where Z is the design matrix and G is the known diagonal variance
matrix derived from eigenvalues. This can be used to rescale the spline
design matrix (or equivalently variance components).
grp = list structure, only added for setting asreml="grp".
For asreml="grp", provides column indexes for each of the 5
random components of the 2D splines in data.plus. Dimensions of
the components can be derived from the values in the dim item.
data.plus = the input data.frame to which has been
added the columns required to fit tensor product splines in asreml-R.
This data.frame can be used to fit the TPS model.
FOr multiple sections, this data.frame will occur
in the component for each section. If asreml.option is set to
mbf, then this component will have the attribute mbf.env
that specifies the environment to which the data.frames
containing the spline bases have been assigned.
An data.frame that holds the spline bases for a section.
It is indexed by columns named col and row.
A single character string that species the name of the column
in the data.frame that contains the factor
that identifies different sections of the data
to which separate spatial models are to be fitted.
A single character string nominating a numeric
column in the data.frame that contains the values of a
covariate indexing the rows of the grid.
A single character string nominating a numeric
column in the data.frame that contains the values of a
covariate indexing the columns of the grid.
A pair of numeric values giving the number of segments into
which the column and row ranges are to be split, respectively, for fitting
a P-spline model (TPPS) (each value specifies the number of internal
knots + 1). If not specified, then (number of unique values - 1) is used
in each dimension; for a grid layout with equal spacing, this gives a knot
at each data value. If sections is not NULL and the grid
differs between the sections, then nsegs will differ between
the sections.
A numeric of length 2. The order of nesting for column
and row dimensions, respectively, in fitting a P-spline model (TPPS).
A value of 1 specifies no nesting, a value of 2 generates a spline with
half the number of segments in that
dimension, etc. The number of segments in each direction must be a
multiple of the order of nesting.
A numeric of length 2. The degree of polynomial spline to
be used for column and row dimensions respectively, in fitting a P-spline
(TPPS).
A numeric of length 2. The order of differencing for
column and row dimensions, respectively, in fitting a P-spline
(TPPS).
A logical indicating whether to rotate the eigenvectors of the
penalty matrix, as described by Piepho, Boer and Williams (2022), when
fitting a P-spline (TPPS). Setting rotateX to TRUE
results in a search for an optimized rotation under a model that omits
the random spline interaction terms. If ngridangles is set to
NULL, the optimal rotation us found using an optimizer
(nloptr::bobyqa). Otherwise, the optimal rotation is found by
exploring the fit over a two-dimensional grid of rotation angle pairs.
The optimization seeks to optimize the criterion nominated in
which.rotacriterion. Rotation of the eigenvectors is only relevant
for difforder values greater than 1 and has only been implemented
for difforder equal to 2.
A numeric of length 2. The angle (in degrees) to be used in
rotating the eignevectors of the penalty matrix of a P-spline (TPPS).
A single character string specifying whether the grp or
mbf methods are to be used to supply externally formed covariate
matrices to asreml when fitting a P-spline (TPPS). Compared
to the mbf method, the grp method is somewhat faster, but
creates large asrtests.objects for which the time it takes
to save them can exceed any gains in execution speed. The grp
method adds columns to the data.frame containing the data.
On the other hand, the mbf method adds only the fixed covariates
to data and stores the random covariates in the environment of the
internal function that calls the spline-fitting function; there are three smaller
data.frames for each section that are not stored in the
asreml.object resulting from the fitted model.
A environment specifying the environment to which the
data.frames containing the spline bases are to be assigned.
If mbf.env is NULL, the data.frames will not be assigned.
Further arguments passed to tpsmmb from package TPSbits.
Chris Brien
The objects are formed using the function tpsmmb from the R package TPSbits
authored by Sue Welham (2022). This function has been extended to allow for sections (see below)
and to allow rotation of the penalty matrix for the linear component of the interaction terms in
TPPCS models (for more information about rotation see Piepho, Boer and Williams, 2022).
Each combination of a row.covar and a col.covar does not have to specify a
single observation; for example, to fit a local spatial variation model to the main units
of a split-unit design, each combination would correspond to a main unit and all subunits
of the main unit would have the same combination.
The data for experiment can be divided sections and the spline bases and associated
data will be produced for each section. If there is more than one sections, then a
list is returned that has a component for each section. The component for
a section contains:
Piepho, H-P, Boer, M. P. & Williams, E. R. (2022) Two-dimensional P-spline smoothing for spatial analysis of plant breeding trials. Biometrical Journal, 64, 835-857.)
Rodriguez-Alvarez, M. X., Boer, M. P., van Eeuwijk, F. A., & Eilers, P. H. C. (2018). Correcting for spatial heterogeneity in plant breeding experiments with P-splines. Spatial Statistics, 23, 52-71.
Welham, S. J. (2022) TPSbits: Creates Structures to Enable Fitting and Examination of 2D Tensor-Product Splines using ASReml-R. Version 1.0.0 https://mmade.org/tpsbits/
addSpatialModel.asrtests, addSpatialModelOnIC.asrtests,
chooseSpatialModelOnIC.asrtests, tpsmmb from TPSbits
if (FALSE) {
data(Wheat.dat)
#Add row and column covariates
Wheat.dat <- within(Wheat.dat,
{
cColumn <- dae::as.numfac(Column)
cColumn <- cColumn - mean(unique(cColumn))
cRow <- dae::as.numfac(Row)
cRow <- cRow - mean(unique(cRow))
})
#Set up the matrices
tps.XZmat <- makeTPPSplineMats(wheat.dat,
row.covar = "cRow", col.covar = "cColumn")
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