tps is a wrapper of tpsmmb function from the TPSbits package to avoid version dependencies but if you're using this function for your research please cite the TPSbits package. This function is internally used by the spl2Dmatrices function to get Tensor-Product P-Spline Mixed Model Bits
(design matrices) for use with sommer and its main function mmer.
tps(
columncoordinates,
rowcoordinates,
nsegments=NULL,
minbound=NULL,
maxbound=NULL,
degree = c(3, 3),
penaltyord = c(2, 2),
nestorder = c(1, 1),
asreml = "grp",
eigenvalues = "include",
method = "Lee",
stub = NULL
)List of length 7, 8 or 9 (according to the asreml and
eigenvalues parameter settings).
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 settings
asreml="grp", asreml="sepgrp" or asreml="own".
For asreml="grp", provides column indexes for each of the 5
random components of the 2D splines.
For asreml="sepgrp", provides column indexes for each of the X and
Z component matrices for the 1D splines, plus the composite smooth x
smooth interaction term. For asreml="own", provides column indexes
for the composite random model.
Dimensions of the components can be derived from the values in the
dim item. The Z terms are scaled by the associated
eigenvalues when eigenvalues="include", but not when
eigenvalues="omit".
eigen = list structure, only added for option setting
eigenvalues="omit". Holds the diagonal elements of the inverse
variance matrix for the terms Xc:Zr (called diagr), Zc:Xr
(called diagc) and Zc:Zr (called diagcr).
A string. Gives the name of data element
holding column locations.
A string. Gives the name of data element
holding row locations.
A list of length 2. Number of segments to split column and row ranges into, respectively (= number of internal knots + 1). If only one number is specified, that value is used in both dimensions. If not specified, (number of unique values - 1) is used in each dimension; for a grid layout (equal spacing) this gives a knot at each data value.
A list of length 2. The lower bound to be used for column and row dimensions respectively; default calculated as the minimum value for each dimension.
A list of length 2. The upper bound to be used for column and row dimensions respectively; default calculated as the maximum value for each dimension.
A list of length 2. The degree of polynomial spline to be used for column and row dimensions respectively; default=3.
A list of length 2. The order of differencing for column and row dimensions, respectively; default=2.
A list of length 2. The order of nesting for column and row dimensions, respectively; default=1 (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 string. Indicates the types of structures to be generated
for use in asreml models; default "mbf". The
appropriate eigenvalue scaling is included within the Z matrices unless
setting scaling="none" is used, and then the scaling factors are
supplied separately in the returned object.
asreml="mbf" indicates the function should put the
spline design matrices into structures for use with "mbf";
asreml="grp" indicates the function should add the
composite spline design matrices (eg. for second-order differencing,
matrices Xr1:Zc, Xr2:Zc, Zr:Xc1, Zr:Xc2 and Zc:Zr) into the data frame
and provide a group list structure for each term;
asreml="sepgrp" indicates the function should generate the
individual X and Z spline design matrices separately (ie. Xc, Xr, Zc and
Zr), plus the smooth x smooth interaction term as a whole (ie. Zc:Zr),
and provide a group list structure for each term.
asreml="own" indicates the function should generate the
composite matrix ( Xr:Zc | Zr:Xc | Zc:Zr ) as a single set of columns.
A string. Indicates whether eigenvalues should be
included within the Z design matrices eigenvalues="include", or
whether this scaling should be omitted (eigenvalues="omit");
default eigenvalues="include". If the eigenvalue scaling is
omitted from the Z design matrices, then it should instead be included in
the model as a variance structure to obtain the correct TPspline model.
A string. Method for forming the penalty; default="Lee"
ie the penalty from Lee, Durban & Eilers (2013, CSDA 61, 22-37). The
alternative method is "Wood" ie. the method from Wood et al (2012,
Stat Comp 23, 341-360).
This option is a research tool and requires further investigation.
A string. Stub to be attached to names in the mbf list to
avoid over-writing structures and general confusion.