tps: Get Tensor Product Spline Mixed Model Incidence Matrices
In sommer: Solving Mixed Model Equations in R

tps	R Documentation

Get Tensor Product Spline Mixed Model Incidence Matrices

Description

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.

Usage

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
)

Arguments

`columncoordinates`	A string. Gives the name of `data` element holding column locations.
`rowcoordinates`	A string. Gives the name of `data` element holding row locations.
`nsegments`	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.
`minbound`	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.
`maxbound`	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.
`degree`	A list of length 2. The degree of polynomial spline to be used for column and row dimensions respectively; default=3.
`penaltyord`	A list of length 2. The order of differencing for column and row dimensions, respectively; default=2.
`nestorder`	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.
`asreml`	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.
`eigenvalues`	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.
`method`	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.
`stub`	A string. Stub to be attached to names in the `mbf` list to avoid over-writing structures and general confusion.

Value

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:
1. "diff.c" = order of differencing used in column dimension
2. "nbc" = number of random basis functions in column dimension
3. "nbcn" = number of nested random basis functions in column dimension used in smooth x smooth term
4. "diff.r" = order of differencing used in column dimension
5. "nbr" = number of random basis functions in column dimension
6. "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).