VASPLINE procedure

Forms two-dimensional spline models for use by the automatic REML procedures (D.B. Baird & E.R. Williams).

Options

`BASIS` = string token	Spline basis to use (thinplate, pspline); default pspl
`KNOTS` = scalar, variate or pointer	Knots to be fitted in spline model, if a scalar, this is the total number of knots to be fitted; if a variate of length 2, this is the number of knots in the ROWS and COLUMNS directions; and if a pointer to 2 variates, these are the values for knots in the ROWS and COLUMNS directions; default – all distinct values of ROWS and COLUMNS
`PENALTYMETHOD` = string token	Which tensor spline penalty to use (isotropic, semiconstrained, unconstrained); default unco
`DEGREE` = scalars	Degree of polynomial used to form the underlying spline; default 3
`DIFFORDER` = scalars	Differencing order for p-spline penalty; default 1
`LINEARPLANE` = string token	Whether to include a linear row × column plane in the fixed model when `DIFFORDER` is one (include, omit); default omit

Parameters

`SPLINEDEFINITION` = pointers	Information required to define each spline model
`DESCRIPTION` = strings	Description of each model to use in output
`REPLICATES` = factors	Replicate factor, if relevant
`ROWS` = factors	Row factor
`COLUMNS` = factors	Column factor

Description

VASPLINE forms spline definitions so that the procedures VABLOCKDESIGN and VAROWCOLUMNDESIGN can model the random variation using a two-dimensional spline model, as in the V2DSPLINE procedure. The plots are assumed to be in a rectangular grid. The row and column factors must be specified by the ROWS and COLUMNS options, respectively. The design may also be resolvable, with the field divided into sections in which each treatment occurs exactly once. The replicate factor should then be specified by the REPLICATES option.

The BASIS option specifies whether to use p-splines (the default), or thin-plate splines to construct the basis. P-splines are tensor splines formed with the TENSORSPLINE procedure. Thin-plate splines are 2-dimensional cubic smoothing splines, formed using the THINPLATE procedure.

The positions of the knots used in the basis functions are specified by the KNOTS parameter. If KNOTS is not set (the default), all distinct values in ROWS and COLUMNS are used as the knot points. Otherwise KNOTS can be if a scalar, specifying the total number of knots to be fitted; the procedure then uses equi-spaced knots divided proportionally to the number of distinct points in the two directions. Alternatively, KNOTS can be a variate of length 2 specifying the number of equi-spaced of knots in the ROWS and COLUMNS directions. Finally, it can be a pointer to 2 variates whose values are used for knots in the ROWS and COLUMNS directions.

The degree of polynomial used to form the underlying tensor spline basis functions is specified by the DEGREE option; default 3. The DIFFORDER option specifies the differencing order to be used with p-spline models. This determines the strength of the penalty (for a given smoothness parameter). The default is to use first-order differencing. For a p-spline model, the underlying fixed polynomial in each dimension has degree d equal to DIFFORDER minus 1. If DIFFORDER=1, there will be no fixed model, but one a fixed polynomial of order 1 can be added using LINEARPLANE=include. This will model any linear trends over rows or columns.

The tensor-spline basis is constructed via interactions of the one-dimensional spline bases, as detailed in the TENSORSPLINE procedure. The PENALTYMETHOD option controls the interaction between the one-dimensional spline bases. An unconstrained penalty (the default) allows a separate smoothing parameter for each term. In this case, the basis pointer has 2d+3 matrices, one for each term. With the semiconstrained penalty, the same smoothing parameter is imposed across the interaction of polynomials in the first dimension with random terms in the second, and for the interaction of random terms in the first dimension with polynomials in the second dimension. An isotropic penalty uses a single common penalty, and the terms are combined into a single matrix.

The SPLINEDEFINITIONS parameter saves the definitions in a pointer containing the following elements:

‘description’

single-line text to describe the model in output;

‘checkfixed’

scalar set to one if the definition includes fixed terms, zero otherwise;

‘fixed’

fixed terms; and

‘random’

random terms.

Options: BASIS, KNOTS, PENALTYMETHOD, DEGREE, DIFFORDER, LINEARPLANE.

Parameters: SPLINEDEFINITION, DESCRIPTION, REPLICATES, ROWS, COLUMNS.

Method

VASPLINE forms the spline basis functions using the THINPLATE or TENSORSPLINE procedures.

Action with RESTRICT

There must be no restrictions on REPLICATES, ROWS and COLUMNS.

Example

CAPTION     'VASPLINE example','Wheat trial in 22 x 15 grid';\
            STYLE=major,plain
SPLOAD      [PRINT=summary] '%Data%/Wheat22x15.gsh'
VASPLINE    [DIFFORDER=2; DEGREE=3] SPLINEDEFINITION=Wheat22x15;\
            DESCRIPTION='p-spline degree 3, order of difference 2';\
            ROWS=Row; COLUMNS=Column
PRINT       [SQUASH=yes] #Wheat22x15 : SKIP     [FILE=output] 1
" fit p-spline degree 3, order of difference 2 " 
VCOMPONENTS [FIXED=#Wheat22x15['fixed']+Rep+RowGrp+ColGrp+Genotype] \
            #Wheat22x15['random']; CONSTRAINTS=positive; INITIAL=0.1
REML        [MAXCYCLE=200] Yield

Updated on April 15, 2025

Was this article helpful?

Yes No