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Fit P-splines

Source: R/spl1D.R, R/spl2D.R, R/spl3D.R
spl1D.Rd

Fit multi dimensional P-splines using sparse implementation.

Usage

spl1D(
  x,
  nseg,
  pord = 2,
  degree = 3,
  scaleX = TRUE,
  xlim = range(x),
  cond = NULL,
  level = NULL
)

spl2D(
  x1,
  x2,
  nseg,
  pord = 2,
  degree = 3,
  scaleX = TRUE,
  x1lim = range(x1),
  x2lim = range(x2),
  cond = NULL,
  level = NULL
)

spl3D(
  x1,
  x2,
  x3,
  nseg,
  pord = 2,
  degree = 3,
  scaleX = TRUE,
  x1lim = range(x1),
  x2lim = range(x2),
  x3lim = range(x3)
)

Arguments

x, x1, x2, x3

The variables in the data containing the values of the x covariates.

nseg

The number of segments

pord

The order of penalty, default pord = 2

degree

The degree of B-spline basis, default degree = 3

scaleX

Should the fixed effects be scaled.

xlim, x1lim, x2lim, x3lim

A numerical vector of length 2 containing the domain of the corresponding x covariate where the knots should be placed. Default set to NULL, when the covariate range will be used.

cond

Conditional factor: splines are defined conditional on the level. Default NULL.

level

The level of the conditional factor. Default NULL.

Value

A list with the following elements:

  • X - design matrix for fixed effect. The intercept is not included.

  • Z - design matrix for random effect.

  • lGinv - a list of precision matrices

  • knots - a list of vectors with knot positions

  • dim.f - the dimensions of the fixed effect.

  • dim.r - the dimensions of the random effect.

  • term.labels.f - the labels for the fixed effect terms.

  • term.labels.r - the labels for the random effect terms.

  • x - a list of vectors for the spline variables.

  • pord - the order of the penalty.

  • degree - the degree of the B-spline basis.

  • scaleX - logical indicating if the fixed effects are scaled.

  • EDnom - the nominal effective dimensions.

Functions

  • spl2D(): 2-dimensional splines

  • spl3D(): 3-dimensional splines

See also

LMMsolve

Examples

## Fit model on john.alpha data from agridat package.
data(john.alpha, package = "agridat")

## Fit a model with a 1-dimensional spline at the plot level.
LMM1_spline <- LMMsolve(fixed = yield ~ rep + gen,
                       spline = ~spl1D(x = plot, nseg = 20),
                       data = john.alpha)

summary(LMM1_spline)
#> Table with effective dimensions and penalties: 
#> 
#>         Term Effective Model Nominal Ratio Penalty
#>  (Intercept)      1.00     1       1  1.00    0.00
#>          rep      2.00     2       2  1.00    0.00
#>          gen     23.00    23      23  1.00    0.00
#>    lin(plot)      1.00     1       1  1.00    0.00
#>      s(plot)      3.99    23      21  0.19 3310.21
#>     residual     41.01    72      45  0.91   13.21
#> 
#>  Total Effective Dimension: 72 

## Fit model on US precipitation data from spam package.
data(USprecip, package = "spam")

## Only use observed data
USprecip <- as.data.frame(USprecip)
USprecip <- USprecip[USprecip$infill == 1, ]

## Fit a model with a 2-dimensional P-spline.
LMM2_spline <- LMMsolve(fixed = anomaly ~ 1,
                       spline = ~spl2D(x1 = lon, x2 = lat, nseg = c(41, 41)),
                       data = USprecip)

summary(LMM2_spline)
#> Table with effective dimensions and penalties: 
#> 
#>           Term Effective Model Nominal Ratio Penalty
#>    (Intercept)      1.00     1       1  1.00    0.00
#>  lin(lon, lat)      3.00     3       3  1.00    0.00
#>         s(lon)    302.60  1936    1932  0.16    0.26
#>         s(lat)    409.09  1936    1932  0.21    0.08
#>       residual   5190.31  5906    5902  0.88   13.53
#> 
#>  Total Effective Dimension: 5906