SpatioTemporal (version 0.9.2)

SVD.smooth.cv: Cross-validation for Smooth Basis Functions

Description

Function that uses cross-validation to evaluate the number of smooth functions needed to describe a data matrix with missing values (c.f. Fuentes et. al. (2006). Can be used to determine reasonable values for n.basis in SVD.smooth.

The function uses leave-one-column-out cross-validation; holding one column out from data, calling SVD.smooth, and then regressing the held out column on the resulting smooth functions. Cross-validation statistics computed include RMSE, R-squared and BIC.

Usage

SVD.smooth.cv(data, n.basis, date.ind=NA, scale.data=TRUE,
              niter=100, conv.reldiff=0.001, df=NULL, spar=NULL)

Arguments

data

Data matrix, with missing values marked by NA.

n.basis

A vector with the number of basis functions for which to run the cross-validation.

date.ind

Vector giving the observation time of each row in data. Same as date.ind in SVD.smooth.

scale.data

Uses scale to scale the data matrix before calling SVD.miss.

niter, conv.reldiff

Controls convergence for SVD.miss.

df, spar

The desired degrees of freedom/smoothing parameter for the spline, see smooth.spline.

Value

• Returns a list with the following components:
• CV.stat
  A data.frame with cross-validation statistics for each of the number of basis functions evaluated. Contains RMSE, R2 (R-squared) and BIC (Bayesian information criterion).
• BIC.all
  A data.frame with the individual BIC values for each column in the data matrix and for each number of basis functions evaluated. Can be used to evaluate how many of the columns would benefit from using more/fewer basis functions.
• smooth.SVD
  A list with length(n.basis) components. Each component contains an array where smooth.SVD[[j]][,,i] is the result of SVD.smooth applied to data[,-i] with n.basis[j] smooth functions. Can be used to investigate how different the smooth functions vary when different columns of the data matrix are dropped.

encoding

latin1

References

M. Fuentes, P. Guttorp, and P. D. Sampson. (2006) Using Transforms to Analyze Space-Time Processes in Statistical methods for spatio-temporal systems (B. Finkenst�dt{Finkenstadt}, L. Held, V. Isham eds.) 77-150

See Also

See also SVD.smooth, SVD.miss, svd, and smooth.spline.

create.data.matrix can be used to create a data matrix from a mesa.data object.

Used by calc.smooth.trends to compute smooth trends for mesa.data.

Examples

#create a data matrix
t <- seq(0,4*pi,len=50)
X <- matrix(cbind(cos(t),sin(2*t)),length(t),2) %*%
  matrix(rnorm(20),2,10)
#add some normal errors
X <- X + .25*rnorm(length(X))
#and mark some data as missing
X[runif(length(X))<.25] <- NA

#compute cross-validation for 1 to 4 basis functions
res.cv <- SVD.smooth.cv(X, n.basis=1:4, niter=100)

#plot cross-validation statistics
par(mfcol=c(2,2),mar=c(4,4,.5,.5))
plot(res.cv$CV.stat$RMSE,type="l",ylab="RMSE")
plot(res.cv$CV.stat$R2,type="l",ylab="R2")
plot(res.cv$CV.stat$BIC,type="l",ylab="BIC")

#plot the BIC for each column, illustrates how many columns that
#improve and how many that worsen when increasing the number of
#basis functions.
pairs(res.cv$BIC.all,panel=function(x,y){points(x,y);abline(0,1)})