case2.b.initial: Initial Estimates of Parameter Functions

In cSFM: Covariate-adjusted Skewed Functional Model (cSFM)

Description

Obtain the initial estimates of functional parameters (mean, var, shape and skewness) when both the mean and variance are covariate depedent but the skewness is covariate independent.

Usage

case2.b.initial(y, tp, cp, nbasis.mean = 10, gam.method = "REML", 
                bin = 10, skew.method = "mle", cate = 1)

Arguments

y	observed data matrix
tp	timepoint vector with length = ncol(y)
cp	covariate vector with length = nrow{y}
nbasis.mean	number of bases when smoothing the mean
gam.method	smoothing method for the mean
bin	the length of bin to estimate the variance
skew.method	estimation method for skewness; See 'Details'
cate	method category, taking values as 1,2,3; See 'Details'

Details

The variance is estimated using binning method with length = bin. The skewness can be estimated by method of moment mome or maximum likelihood mle. Stepwise estimates are used here: the variance is based on the residuals after removing the mean effect; the skewness is based on the scaled residuals after removing both the mean and variance effect.

cate indiates the method cateory as follows:

• cate = 1 all three parameter functions are to be estimated

• cate = 2 the skewnewss parameter is fixed as 0

• cate = 3 the mean to be fixed at 0; typically used when a stepwise estimation procedure is used, e.g. 2cSFM in cSFM.est

Value

A list of initial estimate of parmeters (length 4: mean, variance, shape and skewness).

See Also

cSFM.est

Examples

data(data.simulation)
## Not run: 
cp.hat <- case2.b.initial(y = DST$obs, tp= DST$tp, cp=DST$cp)
# visulize the parameter function and the estimated function
par(mfrow = c(1,2))
persp(DST$cp, DST$tp, exp(DST$pars$logvar), theta=60, phi=15,
      ticktype = "detailed", col="lightblue", 
      xlab = "covariate", ylab = "time",
      zlab="data", main="variance surface")
persp(DST$cp, DST$tp, cp.hat$var, theta=60, phi=15,
      ticktype = "detailed", col="lightblue", 
      xlab = "covariate", ylab = "time",
      zlab="data", main="initial estiamtes")

## End(Not run)

cSFM documentation built on May 29, 2017, 6:10 p.m.