case2.b.initial: Initial Estimates of Parameter Functions

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

observed data matrix

timepoint vector with length = ncol(y)

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'

Value

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

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}

Examples

Run this code

data(data.simulation)
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")