# cp2beta: Transformation between Parameters and B-spline Coefficients In cSFM: Covariate-adjusted Skewed Functional Model (cSFM)

## Description

Given a B-spline basis, transfer parameters (mean, variance, skewness) to the corresponding coefficients, and vice versa.

## Usage

 ```1 2``` ```cp2beta(cp.list, Basis.list) beta2cp(vec.beta, Basis.list) ```

## Arguments

 `cp.list` list of parameters with names to be `(mean, var, skew)` corresponding to (mean, variance, skew) `Basis.list` list of basis matrices for the mean, variance and skewness `vec.beta` vector of coefficients

## Value

`cp2beta` returns a vector of coefficients with the same form of `vec.beta`; `beta2cp` returns a list of parameters with the same form of `cp.list`

## References

[1]. Meng Li, Ana-Maria Staicu and Howard D. Bondell (2013), Incorporating Covariates in Skewed Functional Data Models. http://www.stat.ncsu.edu/information/library/papers/mimeo2654_Li.pdf.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```data(data.simulation) # bivariate for mean and variance; univariate for shape parameter cases = c(2,2,1) # 2 knots at time direction for each parameter nknots.tp = c(2,2,2) # 2 knots at covariate direction for mean and variance nknots.cp = c(2,2) basis.list <- lapply(1:3, function(k) kpbb(DST\$tp, DST\$cp, nknots.tp = nknots.tp[k], nknots.cp= nknots.cp[k], sub.case=cases[k])) cp.hat <- DST\$pars # true parameters cp.hat\$var <- exp(cp.hat\$logvar) # follow the fomart stricely: (mean, var, skew) beta <- cp2beta(cp.hat, basis.list) cp.recover <- beta2cp(beta, basis.list) norm(cp.hat\$mean - cp.recover\$mean) ```

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