# AmpPhaseDecomp: Decomposition for Amplitude and Phase Variation In fda: Functional Data Analysis

 AmpPhaseDecomp R Documentation

## Decomposition for Amplitude and Phase Variation

### Description

Registration is the process of aligning peaks, valleys and other features in a sample of curves. Once the registration has taken place, this function computes two mean squared error measures, one for amplitude variation, and the other for phase variation. It also computes a squared multiple correlation index of the amount of variation in the unregistered functions is due to phase.

### Usage

``````AmpPhaseDecomp(xfd, yfd, hfd, rng=xrng)
``````

### Arguments

 `xfd` a functional data object containing the unregistered curves. `yfd` a functional data object containing the registered curves. `hfd` a functional data object containing the strictly monotone warping functions \$h(t)\$. This is typically returned by the functions `landmarkreg` and `register.fd`. `rng` a vector of length 2 specifying a range of values over which the decomposition is to be computed. Both values must be within the range of the functional data objects in the argument. By default the whole range of the functional data objects is used.

### Details

The decomposition can yield negative values for `MS.phas` if the registration does not improve the alignment of the curves, or if used to compare two registration processes based on different principles, such as is the case for functions `landmarkreg` and `register.fd`.

### Value

a named list with the following components:

 `MS.amp` the mean squared error for amplitude variation. `MS.phas` the mean squared error for phase variation. `RSQR` the squared correlation measure of the proportion of the total variation that is due to phase variation. `C` a constant required for the decomposition. Its value is one if the derivatives the warping functions are independent of the squared registered functions.

### References

Ramsay, James O., Hooker, Giles, and Graves, Spencer (2009), Functional data analysis with R and Matlab, Springer, New York.

Ramsay, James O., and Silverman, Bernard W. (2005), Functional Data Analysis, 2nd ed., Springer, New York.

Ramsay, James O., and Silverman, Bernard W. (2002), Applied Functional Data Analysis, Springer, New York.

`landmarkreg`, `register.fd`, `smooth.morph`
``````#See the analysis for the growth data in the examples.