WFMM
WFMM is a Windows command-line application that implements a Bayesian
wavelet-based functional mixed model methodology for functional data analysis
introduced in Morris and Carroll (2006).
The method extends linear mixed models to functional data consisting of n
curves sampled on the same grid. The user provides a file in Matlab data file
format (*.mat) containing a matrix of data samples of the set of n curves
sampled T times and a description of the model by the design matrix X and
random effects matrix Z, and other parameters controlling the computation. It
provides as output nonparametric estimates of fixed and random effects
functions that have been adaptively regularized as a result of the nonlinear
shrinkage prior imposed on the fixed effects wavelet coefficients.
See the WFMM
User Guide, also included in the download distribution.
We strongly recommend that new users download the example file and run the
example data set. This is a partial spectrum of a MALDI-TOF mass spectrometry
proteomic data set from the pancreatic cancer experiment described in Morris et
al (2007). The plots below show results for the five fixed effects (cancer
effect and four block effects). Open the
included Pancreatic_MYO25_wfmm_example.fig file in Matlab and use the zoom to
see the individual curves. The blue line is ghatns (non-shrunken estimate for
fixed effect), the solid red line is ghat (posterior mean of fixed effect), and
the two red dashed lines are ghat_Q05 (0.05 quantile for fixed effect) and
ghat_Q95 (0.95 quantile for fixed effect).
The example requires Matlab to be installed on your system. After download,
unzip the files into a folder, open a command prompt window in the folder and
type
wfmmdemo.bat
The batch file runs wfmm,
then starts Matlab to plot the results, which should look like the figure
above.
Software developed in C++ and Matlab by Richard Herrick.
References
Morris, JS and Carroll, RJ (2006). Wavelet-based
functional mixed models, Journal of the Royal Statistical Society, Series
B, 68(2): 179-199
Morris, JS, Brown PJ, Herrick, RC, Baggerly KA, and Coombes, KR (2007). Bayesian
Analysis of Mass Spectrometry Proteomic Data using Wavelet Based Functional
Mixed Models, Biometrics (to appear).