Description Usage Arguments Details Value Author(s) References See Also Examples
Performs generalized linear scalar-on-function or scalar-on-image regression in the wavelet domain, by sparse principal component regression (PCR) and sparse partial least squares (PLS).
1 2 3 4 |
y |
scalar outcome vector. |
xfuncs |
functional predictors. For 1D predictors, an n \times d matrix of signals, where n is the length of |
min.scale |
either a scalar, or a vector of values to be compared. Used to control the coarseness level of wavelet decomposition. Possible values are 0,1,…,log_2(d) - 1. |
nfeatures |
number(s) of features, i.e. wavelet coefficients, to retain for prediction of |
ncomp |
number(s) of principal components (if |
method |
either " |
mean.signal.term |
logical: should the mean of each subject's signal be included as a covariate? By default, |
covt |
covariates, if any: an n-row matrix, or a vector of length n. |
filter.number |
argument passed to function |
wavelet.family |
family of wavelets: passed to functions |
family |
generalized linear model family. Current version supports |
cv1 |
logical: should cross-validation be performed (to estimate prediction error) even if a single value is provided for each of |
nfold |
the number of validation sets ("folds") into which the data are divided. |
nsplit |
number of splits into |
store.cv |
logical: should the output include a CV result table? |
store.glm |
logical: should the output include the fitted |
seed |
the seed for random data division. If |
Briefly, the algorithm works by (1) applying the discrete wavelet transform (DWT) to the functional/image predictors; (2) retaining only the nfeatures
wavelet coefficients having the highest variance (for PCR; cf. Johnstone and Lu, 2009) or highest covariance with y
(for PLS); (3) regressing y
on the leading ncomp
PCs or PLS components, along with any scalar covariates; and (4) applying the inverse DWT to the result to obtain the coefficient function estimate fhat
.
This function supports only the standard DWT (see argument type
in wd
) with periodic boundary handling (see argument bc
in wd
).
For 2D predictors, setting min.scale=1
will lead to an error, due to a technical detail regarding imwd
. Please contact the author if a workaround is needed.
See the Details for fpcr
in refund
for a note regarding decorrelation.
An object of class "wcr"
. This is a list that, if store.glm = TRUE
, includes all components of the fitted glm
object. The following components are included even if store.glm = FALSE
:
fitted.values |
the fitted values. |
param.coef |
coefficients for covariates with decorrelation. The model is fitted after decorrelating the functional predictors from any scalar covariates; but for CV, one needs the "undecorrelated" coefficients from the training-set models. |
undecor.coef |
coefficients for covariates without decorrelation. See |
fhat |
coefficient function estimate. |
Rsq |
coefficient of determination. |
tuning.params |
if CV is performed, a 2 \times 4 table giving the indices and values of |
cv.table |
a table giving the CV criterion for each combination of |
se.cv |
if |
family |
generalized linear model family. |
Lan Huo
Johnstone, I. M., and Lu, Y. (2009). On consistency and sparsity for principal components analysis in high dimensions. Journal of the American Statistical Association, 104, 682–693.
Reiss, P. T., Huo, L., Zhao, Y., Kelly, C., and Ogden, R. T. (2014). Wavelet-domain regression and predictive inference in psychiatric neuroimaging. Available at http://works.bepress.com/phil_reiss/29/
1 | # See example for wnet
|
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.