clr {clr}

Curve Linear Regression via dimension reduction

Description

Fits a curve linear regression (CLR) model to data, using dimension reduction based on singular value decomposition.

Usage

clr(Y, X, clust = NULL, qx_estimation = list(method = "pctvar", param =
  0.999), ortho_Y = TRUE, qy_estimation = list(method = "pctvar", param
  = 0.999), d_estimation = list(method = "cor", param = 0.5))

Arguments

Y

An object of class clrdata or matrix, of the response curves (one curve a row).

X

An object of class clrdata or matrix, of the regressor curves (one curve a row).

clust

If needed, a list of row indices for each cluster, to obtain (approximately) homogeneous dependence structure inside each cluster.

qx_estimation

A list containing both values for 'method' (among 'ratio', 'ratioM', 'pctvar', 'fixed') and for 'param' (depending on the selected method), in order to choose how to estimate the dimension of X (in the sense that its Karhunen-Lo\'eve decomposition has qx terms only.

ortho_Y

If TRUE then Y is orthogonalized.

qy_estimation

Same as for qx_estimation, if ortho_Y is set to TRUE.

d_estimation

A list containing both values for 'method' (among 'ratio', 'pctvar', 'cor') and for 'param' (depending on the selected method), in order to choose how to estimate the correlation dimension.

Value

An object of class clr, which can be used to compute predictions. This clr object is a list of lists: one list by cluster of data, each list including:

residuals

The matrix of the residuals of d_hat simple linear regressions.

b_hat

The vector of the estimated coefficient of the d_hat simple straight line regressions.

eta

The matrix of the projections of X.

xi

The matrix of the projections of Y.

qx_hat

The estimated dimension of X.

qy_hat

The estimated dimension of Y.

d_hat

The estimated correlation dimension.

X_mean

The mean of the regressor curves.

X_sd

The standard deviation of the regressor curves.

Y_mean

The mean of the response curves.

ortho_Y

The value which was selected for ortho_Y.

GAMMA

The standardized transformation for X.

INV_DELTA

The standardized transformation for Y to predict if ortho_Y was set to TRUE.

phi

The eigenvectors for Y to predict if ortho_Y was set to FALSE.

idx

The indices of the rows selected from X and Y for the current cluster.

See Also

clr-package, clrdata and predict.clr.

Examples

library(clr)
data(gb_load)
data(clust_train)

clr_load <- clrdata(x = gb_load$ENGLAND_WALES_DEMAND,
                    order_by = gb_load$TIMESTAMP,
                    support_grid = 1:48)

## data cleaning: replace zeros with NA
clr_load[rowSums((clr_load == 0) * 1) > 0, ] <- NA
matplot(t(clr_load), ylab = 'Daily loads', type = 'l')

Y <- clr_load[2:nrow(clr_load), ]
X <- clr_load[1:(nrow(clr_load) - 1), ]

begin_pred <- which(substr(rownames(Y), 1, 4) == '2016')[1]
Y_train <- Y[1:(begin_pred - 1), ]
X_train <- X[1:(begin_pred - 1), ]

## Example without any cluster
model <- clr(Y = Y_train, X = X_train)

## Example with clusters
model <- clr(Y = Y_train, X = X_train, clust = clust_train)