linmod {fda} | R Documentation |
A functional dependent variable y_i(t) is approximated by a single functional covariate x_i(s) plus an intercept function α(t), and the covariate can affect the dependent variable for all values of its argument. The equation for the model is
y_i(t) = β_0(t) + int β_1(s,t) x_i(s) ds + e_i(t)
for i = 1,...,N. The regression function β_1(s,t) is a bivariate function. The final term e_i(t) is a residual, lack of fit or error term. There is no need for values s and t to be on the same continuum.
linmod(xfdobj, yfdobj, betaList, wtvec=NULL)
xfdobj |
a functional data object for the covariate |
yfdobj |
a functional data object for the dependent variable |
betaList |
a list object of length 3. The first element is a functional parameter object specifying a basis and a roughness penalty for the intercept term, the second element is a functional parameter object for the regression function as a function of its first argument s, and the third element is a functional parameter object for the regression function as a function of its second argument t. |
wtvec |
a vector of weights for each observation. Its default value is NULL, in which case the weights are assumed to be 1. |
a named list of length 3 with the following entries:
beta0estfd |
the intercept functional data object. |
beta1estbifd |
a bivariate functional data object for the regression function. |
yhatfdobj |
a functional data object for the approximation to the dependent variable defined by the linear model, if the dependent variable is functional. Otherwise the matrix of approximate values. |
#See the prediction of precipitation using temperature as #the independent variable in the analysis of the daily weather #data.