FREG (version 1.1)

olfreg: Functional ordinal logistic regression model

Description

Functional ordinal logistic regression model in which the response variable is a factor variable whereas the independent variables are functional variables. Independent variables could also be scalar variables.

Usage

olfreg(formula, betalist = NULL)

Arguments

formula

a formula expression of the form response ~ predictors. On the left side of the formula, y is a factor variable whereas on the right side, X can be either functional data object of class fd or a scalar variable of class numeric. The length of a scalar variable must equal the length of a response variable. Similarly, the number of observations of a functional covariate must equal the length of a response variable.

betalist

an optional argument. A list which contains beta regression coefficient functions for independent variables. If betalist is not provided, the number of estimated beta regression coefficient functions for one functional covariate would equal the number of basis functions used to represent that functional covariate. For a scalar variable, beta regression coefficient function is also a functional object whose basis is constant. Needless to say, for a scalar variable, there will be one beta regression coefficient.

Value

call

call of the olfreg function

x.count

number of predictors

xfdlist

a list of functional data objects. The length of the list is equal to the number of predictors

betalist

a list of beta regression coefficient functions

coefficients

estimated beta regression coefficient functions

alpha

estimated intercepts which represent boudaries of categories of dependent factor variable y

ylev

a number of categories of a response variable

fitted.values

fitted probabilities of a dependent factor variable y

loglik

a value of log-likelihood function at optimum

grd

a vector of gradient values at optimum

Hess

Hessian matrix at optimum

df

degrees of freedom

AIC

Akaike information criterion

iteration

number of iterations of Fisher Scoring algorithm needed for convergence

Examples

# NOT RUN {
# cycling dataset
library(fda)
# creation of ordinal variable from HR variable
zoneHR=rep(0,216)
zoneHR[which(rowMeans(cycling$HR[,1:60])<107)]=1
zoneHR[which((rowMeans(cycling$HR[,1:60])<125)&(rowMeans(cycling$HR[,1:60])>107))]=2
zoneHR[which((rowMeans(cycling$HR[,1:60])<142)&(rowMeans(cycling$HR[,1:60])>125))]=3
zoneHR[which((rowMeans(cycling$HR[,1:60])<160)&(rowMeans(cycling$HR[,1:60])>142))]=4
zoneHR[which((rowMeans(cycling$HR[,1:60])>160))]=5
# first functional variable - power (WATTS)
watts = t(cycling$WATTS[,1:60])
# set up a fourier basis system due to its cycling pattern
xbasis = create.fourier.basis(c(1,60),5) # 5 basis functions for example
watts.fd = smooth.basis(c(1:60),watts,xbasis)$fd
zoneHR = as.factor(zoneHR)
formula = zoneHR ~ watts.fd
olfreg.model = olfreg(formula = formula)
# additional functional variable - cadence (CAD)
cad = t(cycling$CAD[,1:60])
# set up a functional variable for cad
xbasis2 = create.bspline.basis(c(1,60), nbasis = 5, norder = 4)
cad.fd = smooth.basis(c(1:60),cad,xbasis2)$fd
formula = zoneHR ~ watts.fd + cad.fd
olfreg.model = olfreg(formula = formula)
# }