Package 'dfrr'

Title:	Dichotomized Functional Response Regression
Description:	Implementing Function-on-Scalar Regression model in which the response function is dichotomized and observed sparsely. This package provides smooth estimations of functional regression coefficients and principal components for the dfrr model.
Authors:	Fatemeh Asgari [aut, cre], Saeed Hayati [aut, ctb]
Maintainer:	Fatemeh Asgari <[email protected]>
License:	GPL-3
Version:	0.1.0
Built:	2025-02-20 04:15:27 UTC
Source:	https://github.com/asgari-fatemeh/dfrr

Help Index

dfrr: Dichotomized Functional Response Regression
Get the basis functions from a dfrr-object
Get estimated coefficients from a dfrr fit
Dichotomized Functional Response Regression
Obtain fitted curves for a dfrr model
Functional principal component analysis of a dfrr fit
Madras Longitudinal Schizophrenia Study.
Obtain model matrix for a dfrr fit
Plot dfrr coefficients
Plot a dfrr fit
Plot dfrr fitted latent functions
Plot dfrr functional principal components
Plot dfrr predictions
QQ-plot for dfrr residuals
Prediction for dichotomized function-on-scalar regression
qq-plot Generic function
Obtain residuals for a dfrr model
Simulating a Simple dfrr Model
Summary for a dfrr fit

dfrr: Dichotomized Functional Response Regression

Description

Implementing Function-on-Scalar Regression model in which the response function is dichotomized and observed sparsely. This package provides smooth estimations of functional regression coefficients and principal components for the dfrr model.

Details

Author(s)

Maintainer: Fatemeh Asgari [email protected]

Authors:

Saeed Hayati [email protected] [contributor]

References

Fatemeh Asgari, Alamatsaz Mohammad Hossein, Hayati Saeed (2021). Dichotomized Functional Response Regression Model. <http://arxive.org/adress_to_paper>

Examples

set.seed(2000)
N<-50;M<-24

X<-rnorm(N,mean=0)
time<-seq(0,1,length.out=M)
Y<-simulate_simple_dfrr(beta0=function(t){cos(pi*t+pi)},
                        beta1=function(t){2*t},
                        X=X,time=time)

dfrr_fit<-dfrr(Y~X,yind=time)


coefs<-coef(dfrr_fit)
  plot(coefs)

fitteds<-fitted(dfrr_fit)
  plot(fitteds)

resids<-residuals(dfrr_fit)
plot(resids)

fpcs<-fpca(dfrr_fit)
plot(fpcs,plot.contour=TRUE,plot.3dsurface = TRUE)

newdata<-data.frame(X=c(1,0))
  preds<-predict(dfrr_fit,newdata=newdata)
  plot(preds)


newdata<-data.frame(X=c(1,0))
newydata<-data.frame(.obs=rep(1,5),.index=c(0.0,0.1,0.2,0.3,0.7),.value=c(1,1,1,0,0))
preds<-predict(dfrr_fit,newdata=newdata,newydata = newydata)
plot(preds)

set.seed(2000)
N<-50;M<-24

X<-rnorm(N,mean=0)
time<-seq(0,1,length.out=M)
Y<-simulate_simple_dfrr(beta0=function(t){cos(pi*t+pi)},
                        beta1=function(t){2*t},
                        X=X,time=time)

dfrr_fit<-dfrr(Y~X,yind=time)


coefs<-coef(dfrr_fit)
  plot(coefs)

fitteds<-fitted(dfrr_fit)
  plot(fitteds)

resids<-residuals(dfrr_fit)
plot(resids)

fpcs<-fpca(dfrr_fit)
plot(fpcs,plot.contour=TRUE,plot.3dsurface = TRUE)

newdata<-data.frame(X=c(1,0))
  preds<-predict(dfrr_fit,newdata=newdata)
  plot(preds)


newdata<-data.frame(X=c(1,0))
newydata<-data.frame(.obs=rep(1,5),.index=c(0.0,0.1,0.2,0.3,0.7),.value=c(1,1,1,0,0))
preds<-predict(dfrr_fit,newdata=newdata,newydata = newydata)
plot(preds)

Get the basis functions from a dfrr-object

Description

Returns the basis functions employed in fitting a dfrr-object.

Usage

basis(object)
basis(object)

Arguments

object

a fitted dfrr-object obtained from invoking the function dfrr.

Examples

set.seed(2000)
N<-50;M<-24

X<-rnorm(N,mean=0)
time<-seq(0,1,length.out=M)
Y<-simulate_simple_dfrr(beta0=function(t){cos(pi*t+pi)},
                        beta1=function(t){2*t},
                        X=X,time=time)
dfrr_fit<-dfrr(Y~X,yind=time)

coefs<-coef(dfrr_fit,return.fourier.coefs=TRUE)

basis<-basis(dfrr_fit)
evaluated_coefs<-coefs%*%t(fda::eval.basis(time,basis))

#Plotting the regression coefficients
par(mfrow=c(1,2))
plot(time,evaluated_coefs[1,],'l',main="Intercept")
plot(time,evaluated_coefs[2,],'l',main="X")

set.seed(2000)
N<-50;M<-24

X<-rnorm(N,mean=0)
time<-seq(0,1,length.out=M)
Y<-simulate_simple_dfrr(beta0=function(t){cos(pi*t+pi)},
                        beta1=function(t){2*t},
                        X=X,time=time)
dfrr_fit<-dfrr(Y~X,yind=time)

coefs<-coef(dfrr_fit,return.fourier.coefs=TRUE)

basis<-basis(dfrr_fit)
evaluated_coefs<-coefs%*%t(fda::eval.basis(time,basis))

#Plotting the regression coefficients
par(mfrow=c(1,2))
plot(time,evaluated_coefs[1,],'l',main="Intercept")
plot(time,evaluated_coefs[2,],'l',main="X")

Get estimated coefficients from a dfrr fit

Description

Returns estimations of the smooth functional regression coefficients $\beta(t)$ . The result is a matrix of either Fourier coefficients or evaluations. See Details.

Usage

## S3 method for class 'dfrr'
coef(
  object,
  standardized = NULL,
  unstandardized = !standardized,
  return.fourier.coefs = NULL,
  return.evaluations = !return.fourier.coefs,
  time_to_evaluate = NULL,
  ...
)
## S3 method for class 'dfrr'
coef(
  object,
  standardized = NULL,
  unstandardized = !standardized,
  return.fourier.coefs = NULL,
  return.evaluations = !return.fourier.coefs,
  time_to_evaluate = NULL,
  ...
)

Arguments

`object`	a `dfrr`-object
`standardized`, `unstandardized`	a `boolean` indicating whether stanadrdized/unstandardized regression coefficients are reported. Only standardized regression coefficients are identifiable, thus the arugment is defaults to `standardized=TRUE`.
`return.fourier.coefs`, `return.evaluations`	a `boolean` indicating whether the Fourier coefficients of regression coefficients are returned (`return.fourier.coefs=TRUE`), or evaluations of the regression coefficients (`return.evaluations=TRUE`). Defaults to `return.fourier.coefs=TRUE`.
`time_to_evaluate`	a numeric vector indicating the set of time points for evaluating the functional regression coefficients, for the case of `return.evaluations=TRUE`.
`...`	dot argument, just for consistency with the generic function

Details

This function will return either the Fourier coefficients or the evaluation of estimated coefficients. Fourier coefficients which are reported are based on the a set of basis which can be determined by basis(dfrr_fit). Thus the evaluation of regression coefficients on the set of time points specified by vector time, equals to fitted(dfrr_fit)%*%t(eval.basis(time,basis(dfrr_fit))).

Consider that the unstandardized estimations are not identifiable. So, it is recommended to extract and report the standardized estimations.

Examples

set.seed(2000)
N<-50;M<-24

X<-rnorm(N,mean=0)
time<-seq(0,1,length.out=M)
Y<-simulate_simple_dfrr(beta0=function(t){cos(pi*t+pi)},
                        beta1=function(t){2*t},
                        X=X,time=time)
dfrr_fit<-dfrr(Y~X,yind=time)

coefs<-coef(dfrr_fit)
plot(coefs)
set.seed(2000)
N<-50;M<-24

X<-rnorm(N,mean=0)
time<-seq(0,1,length.out=M)
Y<-simulate_simple_dfrr(beta0=function(t){cos(pi*t+pi)},
                        beta1=function(t){2*t},
                        X=X,time=time)
dfrr_fit<-dfrr(Y~X,yind=time)

coefs<-coef(dfrr_fit)
plot(coefs)

Dichotomized Functional Response Regression

Description

Implementing Function-on-Scalar Regression model, in which the response function is dichotomized and observed sparsely.

Usage

dfrr(
  formula,
  yind = NULL,
  data = NULL,
  ydata = NULL,
  method = c("REML", "ML"),
  rangeval = NULL,
  basis = NULL,
  times_to_evaluate = NULL,
  ...
)
dfrr(
  formula,
  yind = NULL,
  data = NULL,
  ydata = NULL,
  method = c("REML", "ML"),
  rangeval = NULL,
  basis = NULL,
  times_to_evaluate = NULL,
  ...
)

Arguments

`formula`	an object of class "`formula`" (or one that can be coerced to that class with `as.formula`: a symbolic description of the model to be fitted.
`yind`	a vector with length equal to the number of columns of the matrix of functional responses giving the vector of evaluation points $(t_1,...,t_{G})$ . If not supplied, `yind` is set to `1:ncol(<response>)`.
`data`	an (optional) `data.frame` containing the covariate data. the variable terms will be searched from the columns of `data`, covariates also can be read from the workspace if it is not available in `data`.
`ydata`	an (optional) `data.frame` consists of three columns `.obs`, `.index` and `.value`, supplying the functional responses that are not observed on a regular grid. ydata must be provided if the sampling design is irregular.
`method`	detrmines the estimation method of functional parameters. Defaults to "`REML`" estimation.
`rangeval`	an (optional) vector of length two, indicating the lower and upper limit of the domain of latent functional response. If not specified, it will set by minimum and maximum of `yind` or `.index` column of `ydata`.
`basis`	an (optional) object of class `'basisfd'`. Defaults to cubic bspline basis.
`times_to_evaluate`	a numeric vector indicating the set of time points for evaluating the functional regression coefficients and principal components.
`...`	other arguments that can be passed to the inner function `AMCEM`.

Details

The output is a dfrr-object, which then can be injected into other methods/functions to postprocess the fitted model, including: coef.dfrr,fitted.dfrr, basis, residuals.dfrr, predict.dfrr, fpca, summary.dfrr, model.matrix.dfrr, plot.coef.dfrr, plot.fitted.dfrr, plot.residuals.dfrr, plot.predict.dfrr, plot.fpca.dfrr

Examples

set.seed(2000)
N<-50;M<-24

X<-rnorm(N,mean=0)
time<-seq(0,1,length.out=M)
Y<-simulate_simple_dfrr(beta0=function(t){cos(pi*t+pi)},
                        beta1=function(t){2*t},
                        X=X,time=time)

dfrr_fit<-dfrr(Y~X,yind=time)

plot(dfrr_fit)

##### Fitting dfrr model to the Madras Longitudinal Schizophrenia data
data(madras)
ids<-unique(madras$id)
N<-length(ids)

ydata<-data.frame(.obs=madras$id,.index=madras$month,.value=madras$y)

xdata<-data.frame(Age=rep(NA,N),Gender=rep(NA,N))
for(i in 1:N){
  dt<-madras[madras$id==ids[i],]
  xdata[i,]<-c(dt$age[1],dt$gender[1])
}
rownames(xdata)<-ids


madras_dfrr<-dfrr(Y~Age+Gender+Age*Gender, data=xdata, ydata=ydata, J=11)
coefs<-coef(madras_dfrr)
plot(coefs)

fpcs<-fpca(madras_dfrr)
plot(fpcs)
plot(fpcs,plot.eigen.functions=FALSE,plot.contour=TRUE,plot.3dsurface = TRUE)

par(mfrow=c(2,2))
fitteds<-fitted(madras_dfrr) #Plot first four fitted functions
  plot(fitteds,id=c(1,2,3,4))

resids<-residuals(madras_dfrr)
plot(resids)


newdata<-data.frame(Age=c(1,1,0,0),Gender=c(1,0,1,0))
  preds<-predict(madras_dfrr,newdata=newdata)
  plot(preds)


newdata<-data.frame(Age=c(1,1,0,0),Gender=c(1,0,1,0))
newydata<-data.frame(.obs=rep(1,5),.index=c(0,1,3,4,5),.value=c(1,1,1,0,0))
preds<-predict(madras_dfrr,newdata=newdata,newydata = newydata)
plot(preds)

set.seed(2000)
N<-50;M<-24

X<-rnorm(N,mean=0)
time<-seq(0,1,length.out=M)
Y<-simulate_simple_dfrr(beta0=function(t){cos(pi*t+pi)},
                        beta1=function(t){2*t},
                        X=X,time=time)

dfrr_fit<-dfrr(Y~X,yind=time)

plot(dfrr_fit)

##### Fitting dfrr model to the Madras Longitudinal Schizophrenia data
data(madras)
ids<-unique(madras$id)
N<-length(ids)

ydata<-data.frame(.obs=madras$id,.index=madras$month,.value=madras$y)

xdata<-data.frame(Age=rep(NA,N),Gender=rep(NA,N))
for(i in 1:N){
  dt<-madras[madras$id==ids[i],]
  xdata[i,]<-c(dt$age[1],dt$gender[1])
}
rownames(xdata)<-ids


madras_dfrr<-dfrr(Y~Age+Gender+Age*Gender, data=xdata, ydata=ydata, J=11)
coefs<-coef(madras_dfrr)
plot(coefs)

fpcs<-fpca(madras_dfrr)
plot(fpcs)
plot(fpcs,plot.eigen.functions=FALSE,plot.contour=TRUE,plot.3dsurface = TRUE)

par(mfrow=c(2,2))
fitteds<-fitted(madras_dfrr) #Plot first four fitted functions
  plot(fitteds,id=c(1,2,3,4))

resids<-residuals(madras_dfrr)
plot(resids)


newdata<-data.frame(Age=c(1,1,0,0),Gender=c(1,0,1,0))
  preds<-predict(madras_dfrr,newdata=newdata)
  plot(preds)


newdata<-data.frame(Age=c(1,1,0,0),Gender=c(1,0,1,0))
newydata<-data.frame(.obs=rep(1,5),.index=c(0,1,3,4,5),.value=c(1,1,1,0,0))
preds<-predict(madras_dfrr,newdata=newdata,newydata = newydata)
plot(preds)

Obtain fitted curves for a dfrr model

Description

Fitted curves refer to the estimations of latent functional response curves. The results can be either the Fourier coefficients or evaluation of the fitted functions. See Details.

Usage

## S3 method for class 'dfrr'
fitted(
  object,
  return.fourier.coefs = NULL,
  return.evaluations = !return.fourier.coefs,
  time_to_evaluate = NULL,
  standardized = NULL,
  unstandardized = !standardized,
  ...
)
## S3 method for class 'dfrr'
fitted(
  object,
  return.fourier.coefs = NULL,
  return.evaluations = !return.fourier.coefs,
  time_to_evaluate = NULL,
  standardized = NULL,
  unstandardized = !standardized,
  ...
)

Arguments

`object`	a fitted `dfrr`-object obtained from invoking the function `dfrr`.
`return.fourier.coefs`, `return.evaluations`	a `boolean` indicating whether the Fourier coefficients of the fitted curves are returned (`return.fourier.coefs=TRUE`), or evaluations of the fitted curves (`return.evaluations=TRUE`). Defaults to `return.fourier.coefs=TRUE`.
`time_to_evaluate`	a numeric vector indicating the set of time points for evaluating the fitted latent functions, for the case of `return.evaluations=TRUE`.
`standardized`, `unstandardized`	a `boolean` indicating whether stanadrdized/unstandardized fitted latent curves is reported. Only standardized fitted curves are identifiable, thus the arugment is defaults to `standardized=TRUE`.
`...`	dot argument, just for consistency with the generic function

Details

This function will return either the Fourier coefficients or the evaluation of fitted curves to the binary sequences. Fourier coefficients which are reported are based on the a set of basis which can be determined by basis(dfrr_fit). Thus the evaluation of fitted latent curves on the set of time points specified by vector time, equals to fitted(dfrr_fit)%*%t(eval.basis(time,basis(dfrr_fit))).

Consider that the unstandardized estimations are not identifiable. So, it is recommended to extract and report the standardized estimations.

Examples

set.seed(2000)
N<-50;M<-24

X<-rnorm(N,mean=0)
time<-seq(0,1,length.out=M)
Y<-simulate_simple_dfrr(beta0=function(t){cos(pi*t+pi)},
                        beta1=function(t){2*t},
                        X=X,time=time)
dfrr_fit<-dfrr(Y~X,yind=time)

fitteds<-fitted(dfrr_fit)
plot(fitteds)

set.seed(2000)
N<-50;M<-24

X<-rnorm(N,mean=0)
time<-seq(0,1,length.out=M)
Y<-simulate_simple_dfrr(beta0=function(t){cos(pi*t+pi)},
                        beta1=function(t){2*t},
                        X=X,time=time)
dfrr_fit<-dfrr(Y~X,yind=time)

fitteds<-fitted(dfrr_fit)
plot(fitteds)

Functional principal component analysis of a dfrr fit

Description

fpca() returns estimations of the smooth principal components/eigen-functions and the corresponding eigen-values of the residual function in the dfrr model. The result is a named list containing the vector of eigen-values and the matrix of Fourier coefficients. See Details.

Usage

fpca(object, standardized = NULL, unstandardized = !standardized)
fpca(object, standardized = NULL, unstandardized = !standardized)

Arguments

`object`	a fitted `dfrr`-object obtained from invoking the function `dfrr`.
`standardized`, `unstandardized`	a `boolean` indicating whether stanadrdized/unstandardized pricipal components/eigen-functions are reported. Only standardized pricipal components/eigen-functions are identifiable, thus the arugment is defaults to `standardized=TRUE`.

Details

Fourier coefficients which are reported are based on the a set of basis which can be determined by basis(dfrr_fit). Thus the evaluation of pricipal component/eigen-function on the set of time points specified by vector time, equals to fpca(dfrr_fit)%*%t(eval.basis(time,basis(dfrr_fit))).

Consider that the unstandardized estimations are not identifiable. So, it is recommended to extract and report the standardized estimations.

Value

fpca(dfrr_fit) returns a list containtng the following components:

`values`	a vector containing the eigen-values of the standaridized/unstandardized covariance operator of the residual function term in `dfrr` model, sorted in decreasing order.
`vectors`	a matrix whose columns contain the Fourier coefficients of the principal components/eigen-functions of the standaridized/unstandardized covariance operator of the residual function term in `dfrr` model, sorted based on the corresponding eigen-values.

Examples

set.seed(2000)
N<-50;M<-24

X<-rnorm(N,mean=0)
time<-seq(0,1,length.out=M)
Y<-simulate_simple_dfrr(beta0=function(t){cos(pi*t+pi)},
                        beta1=function(t){2*t},
                        X=X,time=time)
dfrr_fit<-dfrr(Y~X,yind=time)

fpcs<-fpca(dfrr_fit)
plot(fpcs,plot.eigen.functions=TRUE,plot.contour=TRUE,plot.3dsurface = TRUE)

set.seed(2000)
N<-50;M<-24

X<-rnorm(N,mean=0)
time<-seq(0,1,length.out=M)
Y<-simulate_simple_dfrr(beta0=function(t){cos(pi*t+pi)},
                        beta1=function(t){2*t},
                        X=X,time=time)
dfrr_fit<-dfrr(Y~X,yind=time)

fpcs<-fpca(dfrr_fit)
plot(fpcs,plot.eigen.functions=TRUE,plot.contour=TRUE,plot.3dsurface = TRUE)

Madras Longitudinal Schizophrenia Study.

Description

Monthly records of presence/abscence of psychiatric symptom 'thought disorder' of 86 patients over the first year after initial hospitalisation for disease.

Usage

madras
madras

Format

A data frame with 1032 observations and 5 variables

id: identification number of a patient
y: response 'thought disorder': 0 = absent, 1 = present
month: month since hospitalisation
age: age indicator: 0 = less than 20 years, 1 = 20 or over
gender: sex indicator: 0 = male, 1 = female

Source

Diggle PJ, Heagerty P, Liang KY, Zeger SL (2002). The analysis of Longitudinal Data, second ed., pp. 234-43. Oxford University Press, Oxford.
<http://faculty.washington.edu/heagerty/Books/AnalysisLongitudinal/datasets.html>

References

Jokinen J. Fast estimation algorithm for likelihood-based analysis of repeated categorical responses. Computational Statistics and Data Analysis 2006; 51:1509-1522.

Obtain model matrix for a dfrr fit

Description

Obtain model matrix for a dfrr fit

Usage

## S3 method for class 'dfrr'
model.matrix(object, ...)
## S3 method for class 'dfrr'
model.matrix(object, ...)

Arguments

`object`	a `dfrr`-object
`...`	dot argument, just for consistency with the generic function

Plot dfrr coefficients

Description

Plot a coef.dfrr object. The output is the plot of regression coefficients.

Usage

## S3 method for class 'coef.dfrr'
plot(x, select = NULL, ask.hit.return = TRUE, ...)
## S3 method for class 'coef.dfrr'
plot(x, select = NULL, ask.hit.return = TRUE, ...)

Arguments

`x`	a `coef.dfrr`-object.
`select`	a vector of length one or more of indices of regression coefficients to plot.
`ask.hit.return`	a boolean indicating whether to wait for interaction of the user between any two plots.
`...`	graphical parameters passed to `plot`.

Examples

set.seed(2000)
N<-50;M<-24

X<-rnorm(N,mean=0)
time<-seq(0,1,length.out=M)
Y<-simulate_simple_dfrr(beta0=function(t){cos(pi*t+pi)},
                        beta1=function(t){2*t},
                        X=X,time=time)
dfrr_fit<-dfrr(Y~X,yind=time)

coefs<-coef(dfrr_fit)
plot(coefs)

set.seed(2000)
N<-50;M<-24

X<-rnorm(N,mean=0)
time<-seq(0,1,length.out=M)
Y<-simulate_simple_dfrr(beta0=function(t){cos(pi*t+pi)},
                        beta1=function(t){2*t},
                        X=X,time=time)
dfrr_fit<-dfrr(Y~X,yind=time)

coefs<-coef(dfrr_fit)
plot(coefs)

Plot a dfrr fit

Description

Plot the regression coefficients, principal components, kernel function and residuals of a dfrr-object.

Usage

## S3 method for class 'dfrr'
plot(x, plot.kernel = TRUE, ...)
## S3 method for class 'dfrr'
plot(x, plot.kernel = TRUE, ...)

Arguments

`x`	the output of the function fitted.dfrr
`plot.kernel`	a boolean indicating whether plots the kernel function or not. `ggplot2`-package and `plotly`-package is required to plot contour and 3d surface of kernel function.
`...`	graphical parameters passed to `plot.coef.dfrr`

Details

The contour plot of the kernel function is produced if the package ggplot2 is installed. Plotting the 3d surface of the kernel function is also depends on the package plotly. To produce the qq-plot, the package car must be installed.

Examples

set.seed(2000)
N<-50;M<-24

X<-rnorm(N,mean=0)
time<-seq(0,1,length.out=M)
Y<-simulate_simple_dfrr(beta0=function(t){cos(pi*t+pi)},
                        beta1=function(t){2*t},
                        X=X,time=time)
dfrr_fit<-dfrr(Y~X,yind=time)

plot(dfrr_fit)


set.seed(2000)
N<-50;M<-24

X<-rnorm(N,mean=0)
time<-seq(0,1,length.out=M)
Y<-simulate_simple_dfrr(beta0=function(t){cos(pi*t+pi)},
                        beta1=function(t){2*t},
                        X=X,time=time)
dfrr_fit<-dfrr(Y~X,yind=time)

plot(dfrr_fit)

Plot dfrr fitted latent functions

Description

Plot a fitted.dfrr object.

Usage

## S3 method for class 'fitted.dfrr'
plot(
  x,
  id = NULL,
  main = NULL,
  col = "blue",
  lwd = 2,
  lty = "solid",
  cex.circle = 1,
  col.circle = "black",
  ylim = NULL,
  ...
)
## S3 method for class 'fitted.dfrr'
plot(
  x,
  id = NULL,
  main = NULL,
  col = "blue",
  lwd = 2,
  lty = "solid",
  cex.circle = 1,
  col.circle = "black",
  ylim = NULL,
  ...
)

Arguments

`x`	the output of the function fitted.dfrr
`id`	a vector of length one or more containing subject ids to plot. Must be matched with `rownames(<response>)` or the `.obs` column of `ydata`. Defaults to all subject ids.
`main`	a vector of length one or `length(id)` containing the title of plots.
`col`, `lwd`, `lty`, `...`	graphical parameters passed to `plot`
`cex.circle`, `col.circle`	size and color of circles and filled circles.
`ylim`	a vector of length two indicating the range of y-axis of the plot.

Details

The output is the plot of latent curves over the observed binary sequence. The binary sequence is illustrated with circles and filled circles for the values of zero and one, respectively.

Examples

set.seed(2000)
N<-50;M<-24

X<-rnorm(N,mean=0)
time<-seq(0,1,length.out=M)
Y<-simulate_simple_dfrr(beta0=function(t){cos(pi*t+pi)},
                        beta1=function(t){2*t},
                        X=X,time=time)
dfrr_fit<-dfrr(Y~X,yind=time)

fitteds<-fitted(dfrr_fit)
plot(fitteds)

set.seed(2000)
N<-50;M<-24

X<-rnorm(N,mean=0)
time<-seq(0,1,length.out=M)
Y<-simulate_simple_dfrr(beta0=function(t){cos(pi*t+pi)},
                        beta1=function(t){2*t},
                        X=X,time=time)
dfrr_fit<-dfrr(Y~X,yind=time)

fitteds<-fitted(dfrr_fit)
plot(fitteds)

Plot dfrr functional principal components

Description

Plot a fpca.dfrr object.

Usage

## S3 method for class 'fpca.dfrr'
plot(
  x,
  plot.eigen.functions = TRUE,
  select = NULL,
  plot.contour = FALSE,
  plot.3dsurface = FALSE,
  plot.contour.pars = list(breaks = NULL, minor_breaks = NULL, n.breaks = NULL, labels
    = NULL, limits = NULL, colors = NULL, xlab = NULL, ylab = NULL, title = NULL),
  plot.3dsurface.pars = list(xlab = NULL, ylab = NULL, zlab = NULL, title = NULL,
    colors = NULL),
  ask.hit.return = TRUE,
  ...
)
## S3 method for class 'fpca.dfrr'
plot(
  x,
  plot.eigen.functions = TRUE,
  select = NULL,
  plot.contour = FALSE,
  plot.3dsurface = FALSE,
  plot.contour.pars = list(breaks = NULL, minor_breaks = NULL, n.breaks = NULL, labels
    = NULL, limits = NULL, colors = NULL, xlab = NULL, ylab = NULL, title = NULL),
  plot.3dsurface.pars = list(xlab = NULL, ylab = NULL, zlab = NULL, title = NULL,
    colors = NULL),
  ask.hit.return = TRUE,
  ...
)

Arguments

`x`	a `fpca.dfrr`-object to be plotted. It is the output of the function `fpca()`
`plot.eigen.functions`	a `boolean` indicating whether to print the principal components/eigen-functions. Defaults to TRUE.
`select`	a vector of length one or more of indices of eigenfunctions to be plotted.
`plot.contour`	a `boolean` indicating whether to print the contour plot of the kernel function. It requires `ggplot2-package` to be installed. Defaults to FALSE.
`plot.3dsurface`	a `boolean` indicating whether to print the 3d surface plot of the kernel function. It requires the package `plotly` to be installed. Defaults to FALSE.
`plot.contour.pars`	a named list of graphical parameters passed to the function `ggplot`.
`plot.3dsurface.pars`	a named list of graphical parameters passed to the function `plot_ly`.
`ask.hit.return`	a boolean indicating whether to wait for interaction of the user between any two plots.
`...`	graphical parameters passed to `plot` function in drawing 2D eigenfunctions.

Details

This function plots the functional principal components, contour plot and 3d surface of the kernel function.

If ggplot2-package is installed, the contour plot of the kernel function is produced by setting the argument plot.contour=TRUE. Some graphical parameters of the contour plot can be modified by setting the (optional) argument plot.contour.pars.

If the package plotly is installed, the 3d surface of the kernel function is produced by setting the argument plot.3dsurface=TRUE. Some graphical parameters of the 3d surface can be modified by setting the (optional) argument plot.3dsurface.pars.

Examples

set.seed(2000)
N<-50;M<-24

X<-rnorm(N,mean=0)
time<-seq(0,1,length.out=M)
Y<-simulate_simple_dfrr(beta0=function(t){cos(pi*t+pi)},
                        beta1=function(t){2*t},
                        X=X,time=time)
dfrr_fit<-dfrr(Y~X,yind=time)

fpcs<-fpca(dfrr_fit)
plot(fpcs,plot.eigen.functions=TRUE,plot.contour=TRUE,plot.3dsurface=TRUE)

set.seed(2000)
N<-50;M<-24

X<-rnorm(N,mean=0)
time<-seq(0,1,length.out=M)
Y<-simulate_simple_dfrr(beta0=function(t){cos(pi*t+pi)},
                        beta1=function(t){2*t},
                        X=X,time=time)
dfrr_fit<-dfrr(Y~X,yind=time)

fpcs<-fpca(dfrr_fit)
plot(fpcs,plot.eigen.functions=TRUE,plot.contour=TRUE,plot.3dsurface=TRUE)

Plot dfrr predictions

Description

Plot a predict.dfrr object.

Usage

## S3 method for class 'predict.dfrr'
plot(
  x,
  id = NULL,
  main = id,
  col = "blue",
  lwd = 2,
  lty = "solid",
  cex.circle = 1,
  col.circle = "black",
  ylim = NULL,
  ...
)
## S3 method for class 'predict.dfrr'
plot(
  x,
  id = NULL,
  main = id,
  col = "blue",
  lwd = 2,
  lty = "solid",
  cex.circle = 1,
  col.circle = "black",
  ylim = NULL,
  ...
)

Arguments

`x`	a `predict.dfrr`-object
`id`	a vector of length one or more containing subject ids to plot. Must be matched with `rownames(newdata)`. Defaults to all subject ids.
`main`	a vector of length one or `length(id)` containing the title of plots.
`col`, `lwd`, `lty`, `...`	graphical parameters passed to `plot`
`cex.circle`, `col.circle`	size and color of circles and filled circles.
`ylim`	a vector of length two indicating the range of y-axis of the plot.

Details

The output is the plot of predictions of latent functions given the new covariates. For the case in which newydata is also given, the predictions are plotted over the observed binary sequence. The binary sequence is illustrated with circles and filled circles for the values of zero and one, respectively.

References

Choi, H., & Reimherr, M. A geometric approach to confidence regions and bands for functional parameters . Journal of the Royal Statistical Society, Series B Statistical methodology 2018; 80:239-260.

Examples

set.seed(2000)
N<-50;M<-24

X<-rnorm(N,mean=0)
time<-seq(0,1,length.out=M)
Y<-simulate_simple_dfrr(beta0=function(t){cos(pi*t+pi)},
                        beta1=function(t){2*t},
                        X=X,time=time)
dfrr_fit<-dfrr(Y~X,yind=time)


newdata<-data.frame(X=c(1,0))
  preds<-predict(dfrr_fit,newdata=newdata)
  plot(preds)

newdata<-data.frame(X=c(1,0))
newydata<-data.frame(.obs=rep(1,5),.index=c(0.0,0.1,0.2,0.3,0.7),.value=c(1,1,1,0,0))
preds<-predict(dfrr_fit,newdata=newdata,newydata = newydata)
plot(preds)

set.seed(2000)
N<-50;M<-24

X<-rnorm(N,mean=0)
time<-seq(0,1,length.out=M)
Y<-simulate_simple_dfrr(beta0=function(t){cos(pi*t+pi)},
                        beta1=function(t){2*t},
                        X=X,time=time)
dfrr_fit<-dfrr(Y~X,yind=time)


newdata<-data.frame(X=c(1,0))
  preds<-predict(dfrr_fit,newdata=newdata)
  plot(preds)

newdata<-data.frame(X=c(1,0))
newydata<-data.frame(.obs=rep(1,5),.index=c(0.0,0.1,0.2,0.3,0.7),.value=c(1,1,1,0,0))
preds<-predict(dfrr_fit,newdata=newdata,newydata = newydata)
plot(preds)

QQ-plot for dfrr residuals

Description

The output gives the qq-plot of estimated measurment error.

Usage

## S3 method for class 'residuals.dfrr'
plot(x, ...)

## S3 method for class 'dfrr'
qq(x, ...)
## S3 method for class 'residuals.dfrr'
plot(x, ...)

## S3 method for class 'dfrr'
qq(x, ...)

Arguments

`x`	a `residuals.dfrr`-object.
`...`	graphical parameters passed to `car::qqPlot`

Examples


N<-50;M<-24

X<-rnorm(N,mean=0)
time<-seq(0,1,length.out=M)
Y<-simulate_simple_dfrr(beta0=function(t){cos(pi*t+pi)},
                        beta1=function(t){2*t},
                        X=X,time=time)
dfrr_fit<-dfrr(Y~X,yind=time)

resid<-residuals(dfrr_fit)
plot(resid)
#qq(dfrr_fit)

N<-50;M<-24

X<-rnorm(N,mean=0)
time<-seq(0,1,length.out=M)
Y<-simulate_simple_dfrr(beta0=function(t){cos(pi*t+pi)},
                        beta1=function(t){2*t},
                        X=X,time=time)
dfrr_fit<-dfrr(Y~X,yind=time)

resid<-residuals(dfrr_fit)
plot(resid)
#qq(dfrr_fit)

Prediction for dichotomized function-on-scalar regression

Description

Takes a dfrr-object created by dfrr() and returns predictions given a new set of values for a model covariates and an optional ydata-like data.frame of observations for the dichotomized response.

Usage

## S3 method for class 'dfrr'
predict(
  object,
  newdata,
  newydata = NULL,
  standardized = NULL,
  unstandardized = !standardized,
  return.fourier.coefs = NULL,
  return.evaluations = !return.fourier.coefs,
  time_to_evaluate = NULL,
  ...
)
## S3 method for class 'dfrr'
predict(
  object,
  newdata,
  newydata = NULL,
  standardized = NULL,
  unstandardized = !standardized,
  return.fourier.coefs = NULL,
  return.evaluations = !return.fourier.coefs,
  time_to_evaluate = NULL,
  ...
)

Arguments

`object`	a fitted `dfrr`-object obtained from invoking the function `dfrr`.
`newdata`	a `data.frame` containing the values of all of the model covariates at which the latent functional response is going to be predicted.
`newydata`	(optional) a `ydata`-like `data.frame` containing the values of dichotomized response sparsly observed in the domain of function.
`standardized`, `unstandardized`	a `boolean` indicating whether stanadrdized/unstandardized predictions are reported. Defaults to `standardized=TRUE`.
`return.fourier.coefs`, `return.evaluations`	a `boolean` indicating whether the Fourier coefficients of predictions are returned (`return.fourier.coefs=TRUE`), or evaluations of the predictions (`return.evaluations=TRUE`). Defaults to `return.evaluations=TRUE`.
`time_to_evaluate`	a numeric vector indicating the set of time points for evaluating the predictions, for the case of `return.evaluations=TRUE`.
`...`	dot argument, just for consistency with the generic function

Details

This function will return either the Fourier coefficients or the evaluation of predictions. Fourier coefficients which are reported are based on the a set of basis which can be determined by basis(dfrr_fit). Thus the evaluation of predictions on the set of time points specified by vector time, equals to fitted(dfrr_fit,return.fourier.coefs=T)%*%t(eval.basis(time,basis(dfrr_fit))).

Examples

set.seed(2000)
N<-50;M<-24

X<-rnorm(N,mean=0)
time<-seq(0,1,length.out=M)
Y<-simulate_simple_dfrr(beta0=function(t){cos(pi*t+pi)},
                        beta1=function(t){2*t},
                        X=X,time=time)
dfrr_fit<-dfrr(Y~X,yind=time)


newdata<-data.frame(X=c(1,0))
  preds<-predict(dfrr_fit,newdata=newdata)
  plot(preds)

newdata<-data.frame(X=c(1,0))
newydata<-data.frame(.obs=rep(1,5),.index=c(0.0,0.1,0.2,0.3,0.7),.value=c(1,1,1,0,0))
preds<-predict(dfrr_fit,newdata=newdata,newydata = newydata)
plot(preds)

set.seed(2000)
N<-50;M<-24

X<-rnorm(N,mean=0)
time<-seq(0,1,length.out=M)
Y<-simulate_simple_dfrr(beta0=function(t){cos(pi*t+pi)},
                        beta1=function(t){2*t},
                        X=X,time=time)
dfrr_fit<-dfrr(Y~X,yind=time)


newdata<-data.frame(X=c(1,0))
  preds<-predict(dfrr_fit,newdata=newdata)
  plot(preds)

newdata<-data.frame(X=c(1,0))
newydata<-data.frame(.obs=rep(1,5),.index=c(0.0,0.1,0.2,0.3,0.7),.value=c(1,1,1,0,0))
preds<-predict(dfrr_fit,newdata=newdata,newydata = newydata)
plot(preds)

qq-plot Generic function

Description

This is a generic function for qq() method.

Usage

qq(x, ...)
qq(x, ...)

Arguments

`x`	an object
`...`	extra parameters passed to S3 methods

Obtain residuals for a dfrr model

Description

Returns the residuals of a fitted dfrr model. A dfrr model is of the form:

$Y_{i}(t)=I(W_{i}(t)>0),$

in which $I(.)$ is the indicator function and $W_{i}(t)=Z_{i}(t)+\epsilon_{i}(t)\times\sigma^2$ , where $Z_{i}(t)$ is the functional part of the model and $epsilon_{i}(t)\times\sigma^2$ is the measurement error. The functional part of the model, consisting a location and a residual function of the form:

$Z_{i}(t)=\sum_{j=1}^{q}\beta_{j}(t)*x_{ji}+\varepsilon_{i}(t),$

and $\epsilon_{i}(t)$ are iid standard normal for each $i$ and $t$ . The residuals reported in the output of this functions is the estimation of the measurement error of the model i.e. $\epsilon_{i}(t)\times\sigma^2$ , which is estimated by:

$E(W_{i}(t)-Z_{i}(t)\mid Y_{i}(t)).$

Usage

## S3 method for class 'dfrr'
residuals(object, standardized = NULL, unstandardized = !standardized, ...)
## S3 method for class 'dfrr'
residuals(object, standardized = NULL, unstandardized = !standardized, ...)

Arguments

`object`	a fitted `dfrr`-object obtained from invoking the function `dfrr`.
`standardized`, `unstandardized`	a `boolean` indicating whether stanadrdized/unstandardized residuals are reported. Defaults to `standardized=TRUE`.
`...`	dot argument, just for consistency with the generic function

Examples

set.seed(2000)
N<-50;M<-24

X<-rnorm(N,mean=0)
time<-seq(0,1,length.out=M)
Y<-simulate_simple_dfrr(beta0=function(t){cos(pi*t+pi)},
                        beta1=function(t){2*t},
                        X=X,time=time)
dfrr_fit<-dfrr(Y~X,yind=time)

resid<-residuals(dfrr_fit)

plot(resid)
#qq(dfrr_fit)

set.seed(2000)
N<-50;M<-24

X<-rnorm(N,mean=0)
time<-seq(0,1,length.out=M)
Y<-simulate_simple_dfrr(beta0=function(t){cos(pi*t+pi)},
                        beta1=function(t){2*t},
                        X=X,time=time)
dfrr_fit<-dfrr(Y~X,yind=time)

resid<-residuals(dfrr_fit)

plot(resid)
#qq(dfrr_fit)

Simulating a Simple `dfrr` Model

Description

Simulation from a simple dfrr model:

$Y_{i}(t)=I(\beta_0(t)+\beta_1(t)*x_{i}+\varepsilon_{i}(t)+\epsilon_{i}(t)\times\sigma^2>0),$

where $I(.)$ is the indicator function, $\varepsilon_{i}$ is a Gaussian random function, and $\epsilon_{i}(t)$ are iid standard normal for each $i$ and $t$ independent of $\varepsilon_{i}$ . For demonstration purpose only.

Usage

simulate_simple_dfrr(
  beta0 = function(t) {     cos(pi * t + pi) },
  beta1 = function(t) {     2 * t },
  X = rnorm(50),
  time = seq(0, 1, length.out = 24),
  sigma2 = 0.2
)
simulate_simple_dfrr(
  beta0 = function(t) {     cos(pi * t + pi) },
  beta1 = function(t) {     2 * t },
  X = rnorm(50),
  time = seq(0, 1, length.out = 24),
  sigma2 = 0.2
)

Arguments

`beta0`, `beta1`	(optional) functional intercept and slope parameters
`X`	an (optional) vector consists of scalar covariate
`time`	an (optional) vector of time points for which, each sample curve is observed at.
`sigma2`	variance of the measurement error in the `dfrr` model

Examples

N<-50;M<-24
X<-rnorm(N,mean=0)
time<-seq(0,1,length.out=M)
Y<-simulate_simple_dfrr(beta0=function(t){cos(pi*t+pi)},
                        beta1=function(t){2*t},
                        X=X,time=time)
N<-50;M<-24
X<-rnorm(N,mean=0)
time<-seq(0,1,length.out=M)
Y<-simulate_simple_dfrr(beta0=function(t){cos(pi*t+pi)},
                        beta1=function(t){2*t},
                        X=X,time=time)

Summary for a dfrr fit

Description

Summarise a fitted dfrr-object. Not implemented.

Usage

## S3 method for class 'dfrr'
summary(object, ...)
## S3 method for class 'dfrr'
summary(object, ...)

Arguments

`object`	a `dfrr`-object
`...`	dot argument, just for consistency with the generic function

Package 'dfrr'

Help Index

dfrr: Dichotomized Functional Response Regression

Description

Details

Author(s)

References

See Also

Examples

Get the basis functions from a dfrr-object

Description

Usage

Arguments

Examples

Get estimated coefficients from a dfrr fit

Description

Usage

Arguments

Details

See Also

Examples

Dichotomized Functional Response Regression

Description

Usage

Arguments

Details

Examples

Obtain fitted curves for a dfrr model

Description

Usage

Arguments

Details

See Also

Examples

Functional principal component analysis of a dfrr fit

Description

Usage

Arguments

Details

Value

See Also

Examples

Madras Longitudinal Schizophrenia Study.

Description

Usage

Format

Source

References

Obtain model matrix for a dfrr fit

Description

Usage

Arguments

Plot dfrr coefficients

Description

Usage

Arguments

Examples

Plot a dfrr fit

Description

Usage

Arguments

Details

Examples

Plot dfrr fitted latent functions

Description

Usage

Arguments

Details

Examples

Plot dfrr functional principal components

Description

Usage

Arguments

Details

Examples

Plot dfrr predictions

Description

Usage

Arguments

Details

Simulating a Simple `dfrr` Model