Package 'LongituRF' reference manual

Title:	Random Forests for Longitudinal Data
Description:	Random forests are a statistical learning method widely used in many areas of scientific research essentially for its ability to learn complex relationships between input and output variables and also its capacity to handle high-dimensional data. However, current random forests approaches are not flexible enough to handle longitudinal data. In this package, we propose a general approach of random forests for high-dimensional longitudinal data. It includes a flexible stochastic model which allows the covariance structure to vary over time. Furthermore, we introduce a new method which takes intra-individual covariance into consideration to build random forests. The method is fully detailled in Capitaine et.al. (2020) <doi:10.1177/0962280220946080> Random forests for high-dimensional longitudinal data.
Authors:	Louis Capitaine [aut, cre]
Maintainer:	Louis Capitaine <[email protected]>
License:	GPL-2
Version:	0.9
Built:	2025-01-22 05:42:00 UTC
Source:	https://github.com/sistm/longiturf

Longitudinal data generator

Description

Simulate longitudinal data according to the semi-parametric stochastic mixed-effects model given by:

$Y_i(t)=f(X_i(t))+Z_i(t)\beta_i + \omega_i(t)+\epsilon_i$

with $Y_i(t)$ the output at time $t$ for the $i$ th individual; $X_i(t)$ the input predictors (fixed effects) at time $t$ for the $i$ th individual; $Z_i(t)$ are the random effects at time $t$ for the $i$ th individual; $\omega_i(t)$ is a Brownian motion with volatility $\gamma^2=0.8$ at time $t$ for the $i$ th individual; $\epsilon_i$ is the residual error with variance $\sigma^2=0.5$ . The data are simulated according to the simulations in low dimensional in the low dimensional scheme of the paper <doi:10.1177/0962280220946080>

Usage

DataLongGenerator(n = 50, p = 6, G = 6)
DataLongGenerator(n = 50, p = 6, G = 6)

Arguments

`n`	[numeric]: Number of individuals. The default value is `n=50`.
`p`	[numeric]: Number of predictors. The default value is `p=6`.
`G`	[numeric]: Number of groups of predictors with temporal behavior, generates `p-G` input variables with no temporal behavior.

Value

a list of the following elements:

Y: vector of the output trajectories.
X : matrix of the fixed-effects predictors.
Z: matrix of the random-effects predictors.
id: vector of the identifiers for each individual.
time: vector the the time measurements for each individual.

Examples

oldpar <- par()
oldopt <- options()
data <- DataLongGenerator(n=17, p=6,G=6) # Generate the data
# Let's see the output :
w <- which(data$id==1)
plot(data$time[w],data$Y[w],type="l",ylim=c(min(data$Y),max(data$Y)), col="grey")
for (i in unique(data$id)){
  w <- which(data$id==i)
  lines(data$time[w],data$Y[w], col='grey')
}
# Let's see the fixed effects predictors:
par(mfrow=c(2,3), mar=c(2,3,3,2))
for (i in 1:ncol(data$X)){
  w <- which(data$id==1)
  plot(data$time[w],data$X[w,i], col="grey",ylim=c(min(data$X[,i]),
  max(data$X[,i])),xlim=c(1,max(data$time)),main=latex2exp::TeX(paste0("$X^{(",i,")}$")))
  for (k in unique(data$id)){
    w <- which(data$id==k)
    lines(data$time[w],data$X[w,i], col="grey")
  }
}
par(oldpar)
options(oldopt)

oldpar <- par()
oldopt <- options()
data <- DataLongGenerator(n=17, p=6,G=6) # Generate the data
# Let's see the output :
w <- which(data$id==1)
plot(data$time[w],data$Y[w],type="l",ylim=c(min(data$Y),max(data$Y)), col="grey")
for (i in unique(data$id)){
  w <- which(data$id==i)
  lines(data$time[w],data$Y[w], col='grey')
}
# Let's see the fixed effects predictors:
par(mfrow=c(2,3), mar=c(2,3,3,2))
for (i in 1:ncol(data$X)){
  w <- which(data$id==1)
  plot(data$time[w],data$X[w,i], col="grey",ylim=c(min(data$X[,i]),
  max(data$X[,i])),xlim=c(1,max(data$time)),main=latex2exp::TeX(paste0("$X^{(",i,")}$")))
  for (k in unique(data$id)){
    w <- which(data$id==k)
    lines(data$time[w],data$X[w,i], col="grey")
  }
}
par(oldpar)
options(oldopt)

(S)MERF algorithm

Description

(S)MERF is an adaptation of the random forest regression method to longitudinal data introduced by Hajjem et. al. (2014) <doi:10.1080/00949655.2012.741599>. The model has been improved by Capitaine et. al. (2020) <doi:10.1177/0962280220946080> with the addition of a stochastic process. The algorithm will estimate the parameters of the following semi-parametric stochastic mixed-effects model:

$Y_i(t)=f(X_i(t))+Z_i(t)\beta_i + \omega_i(t)+\epsilon_i$

with $Y_i(t)$ the output at time $t$ for the $i$ th individual; $X_i(t)$ the input predictors (fixed effects) at time $t$ for the $i$ th individual; $Z_i(t)$ are the random effects at time $t$ for the $i$ th individual; $\omega_i(t)$ is the stochastic process at time $t$ for the $i$ th individual which model the serial correlations of the output measurements; $\epsilon_i$ is the residual error.

Usage

MERF(
  X,
  Y,
  id,
  Z,
  iter = 100,
  mtry = ceiling(ncol(X)/3),
  ntree = 500,
  time,
  sto,
  delta = 0.001
)
MERF(
  X,
  Y,
  id,
  Z,
  iter = 100,
  mtry = ceiling(ncol(X)/3),
  ntree = 500,
  time,
  sto,
  delta = 0.001
)

Arguments

`X`	[matrix]: A `N`x`p` matrix containing the `p` predictors of the fixed effects, column codes for a predictor.
`Y`	[vector]: A vector containing the output trajectories.
`id`	[vector]: Is the vector of the identifiers for the different trajectories.
`Z`	[matrix]: A `N`x`q` matrix containing the `q` predictor of the random effects.
`iter`	[numeric]: Maximal number of iterations of the algorithm. The default is set to `iter=100`
`mtry`	[numeric]: Number of variables randomly sampled as candidates at each split. The default value is `p/3`.
`ntree`	[numeric]: Number of trees to grow. This should not be set to too small a number, to ensure that every input row gets predicted at least a few times. The default value is `ntree=500`.
`time`	[vector]: Is the vector of the measurement times associated with the trajectories in `Y`,`Z` and `X`.
`sto`	[character]: Defines the covariance function of the stochastic process, can be either `"none"` for no stochastic process, `"BM"` for Brownian motion, `OrnUhl` for standard Ornstein-Uhlenbeck process, `BBridge` for Brownian Bridge, `fbm` for Fractional Brownian motion; can also be a function defined by the user.
`delta`	[numeric]: The algorithm stops when the difference in log likelihood between two iterations is smaller than `delta`. The default value is set to O.O01

Value

A fitted (S)MERF model which is a list of the following elements:

forest: Random forest obtained at the last iteration.
random_effects : Predictions of random effects for different trajectories.
id_btilde: Identifiers of individuals associated with the predictions random_effects.
var_random_effects: Estimation of the variance covariance matrix of random effects.
sigma_sto: Estimation of the volatility parameter of the stochastic process.
sigma: Estimation of the residual variance parameter.
time: The vector of the measurement times associated with the trajectories in Y,Z and X.
sto: Stochastic process used in the model.
Vraisemblance: Log-likelihood of the different iterations.
id: Vector of the identifiers for the different trajectories.
OOB: OOB error of the fitted random forest at each iteration.

Examples

set.seed(123)
data <- DataLongGenerator(n=20) # Generate the data composed by n=20 individuals.
# Train a SMERF model on the generated data. Should take ~ 50 seconds
# The data are generated with a Brownian motion,
# so we use the parameter sto="BM" to specify a Brownian motion as stochastic process
smerf <- MERF(X=data$X,Y=data$Y,Z=data$Z,id=data$id,time=data$time,mtry=2,ntree=500,sto="BM")
smerf$forest # is the fitted random forest (obtained at the last iteration).
smerf$random_effects # are the predicted random effects for each individual.
smerf$omega # are the predicted stochastic processes.
plot(smerf$Vraisemblance) # evolution of the log-likelihood.
smerf$OOB # OOB error at each iteration.


set.seed(123)
data <- DataLongGenerator(n=20) # Generate the data composed by n=20 individuals.
# Train a SMERF model on the generated data. Should take ~ 50 seconds
# The data are generated with a Brownian motion,
# so we use the parameter sto="BM" to specify a Brownian motion as stochastic process
smerf <- MERF(X=data$X,Y=data$Y,Z=data$Z,id=data$id,time=data$time,mtry=2,ntree=500,sto="BM")
smerf$forest # is the fitted random forest (obtained at the last iteration).
smerf$random_effects # are the predicted random effects for each individual.
smerf$omega # are the predicted stochastic processes.
plot(smerf$Vraisemblance) # evolution of the log-likelihood.
smerf$OOB # OOB error at each iteration.

(S)MERT algorithm

Description

(S)MERT is an adaptation of the random forest regression method to longitudinal data introduced by Hajjem et. al. (2011) <doi:10.1016/j.spl.2010.12.003>. The model has been improved by Capitaine et. al. (2020) <doi:10.1177/0962280220946080> with the addition of a stochastic process. The algorithm will estimate the parameters of the following semi-parametric stochastic mixed-effects model:

$Y_i(t)=f(X_i(t))+Z_i(t)\beta_i + \omega_i(t)+\epsilon_i$

with $Y_i(t)$ the output at time $t$ for the $i$ th individual; $X_i(t)$ the input predictors (fixed effects) at time $t$ for the $i$ th individual; $Z_i(t)$ are the random effects at time $t$ for the $i$ th individual; $\omega_i(t)$ is the stochastic process at time $t$ for the $i$ th individual which model the serial correlations of the output measurements; $\epsilon_i$ is the residual error.

Usage

MERT(X, Y, id, Z, iter = 100, time, sto, delta = 0.001)
MERT(X, Y, id, Z, iter = 100, time, sto, delta = 0.001)

Arguments

`X`	[matrix]: A `N`x`p` matrix containing the `p` predictors of the fixed effects, column codes for a predictor.
`Y`	[vector]: A vector containing the output trajectories.
`id`	[vector]: Is the vector of the identifiers for the different trajectories.
`Z`	[matrix]: A `N`x`q` matrix containing the `q` predictor of the random effects.
`iter`	[numeric]: Maximal number of iterations of the algorithm. The default is set to `iter=100`
`time`	[vector]: Is the vector of the measurement times associated with the trajectories in `Y`,`Z` and `X`.
`sto`	[character]: Defines the covariance function of the stochastic process, can be either `"none"` for no stochastic process, `"BM"` for Brownian motion, `OrnUhl` for standard Ornstein-Uhlenbeck process, `BBridge` for Brownian Bridge, `fbm` for Fractional Brownian motion; can also be a function defined by the user.
`delta`	[numeric]: The algorithm stops when the difference in log likelihood between two iterations is smaller than `delta`. The default value is set to O.O01

Value

A fitted (S)MERF model which is a list of the following elements:

forest: Tree obtained at the last iteration.
random_effects : Predictions of random effects for different trajectories.
id_btilde: Identifiers of individuals associated with the predictions random_effects.
var_random_effects: Estimation of the variance covariance matrix of random effects.
sigma_sto: Estimation of the volatility parameter of the stochastic process.
sigma: Estimation of the residual variance parameter.
time: The vector of the measurement times associated with the trajectories in Y,Z and X.
sto: Stochastic process used in the model.
Vraisemblance: Log-likelihood of the different iterations.
id: Vector of the identifiers for the different trajectories.

Examples

set.seed(123)
data <- DataLongGenerator(n=20) # Generate the data composed by n=20 individuals.
# Train a SMERF model on the generated data. Should take ~ 50 secondes
# The data are generated with a Brownian motion,
# so we use the parameter sto="BM" to specify a Brownian motion as stochastic process
smert <- MERF(X=data$X,Y=data$Y,Z=data$Z,id=data$id,time=data$time,sto="BM")
smert$forest # is the fitted random forest (obtained at the last iteration).
smert$random_effects # are the predicted random effects for each individual.
smert$omega # are the predicted stochastic processes.
plot(smert$Vraisemblance) #evolution of the log-likelihood.


set.seed(123)
data <- DataLongGenerator(n=20) # Generate the data composed by n=20 individuals.
# Train a SMERF model on the generated data. Should take ~ 50 secondes
# The data are generated with a Brownian motion,
# so we use the parameter sto="BM" to specify a Brownian motion as stochastic process
smert <- MERF(X=data$X,Y=data$Y,Z=data$Z,id=data$id,time=data$time,sto="BM")
smert$forest # is the fitted random forest (obtained at the last iteration).
smert$random_effects # are the predicted random effects for each individual.
smert$omega # are the predicted stochastic processes.
plot(smert$Vraisemblance) #evolution of the log-likelihood.

Predict with longitudinal trees and random forests.

Description

Predict with longitudinal trees and random forests.

Usage

## S3 method for class 'longituRF'
predict(object, X, Z, id, time, ...)
## S3 method for class 'longituRF'
predict(object, X, Z, id, time, ...)

Arguments

`object`	: a `longituRF` output of (S)MERF; (S)REEMforest; (S)MERT or (S)REEMtree function.
`X`	[matrix]: matrix of the fixed effects for the new observations to be predicted.
`Z`	[matrix]: matrix of the random effects for the new observations to be predicted.
`id`	[vector]: vector of the identifiers of the new observations to be predicted.
`time`	[vector]: vector of the time measurements of the new observations to be predicted.
`...`	: low levels arguments.

Value

vector of the predicted output for the new observations.

Examples


set.seed(123)
data <- DataLongGenerator(n=20) # Generate the data composed by n=20 individuals.
REEMF <- REEMforest(X=data$X,Y=data$Y,Z=data$Z,id=data$id,time=data$time,mtry=2,ntree=500,sto="BM")
# Then we predict on the learning sample :
pred.REEMF <- predict(REEMF, X=data$X,Z=data$Z,id=data$id, time=data$time)
# Let's have a look at the predictions
# the predictions are in red while the real output trajectories are in blue:
par(mfrow=c(4,5),mar=c(2,2,2,2))
for (i in unique(data$id)){
  w <- which(data$id==i)
  plot(data$time[w],data$Y[w],type="l",col="blue")
  lines(data$time[w],pred.REEMF[w], col="red")
}
# Train error :
mean((pred.REEMF-data$Y)^2)

# The same function can be used with a fitted SMERF model:
smerf <-MERF(X=data$X,Y=data$Y,Z=data$Z,id=data$id,time=data$time,mtry=2,ntree=500,sto="BM")
pred.smerf <- predict(smerf, X=data$X,Z=data$Z,id=data$id, time=data$time)
# Train error :
mean((pred.smerf-data$Y)^2)
# This function can be used even on a MERF model (when no stochastic process is specified)
merf <-MERF(X=data$X,Y=data$Y,Z=data$Z,id=data$id,time=data$time,mtry=2,ntree=500,sto="none")
pred.merf <- predict(merf, X=data$X,Z=data$Z,id=data$id, time=data$time)
# Train error :
mean((pred.merf-data$Y)^2)


set.seed(123)
data <- DataLongGenerator(n=20) # Generate the data composed by n=20 individuals.
REEMF <- REEMforest(X=data$X,Y=data$Y,Z=data$Z,id=data$id,time=data$time,mtry=2,ntree=500,sto="BM")
# Then we predict on the learning sample :
pred.REEMF <- predict(REEMF, X=data$X,Z=data$Z,id=data$id, time=data$time)
# Let's have a look at the predictions
# the predictions are in red while the real output trajectories are in blue:
par(mfrow=c(4,5),mar=c(2,2,2,2))
for (i in unique(data$id)){
  w <- which(data$id==i)
  plot(data$time[w],data$Y[w],type="l",col="blue")
  lines(data$time[w],pred.REEMF[w], col="red")
}
# Train error :
mean((pred.REEMF-data$Y)^2)

# The same function can be used with a fitted SMERF model:
smerf <-MERF(X=data$X,Y=data$Y,Z=data$Z,id=data$id,time=data$time,mtry=2,ntree=500,sto="BM")
pred.smerf <- predict(smerf, X=data$X,Z=data$Z,id=data$id, time=data$time)
# Train error :
mean((pred.smerf-data$Y)^2)
# This function can be used even on a MERF model (when no stochastic process is specified)
merf <-MERF(X=data$X,Y=data$Y,Z=data$Z,id=data$id,time=data$time,mtry=2,ntree=500,sto="none")
pred.merf <- predict(merf, X=data$X,Z=data$Z,id=data$id, time=data$time)
# Train error :
mean((pred.merf-data$Y)^2)

(S)REEMforest algorithm

Description

(S)REEMforest algorithm

Usage

REEMforest(
  X,
  Y,
  id,
  Z,
  iter = 100,
  mtry,
  ntree = 500,
  time,
  sto,
  delta = 0.001
)
REEMforest(
  X,
  Y,
  id,
  Z,
  iter = 100,
  mtry,
  ntree = 500,
  time,
  sto,
  delta = 0.001
)

Arguments

`X`	[matrix]: A `N`x`p` matrix containing the `p` predictors of the fixed effects, column codes for a predictor.
`Y`	[vector]: A vector containing the output trajectories.
`id`	[vector]: Is the vector of the identifiers for the different trajectories.
`Z`	[matrix]: A `N`x`q` matrix containing the `q` predictor of the random effects.
`iter`	[numeric]: Maximal number of iterations of the algorithm. The default is set to `iter=100`
`mtry`	[numeric]: Number of variables randomly sampled as candidates at each split. The default value is `p/3`.
`ntree`	[numeric]: Number of trees to grow. This should not be set to too small a number, to ensure that every input row gets predicted at least a few times. The default value is `ntree=500`.
`time`	[time]: Is the vector of the measurement times associated with the trajectories in `Y`,`Z` and `X`.
`sto`	[character]: Defines the covariance function of the stochastic process, can be either `"none"` for no stochastic process, `"BM"` for Brownian motion, `OrnUhl` for standard Ornstein-Uhlenbeck process, `BBridge` for Brownian Bridge, `fbm` for Fractional Brownian motion; can also be a function defined by the user.
`delta`	[numeric]: The algorithm stops when the difference in log likelihood between two iterations is smaller than `delta`. The default value is set to O.O01

Details

(S)REEMforest is an adaptation of the random forest regression method to longitudinal data introduced by Capitaine et. al. (2020) <doi:10.1177/0962280220946080>. The algorithm will estimate the parameters of the following semi-parametric stochastic mixed-effects model:

$Y_i(t)=f(X_i(t))+Z_i(t)\beta_i + \omega_i(t)+\epsilon_i$

with $Y_i(t)$ the output at time $t$ for the $i$ th individual; $X_i(t)$ the input predictors (fixed effects) at time $t$ for the $i$ th individual; $Z_i(t)$ are the random effects at time $t$ for the $i$ th individual; $\omega_i(t)$ is the stochastic process at time $t$ for the $i$ th individual which model the serial correlations of the output measurements; $\epsilon_i$ is the residual error.

Value

A fitted (S)REEMforest model which is a list of the following elements:

forest: Random forest obtained at the last iteration.
random_effects : Predictions of random effects for different trajectories.
id_btilde: Identifiers of individuals associated with the predictions random_effects.
var_random_effects: Estimation of the variance covariance matrix of random effects.
sigma_sto: Estimation of the volatility parameter of the stochastic process.
sigma: Estimation of the residual variance parameter.
time: The vector of the measurement times associated with the trajectories in Y,Z and X.
sto: Stochastic process used in the model.
Vraisemblance: Log-likelihood of the different iterations.
id: Vector of the identifiers for the different trajectories.
OOB: OOB error of the fitted random forest at each iteration.

Examples


set.seed(123)
data <- DataLongGenerator(n=20) # Generate the data composed by n=20 individuals.
# Train a SREEMforest model on the generated data. Should take ~ 50 secondes
# The data are generated with a Brownian motion
#  so we use the parameter sto="BM" to specify a Brownian motion as stochastic process
SREEMF <- REEMforest(X=data$X,Y=data$Y,Z=data$Z,id=data$id,time=data$time,mtry=2,ntree=500,sto="BM")
SREEMF$forest # is the fitted random forest (obtained at the last iteration).
SREEMF$random_effects # are the predicted random effects for each individual.
SREEMF$omega # are the predicted stochastic processes.
plot(SREEMF$Vraisemblance) #evolution of the log-likelihood.
SREEMF$OOB # OOB error at each iteration.


set.seed(123)
data <- DataLongGenerator(n=20) # Generate the data composed by n=20 individuals.
# Train a SREEMforest model on the generated data. Should take ~ 50 secondes
# The data are generated with a Brownian motion
#  so we use the parameter sto="BM" to specify a Brownian motion as stochastic process
SREEMF <- REEMforest(X=data$X,Y=data$Y,Z=data$Z,id=data$id,time=data$time,mtry=2,ntree=500,sto="BM")
SREEMF$forest # is the fitted random forest (obtained at the last iteration).
SREEMF$random_effects # are the predicted random effects for each individual.
SREEMF$omega # are the predicted stochastic processes.
plot(SREEMF$Vraisemblance) #evolution of the log-likelihood.
SREEMF$OOB # OOB error at each iteration.

(S)REEMtree algorithm

Description

(S)REEMtree is an adaptation of the random forest regression method to longitudinal data introduced by Sela and Simonoff. (2012) <doi:10.1007/s10994-011-5258-3>. The algorithm will estimate the parameters of the following semi-parametric stochastic mixed-effects model:

$Y_i(t)=f(X_i(t))+Z_i(t)\beta_i + \omega_i(t)+\epsilon_i$

with $Y_i(t)$ the output at time $t$ for the $i$ th individual; $X_i(t)$ the input predictors (fixed effects) at time $t$ for the $i$ th individual; $Z_i(t)$ are the random effects at time $t$ for the $i$ th individual; $\omega_i(t)$ is the stochastic process at time $t$ for the $i$ th individual which model the serial correlations of the output measurements; $\epsilon_i$ is the residual error.

Usage

REEMtree(X, Y, id, Z, iter = 10, time, sto, delta = 0.001)
REEMtree(X, Y, id, Z, iter = 10, time, sto, delta = 0.001)

Arguments

`X`	[matrix]: A `N`x`p` matrix containing the `p` predictors of the fixed effects, column codes for a predictor.
`Y`	[vector]: A vector containing the output trajectories.
`id`	[vector]: Is the vector of the identifiers for the different trajectories.
`Z`	[matrix]: A `N`x`q` matrix containing the `q` predictor of the random effects.
`iter`	[numeric]: Maximal number of iterations of the algorithm. The default is set to `iter=100`
`time`	[vector]: Is the vector of the measurement times associated with the trajectories in `Y`,`Z` and `X`.
`sto`	[character]: Defines the covariance function of the stochastic process, can be either `"none"` for no stochastic process, `"BM"` for Brownian motion, `OrnUhl` for standard Ornstein-Uhlenbeck process, `BBridge` for Brownian Bridge, `fbm` for Fractional Brownian motion; can also be a function defined by the user.
`delta`	[numeric]: The algorithm stops when the difference in log likelihood between two iterations is smaller than `delta`. The default value is set to O.O01

Value

A fitted (S)MERF model which is a list of the following elements:

forest: Tree obtained at the last iteration.
random_effects : Predictions of random effects for different trajectories.
id_btilde: Identifiers of individuals associated with the predictions random_effects.
var_random_effects: Estimation of the variance covariance matrix of random effects.
sigma_sto: Estimation of the volatility parameter of the stochastic process.
sigma: Estimation of the residual variance parameter.
time: The vector of the measurement times associated with the trajectories in Y,Z and X.
sto: Stochastic process used in the model.
Vraisemblance: Log-likelihood of the different iterations.
id: Vector of the identifiers for the different trajectories.

Examples

set.seed(123)
data <- DataLongGenerator(n=20) # Generate the data composed by n=20 individuals.
# Train a SREEMtree model on the generated data.
# The data are generated with a Brownian motion,
# so we use the parameter sto="BM" to specify a Brownian motion as stochastic process
X.fixed.effects <- as.data.frame(data$X)
sreemt <- REEMtree(X=X.fixed.effects,Y=data$Y,Z=data$Z,id=data$id,time=data$time,
sto="BM", delta=0.0001)
sreemt$forest # is the fitted random forest (obtained at the last iteration).
sreemt$random_effects # are the predicted random effects for each individual.
sreemt$omega # are the predicted stochastic processes.
plot(sreemt$Vraisemblance) #evolution of the log-likelihood.

set.seed(123)
data <- DataLongGenerator(n=20) # Generate the data composed by n=20 individuals.
# Train a SREEMtree model on the generated data.
# The data are generated with a Brownian motion,
# so we use the parameter sto="BM" to specify a Brownian motion as stochastic process
X.fixed.effects <- as.data.frame(data$X)
sreemt <- REEMtree(X=X.fixed.effects,Y=data$Y,Z=data$Z,id=data$id,time=data$time,
sto="BM", delta=0.0001)
sreemt$forest # is the fitted random forest (obtained at the last iteration).
sreemt$random_effects # are the predicted random effects for each individual.
sreemt$omega # are the predicted stochastic processes.
plot(sreemt$Vraisemblance) #evolution of the log-likelihood.

Stability score function for (S)MERF and (S)REEMforest methods

Description

Computes the stability scores for (S)MERF and (S)REEMforest methods.

Usage

Stability_Score(
  X,
  Y,
  Z,
  id,
  time,
  mtry,
  ntree,
  sto = "BM",
  method = "MERF",
  eta = c(1:ncol(X)),
  nvars = c(1:ncol(X))
)
Stability_Score(
  X,
  Y,
  Z,
  id,
  time,
  mtry,
  ntree,
  sto = "BM",
  method = "MERF",
  eta = c(1:ncol(X)),
  nvars = c(1:ncol(X))
)

Arguments

`X`	[matrix]: A `N`x`p` matrix containing the `p` predictors of the fixed effects, column codes for a predictor.
`Y`	[vector]: A vector containing the output trajectories.
`Z`	[matrix]: A `N`x`q` matrix containing the `q` predictor of the random effects.
`id`	[vector]: Is the vector of the identifiers for the different trajectories.
`time`	[vector]: Is the vector of the measurement times associated with the trajectories in `Y`,`Z` and `X`.
`mtry`	[numeric]: Number of variables ramdomly picked to split each node.
`ntree`	[numeric]: Number of trees in the RF.
`sto`	[string]: Defines the covariance function of the stochastic process, can be either `"none"` for no stochastic process, `"BM"` for Brownian motion, `OrnUhl` for standard Ornstein-Uhlenbeck process, `BBridge` for Brownian Bridge, `fbm` for Fractional Brownian motion; can also be a function defined by the user.
`method`	[string]: Defines the method to be used, can be either "MERF" or "REEMforest".
`eta`	[numeric]: The size of the neighborhood for the stability score. Can be a vector, in this case, returns the stability scores corresponding to all the values of the vector.
`nvars`	[numeric]: The number of variables to consider among the most impotant variables. Can be a vector, in this case, the function returns the stability scores corresponding to all the values of the vector.

Value

A matrix with all the stability scores corresponding to the eta and nvars values. The $i$th row corresponds to the $i$th value of eta while the $i$th column corresponds to the $i$ value of nvars.

Package 'LongituRF'

Help Index

Longitudinal data generator

Description

Usage

Arguments

Value

Examples

(S)MERF algorithm

Description

Usage

Arguments

Value

Examples

(S)MERT algorithm

Description

Usage

Arguments

Value

Examples

Predict with longitudinal trees and random forests.

Description

Usage

Arguments

Value

Examples

(S)REEMforest algorithm

Description

Usage

Arguments

Details

Value

Examples

(S)REEMtree algorithm

Description

Usage

Arguments

Value

Examples

Stability score function for (S)MERF and (S)REEMforest methods

Description

Usage

Arguments

Value