| Type: | Package |
| Title: | Group Based Modeling Trajectory |
| Description: | Estimation of group-based trajectory models, including finite mixture models for longitudinal data, supporting censored normal, zero-inflated Poisson, logit, and beta distributions, using expectation-maximization and quasi-Newton methods, with tools for model selection, diagnostics, and visualization of latent trajectory groups, <doi:10.4159/9780674041318>, Nagin, D. (2005). Group-Based Modeling of Development. Cambridge, MA: Harvard University Press. and Noel (2022), https://orbilu.uni.lu/, thesis. |
| Version: | 0.11.1 |
| Date: | 2025-05-18 |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| Imports: | Rcpp (≥ 1.0.4.6), minpack.lm, numDeriv, ucminf, MASS, capushe, stats |
| LinkingTo: | Rcpp, RcppArmadillo |
| RoxygenNote: | 7.3.2 |
| Encoding: | UTF-8 |
| URL: | https://github.com/gitedric/trajeR |
| BugReports: | https://github.com/gitedric/trajeR/issues |
| Depends: | R (≥ 2.10) |
| Suggests: | spelling |
| Language: | en-US |
| LazyData: | true |
| NeedsCompilation: | yes |
| Packaged: | 2025-05-19 19:02:02 UTC; cedric |
| Author: | Cédric Noel [aut, cre], Jang Schiltz [aut] |
| Maintainer: | Cédric Noel <cedric.noel@univ-lorraine.fr> |
| Repository: | CRAN |
| Date/Publication: | 2025-05-21 15:50:02 UTC |
Average Posterior Probability
Description
Calculate the Average Posterior Probability. Average Posterior Probability (AvePP) is the average posterior probability of membership for each group for those individuals that were assigned to.
Usage
AvePP(sol, Y, A, X = NULL)
Arguments
sol |
Trajectory's object. An object of type Trajectory. |
Y |
Matrix. A matrix containing the variables in the model. |
A |
Matrix. A matrix containing the time variable data. |
X |
Matrix. An optional matrix that modifies the probability of belong to group. By default its value is a one column matrix with value 1. |
Value
A vector of reals. The average posterior probability.
Examples
data <- read.csv(system.file("extdata", "CNORM2gr.csv", package = "trajeR"))
data <- as.matrix(data)
sol <- trajeR(Y = data[, 2:6], A = data[, 7:11], degre = c(2, 2), Model = "CNORM", Method = "EM")
AvePP(sol, Y = data[, 2:6], A = data[, 7:11])
Confidence interval
Description
Calculate the confidence interval of the probabilities with bootstrap method. We have to specify the number of the repetitions of bootstrap and the degree of confidence.
Usage
ConfIntT(sol, Y, A, nb = 10000, alpha = 0.98)
Arguments
sol |
Trajectory's object. An object of type Trajectory. |
Y |
Matrix. A matrix containing the variables in the model. |
A |
Matrix. A matrix containing the time variable data. |
nb |
An integer. The number of repetitions in the bootstrap method. |
alpha |
A number. The degree of confidence of the interval. |
Value
A vector of reals. The two bounds of the confidence interval given a degree of confidence.
Examples
data <- read.csv(system.file("extdata", "CNORM2gr.csv", package = "trajeR"))
data <- as.matrix(data)
sol <- trajeR(Y = data[, 2:6], A = data[, 7:11], degre = c(2, 2), Model = "CNORM", Method = "EM")
ConfIntT(sol, Y = data[, 2:6], A = data[, 7:11])
Membership's probabilities
Description
GroupProb calculate the membership probability of each value of the data.
Usage
GroupProb(Obj, Y, A, TCOV = NULL, X = NULL)
Arguments
Obj |
Trajectory's object. A trajectory object that is return by |
Y |
Matrix. A real matrix. The data. |
A |
Matrix. A real matrix. The time variable. |
TCOV |
Matrix. A real matrix. Optional, by default the value is NULL. It contained the time dependent covariate. |
X |
Matrix. A real matrix. Optional, by default the value is NULL. It contained a covariate that modify the probability membership. |
Value
a real matrix. For each individual i in the data, this matrix contained the membership probability of each group.
Examples
data <- read.csv(system.file("extdata", "CNORM2gr.csv", package = "trajeR"))
data <- as.matrix(data)
sol <- trajeR(Y = data[, 2:6], A = data[, 7:11], degre = c(2, 2), Model = "CNORM", Method = "EM")
GroupProb(sol, Y = data[, 2:6], A = data[, 7:11])
Profiles of each group
Description
GroupProfiles calculate the profile of a group regarding covariate. It is a
cross tabulation of individual level trajectory group assignments with
individual level characteristic that might be associated with trajectory
group membership.
Usage
GroupProfiles(sol, Y, A, X)
Arguments
sol |
Trajectory's object. A object of type trajectory. |
Y |
Matrix. A matrix containing the variables in the model. |
A |
Matrix. A matrix containing the time variable data. |
X |
Matrix. An optional matrix that modify the probability of belong to group. By default its value is a matrix with one column with value 1. |
Value
A table of real.
Examples
data <- read.csv(system.file("extdata", "CNORM2gr.csv", package = "trajeR"))
data <- as.matrix(data)
sol <- trajeR(
Y = data[, 2:6], A = data[, 7:11], Risk = data[, 12],
degre = c(2, 2), Model = "CNORM", Method = "L"
)
GroupProfiles(sol, Y = data[, 2:6], A = data[, 7:11], X = data[, 12])
Odds of Correct Classification
Description
Calculate Odds of Correct Classification. The Odds of Correct Classification for group k (OCCj) is the ratio between the odds of a correct classification into group j on the basis of the posterior probability rule and the odds of correct assignment based on random assignments with the probability of assignment to group j is the probability estimate by the model.
Usage
OCC(sol, Y, A)
Arguments
sol |
Trajectory's object. An object of type Trajectory. |
Y |
Matrix. A matrix containing the variables in the model. |
A |
Matrix. A matrix containing the time variable data. |
Value
A vector of reals. The Odds of Correct Classification.
Examples
data <- read.csv(system.file("extdata", "CNORM2gr.csv", package = "trajeR"))
data <- as.matrix(data)
sol <- trajeR(Y = data[, 2:6], A = data[, 7:11], degre = c(2, 2), Model = "CNORM", Method = "EM")
OCC(sol, Y = data[, 2:6], A = data[, 7:11])
Adequacy of the model
Description
Calculate the summary of the five methods : assignment proportion, average posterior probability, confidence interval, odds of Correct Classification.
Usage
adequacy(sol, Y, A, nb = 10000, alpha = 0.98)
Arguments
sol |
Trajectory's object. An object of type Trajectory. |
Y |
Matrix. A matrix containing the variables in the model. |
A |
Matrix. A matrix containing the time variable data. |
nb |
Integer. The numbers of repetitions in the bootstrap method. |
alpha |
Real. The degree of confidence of the interval. |
Value
A table of reals. A table with 5 rows: the estimate probabilities, the two bounds of the confidence interval, the proportion of assignment, the Average Posterior Probability and the Odds of Correct Classification.
Examples
data <- read.csv(system.file("extdata", "CNORM2gr.csv", package = "trajeR"))
data <- as.matrix(data)
sol <- trajeR(Y = data[, 2:6], A = data[, 7:11], degre = c(2, 2), Model = "CNORM", Method = "EM")
adequacy(sol, Y = data[, 2:6], A = data[, 7:11])
Simulated CNORM Dataset (data01)
Description
The data01 dataset is a simulated dataset included in the package. It contains
500 trajectories with 10 time-points each, simulating a 3-group solution. The parameters
for the groups are summarized in the table below:
| Parameter | Group 1 | Group 2 | Group 3 |
\beta_{k0} | 2.797 | 7.000 | 19.545 |
\beta_{k1} | 8.809 | -0.297 | -0.407 |
\beta_{k2} | -3.201 | 0.463 | 0.026 |
\beta_{k3} | 0.000 | -0.021 | 0.000 |
\pi_k | 0.32 | 0.54 | 0.14 |
\sigma_k | 4.000 | 4.000 | 4.000 |
Usage
dataNORM01
Format
A data frame with 500 rows and 43 columns:
- Columns 2:11
Matrix of real numbers (variable of interest, Y).
- Columns 12:21
Matrix of time points (1 to 10, A).
- Columns 22:31
Matrix of binary values (0 or 1, time-dependent covariate W).
- Columns 32:41
Matrix of real numbers (additional time-dependent covariate W).
- Columns 42:43
Matrix of binary values (0 or 1, covariate X).
Details
The dataset includes the following variables:
-
Y(columns 2:11): Matrix of real numbers representing the variable of interest. -
A(columns 12:21): Matrix of time points (1 to 10). -
W(columns 22:31): Matrix with values 0 and 1, indicating the presence or absence of a characteristic. -
W(columns 32:41): Matrix of real numbers (additional time-dependent covariate). -
X(columns 42:43): Matrix with values 0 and 1, influencing group membership probability.
Source
Simulated data for illustrative purposes.
Differential
Description
Differential
Usage
diffaitbeta(betak, i, t, A, TCOV, fct, diffct)
Arguments
betak |
Vector of integer. |
i |
Integer. |
t |
Real. |
A |
Matrix of real. |
TCOV |
Matrix of real. |
fct |
Function. |
diffct |
Function. |
Value
real. Compute the value of the differential function fct for individual i, time t and group k.
Function fait
Description
Function fait
Usage
fait(betak, i, t, A, TCOV, fct, diffct)
Arguments
betak |
Vector of integer. |
i |
Integer. |
t |
Real. |
A |
Matrix of real. |
TCOV |
Matrix of real. |
fct |
Function. |
diffct |
Function. |
Value
real. Compute the value of the function fct for individual i, time t and group k.
plot trajectory
Description
plot trajectory
Usage
plotrajeR(Obj, ...)
Arguments
Obj |
an object of class " |
... |
optional parameters |
Value
a graphic.
Examples
data <- read.csv(system.file("extdata", "CNORM2gr.csv", package = "trajeR"))
data <- as.matrix(data)
sol <- trajeR(Y = data[, 2:6], A = data[, 7:11], degre = c(2, 2), Model = "CNORM", Method = "EM")
plotrajeR(sol)
plot BETA trajectory
Description
plot BETA trajectory
Usage
## S3 method for class 'Trajectory.BETA'
plotrajeR(
Obj,
plotcov = NULL,
col = "black",
Y = NULL,
A = NULL,
Risk = NULL,
TCOV = NULL,
mean = FALSE,
alpha = 1,
...
)
Arguments
Obj |
an object of class " |
plotcov |
an optional vector or matrix with the same length as the time period. Default value is NULL. |
col |
an optional vector. The vector of colors. It must contain a color for each trajectory and each points of groups. Its length is the double of the number of group. Default value is a grayscale. |
Y |
Matrix. A matrix containing the variables in the model. |
A |
Matrix. A matrix containing the time variable data. |
Risk |
Matrix. An optional matrix that modify the probability of belong to group. By default its value is a matrix with one column with value 1. |
TCOV |
Matrix. An optional matrix containing the time covariate that influence the trajectory themselves. By default its value is NULL. |
mean |
an optional logical. Indicate if the mean of ech group and time value must be draw. |
alpha |
on optional real. Indicate the alpha channel of the points color. |
... |
optional parameters |
Value
a graphic.
plot CNORM trajectory
Description
plot CNORM trajectory
Usage
## S3 method for class 'Trajectory.CNORM'
plotrajeR(
Obj,
plotcov = NULL,
col = "black",
Y = NULL,
A = NULL,
Risk = NULL,
mean = FALSE,
alpha = 1,
...
)
Arguments
Obj |
an object of class " |
plotcov |
an optional vector or matrix with the same length as the time period. Default value is NULL. |
col |
an optional vector. The vector of colors. It must contain a color for each trajectory and each points of groups. Its length is the double of the number of group. Default value is a grayscale. |
Y |
Matrix. A matrix containing the variables in the model. |
A |
Matrix. A matrix containing the time variable data. |
Risk |
Matrix. An optional matrix that modify the probability of belong to group. By default its value is a matrix with one column with value 1. |
mean |
an optional logical. Indicate if the mean of ech group and time value must be draw. |
alpha |
on optional real. Indicate the alpha channel of the points color. |
... |
optional parameters |
Value
a graphic.
plot LOGIT trajectory
Description
plot LOGIT trajectory
Usage
## S3 method for class 'Trajectory.LOGIT'
plotrajeR(
Obj,
plotcov = NULL,
dec = 0,
col = "black",
Y = NULL,
A = NULL,
Risk = NULL,
mean = FALSE,
alpha = 1,
...
)
Arguments
Obj |
an object of class " |
plotcov |
an optional vector or matrix with the same length as the time period. Default value is NULL. |
dec |
an optional real. It precise the shift to draw the data points. |
col |
an optional vector. The vector of colors. It must contain a color for each trajectory and each points of groups. Its length is the double of the number of group. Default value is a grayscale. |
Y |
Matrix. A matrix containing the variables in the model. |
A |
Matrix. A matrix containing the time variable data. |
Risk |
Matrix. An optional matrix that modify the probability of belong to group. By default its value is a matrix with one column with value 1. |
mean |
an optional logical. Indicate if the mean of ech group and time value must be draw. |
alpha |
on optional real. Indicate the alpha channel of the points color. |
... |
optional parameters |
Value
a graphic.
plot Non Linear trajectory
Description
plot Non Linear trajectory
Usage
## S3 method for class 'Trajectory.NL'
plotrajeR(
Obj,
plotcov = NULL,
col = "black",
Y = NULL,
A = NULL,
Risk = NULL,
mean = FALSE,
alpha = 1,
TCOV = NULL,
...
)
Arguments
Obj |
an object of class " |
plotcov |
an optional vector or matrix with the same length as the time period. Default value is NULL. |
col |
an optional vector. The vector of colors. It must contain a color for each trajectory and each points of groups. Its length is the double of the number of group. Default value is a grayscale. |
Y |
Matrix. A matrix containing the variables in the model. |
A |
Matrix. A matrix containing the time variable data. |
Risk |
Matrix. An optional matrix that modify the probability of belong to group. By default its value is a matrix with one column with value 1. |
mean |
an optional logical. Indicate if the mean of ech group and time value must be draw. |
alpha |
on optional real. Indicate the alpha channel of the points color. |
TCOV |
Matrix. An optional matrix containing the time covariate that influence the trajectory themselves. By default its value is NULL. |
... |
optional parameters |
Value
a graphic.
plot POIS trajectory
Description
plot POIS trajectory
Usage
## S3 method for class 'Trajectory.POIS'
plotrajeR(
Obj,
plotcov = NULL,
dec = 0,
col = "black",
Y = NULL,
A = NULL,
Risk = NULL,
TCOV = NULL,
mean = FALSE,
alpha = 1,
...
)
Arguments
Obj |
an object of class " |
plotcov |
an optional vector or matrix with the same length as the time period. Default value is NULL. |
dec |
an optional real. It precise the shift to draw the data points. |
col |
an optional vector. The vector of colors. It must contain a color for each trajectory and each points of groups. Its length is the double of the number of group. Default value is a grayscale. |
Y |
Matrix. A matrix containing the variables in the model. |
A |
Matrix. A matrix containing the time variable data. |
Risk |
Matrix. An optional matrix that modify the probability of belong to group. By default its value is a matrix with one column with value 1. |
TCOV |
Matrix. An optional matrix containing the time covariate that influence the trajectory themselves. By default its value is NULL. |
mean |
an optional logical. Indicate if the mean of ech group and time value must be draw. |
alpha |
on optional real. Indicate the alpha channel of the points color. |
... |
optional parameters |
Value
a graphic.
plot ZIP trajectory
Description
plot ZIP trajectory
Usage
## S3 method for class 'Trajectory.ZIP'
plotrajeR(
Obj,
plotcov = NULL,
dec = 0,
col = "black",
Y = NULL,
A = NULL,
Risk = NULL,
TCOV = NULL,
mean = FALSE,
alpha = 1,
...
)
Arguments
Obj |
an object of class " |
plotcov |
an optional vector or matrix with the same length as the time period. Default value is NULL. |
dec |
an optional real. It precise the shift to draw the data points. |
col |
an optional vector. The vector of colors. It must contain a color for each trajectory and each points of groups. Its length is the double of the number of group. Default value is a grayscale. |
Y |
Matrix. A matrix containing the variables in the model. |
A |
Matrix. A matrix containing the time variable data. |
Risk |
Matrix. An optional matrix that modify the probability of belong to group. By default its value is a matrix with one column with value 1. |
TCOV |
Matrix. An optional matrix containing the time covariate that influence the trajectory themselves. By default its value is NULL. |
mean |
an optional logical. Indicate if the mean of ech group and time value must be draw. |
alpha |
on optional real. Indicate the alpha channel of the points color. |
... |
optional parameters |
Value
a graphic.
Print BETA
Description
Print method for an object of class "Trajectory.BETA".
Usage
## S3 method for class 'Trajectory.BETA'
print(x, ...)
Arguments
x |
Trajectory's object. An object of class " |
... |
optional parameters |
Value
The print of Obj.
Examples
data <- read.csv(system.file("extdata", "BETA2gr.csv", package = "trajeR"))
data <- as.matrix(data)
data[, 2:6] <- data[, 2:6] * (nrow(data[, 2:6]) - 1 + 0.5) / nrow(data[, 2:6])
sol <- trajeR(
Y = data[, 2:6], A = data[, 7:11], itermax = 50,
degre = c(2, 2), degre.phi = c(1, 1), Model = "BETA", Method = "L"
)
sol
Print CNORM
Description
Print method for an object of class "Trajectory.CNORM".
Usage
## S3 method for class 'Trajectory.CNORM'
print(x, ...)
Arguments
x |
Trajectory's object. An object of class " |
... |
optional parameters |
Value
The print of Obj.
Examples
data <- read.csv(system.file("extdata", "CNORM2gr.csv", package = "trajeR"))
data <- as.matrix(data)
sol <- trajeR(Y = data[, 2:6], A = data[, 7:11], degre = c(2, 2), Model = "CNORM", Method = "EM")
sol
Print LOGIT
Description
Print method for an object of class "Trajectory.LOGIT".
Usage
## S3 method for class 'Trajectory.LOGIT'
print(x, ...)
Arguments
x |
Trajectory's object. . An object of class " |
... |
optional parameters |
Value
The print of Obj.
Examples
data <- read.csv(system.file("extdata", "LOGIT2gr.csv", package = "trajeR"))
data <- as.matrix(data)
sol <- trajeR(Y = data[, 2:6], A = data[, 7:11], degre = c(1, 2), Model = "LOGIT", Method = "L")
sol
print NL trajectory
Description
Print method for an object of class "Trajectory.NL".
Usage
## S3 method for class 'Trajectory.NL'
print(x, ...)
Arguments
x |
Trajectory's object. . An object of class " |
... |
optional parameters |
Value
The print of Obj.
Print POIS
Description
Print method for an object of class "Trajectory.POIS".
Usage
## S3 method for class 'Trajectory.POIS'
print(x, ...)
Arguments
x |
Trajectory's object. . An object of class " |
... |
optional parameters |
Value
The print of Obj.
Examples
data <- read.csv(system.file("extdata", "POIS2gr.csv", package = "trajeR"))
data <- as.matrix(data)
sol <- trajeR(
Y = data[, 2:6], A = data[, 7:11],
degre = c(2, 2), Model = "POIS", Method = "L", hessian = FALSE
)
sol
Print ZIP
Description
Print method for an object of class "Trajectory.ZIP".
Usage
## S3 method for class 'Trajectory.ZIP'
print(x, ...)
Arguments
x |
Trajectory's object. An object of class " |
... |
optional parameters |
Value
The print of Obj.
Examples
data <- read.csv(system.file("extdata", "ZIP2gr.csv", package = "trajeR"))
data <- as.matrix(data)
sol <- trajeR(
Y = data[, 2:6], A = data[, 7:11],
degre = c(1, 2), degre.nu = c(1, 1), Model = "ZIP", Method = "L"
)
sol
Assignment proportion
Description
Calculate the proportion of individuals in a given group. That is the ratio of the number of individuals in one group and all the individuals.
Usage
propAssign(sol, Y, A)
Arguments
sol |
Trajectory's object. An object of type Trajectory. |
Y |
Matrix. A matrix containing the variables in the model. |
A |
Matrix. A matrix containing the time variable data. |
Value
A vector of real. The proportion.
Examples
data <- read.csv(system.file("extdata", "CNORM2gr.csv", package = "trajeR"))
data <- as.matrix(data)
sol <- trajeR(Y = data[, 2:6], A = data[, 7:11], degre = c(2, 2), Model = "CNORM", Method = "EM")
propAssign(sol, Y = data[, 2:6], A = data[, 7:11])
Fitting longitudinal mixture models
Description
trajeR is used to fit longitudinal mixture models. It used 3 types of mixture models : LOGIT, ZIP and censored Normal.
Usage
trajeR(
Y,
A,
Risk = NULL,
TCOV = NULL,
degre = NULL,
degre.nu = 0,
degre.phi = 0,
Model,
Method = "L",
ssigma = FALSE,
ymax = max(Y, na.rm = TRUE) + 1,
ymin = min(Y, na.rm = TRUE) - 1,
hessian = TRUE,
itermax = 100,
paraminit = NULL,
ProbIRLS = TRUE,
refgr = 1,
fct = NULL,
diffct = NULL,
nbvar = NULL,
ng.nl = NULL,
nls.lmiter = 50
)
Arguments
Y |
Matrix. A matrix containing the variables in the model. |
A |
Matrix. A matrix containing the time variable data. |
Risk |
Matrix. An optional matrix that modify the probability of belong to group. By default its value is a matrix with one column with value 1. |
TCOV |
Matrix. An optional matrix containing the time covariate that influence the trajectory themselves. By default its value is NULL. |
degre |
Vector of integer. The degree of every polynomial function. |
degre.nu |
Vector of integer. The degree of all Poisson part for a ZIP model. |
degre.phi |
Vector of integer. The degree of beta parameter for a BETA model. |
Model |
String. The model used. The value are LOGIT for a Logit Mixture model, CNORM for a Censored Normal Mixture Model or ZIP for Zero Inflated Poisson Mixture model. |
Method |
String. Determine the method used for find the parameters of the model. The value are L for the Maximum Likelihood Estimation, EM for Expectation Maximization method with quasi newton method inside, EMIWRLS for Expectation Maximization method with Iterative Weighted Least Square. |
ssigma |
Logical. By default its value is FALSE. For the CNORM model, indicate if we want the same sigma for all normal density function. |
ymax |
Real. For the CNORM model, indicate the maximum value of the data. It concern only the model with censored data. By default its value is the maximum value of the data plus 1. |
ymin |
Real. For the CNORM model, indicate the minimum value of the data. It concern only the model with censored data. By default its value is the maximum value of the data minus 1. |
hessian |
Logical. Indicate if we want calculate the hessian matrix. Default is FALSE.
If the method use is Likelihood, the hessian is calculated by inverting the Information's Fisher Matrix.
To avoid numerically singular matrix we find the pseudo inverse matrix by using the |
itermax |
Integer. Indicate the maximal number of iteration for |
paraminit |
Vector. The vector of initial parameters. By default |
ProbIRLS |
Logical. Indicate the method to sue in the search of predictor's probability. If TRUE (by default) we use IRLS method and if FALSE we use optimization method. |
refgr |
Integer. The number of reference group. By default is 1. |
fct |
Function. The definition of the function f in the definition in nonlinear model. |
diffct |
Function. The differential of the function f in the nonlinear model. |
nbvar |
Integer. The number of variable in the nonlinear model. |
ng.nl |
Integer. The number of group for a non linear model. |
nls.lmiter |
Integer. In the case of non linear model, the maximum number of iterations allowed. |
Details
Models for trajeR is, by default, a polynomial regression of the time value parameters for each groups. The number fo group is controlled by the integer ng.
We can specify the degre of the polynomial shape for each groups by the vector degre.
Value
return an object of class "Trajectory.LOGIT".
The generic accessor functions beta, delta, theta, sd, tab, Likelihood,
ng, model and method extract various useful features of the value returned by trajeR.
An object of class "Trajectory.LOGIT" is a list containing at least the following components:
betaa vector of the parameters beta.
deltaa vector of the parameter delta. Only if we use time covariate.
thetaa vector with the parameter theta if there exist a covariate X that modify the probability or the probability of group membership.
sda vector of the standard deviation of the parameters.
taba matrix with all the parameters and standard deviation.
Likelihooda real with the Likelihood obtained by the parameters.
nga integer with the number of group.
modela string with the model used.
methoda string with the method used.
Examples
data("dataNORM01")
solL <- trajeR(dataNORM01[, 1:5], dataNORM01[, 6:10],
ng = 3, degre = c(2, 2, 2),
Model = "CNORM", Method = "L", ssigma = FALSE,
hessian = TRUE
)
Internal function to fit Beta regression
Description
Internal function to fit Beta regression
Usage
trajeR.BETA(
Y,
A,
X,
TCOV,
ng,
nx,
n,
nbeta,
nphi,
nw,
ntheta,
period,
degre,
theta,
beta,
phi,
delta,
pi,
Method,
hessian,
itermax,
paraminit,
EMIRLS,
refgr
)
Arguments
Y |
Matrix. A matrix containing the variables in the model. |
A |
Matrix. A matrix containing the time variable data. |
X |
Matrix. An optional matrix that modify the probability of belong to group. By default its value is a matrix with one column with value 1. |
TCOV |
Matrix. An optional matrix containing the time covariate that influence the trajectory themselves. By default its value is NULL. |
ng |
Integer. The number of groups. |
nx |
Integer. The number of covariates. |
n |
Integer. Number of individuals. |
nbeta |
Vector of integers. Number of beta parameters for each group. |
nphi |
Vector of integers. Number of phi parameters for each group. |
nw |
Integer. Number of time dependent covariate. |
ntheta |
Vector of integers. Number of theta parameters for each group. |
period |
Integer. |
degre |
Vector of integer. The degree of every polynomial function. |
theta |
Vector of real. The parameter for calculated the group membership probability. |
beta |
Vector of real. The beta parameter. |
phi |
Vector of real. The phi parameter. |
delta |
Vector of real. The delta parameter. |
pi |
Vector of real. The group membership probability. |
Method |
String. Determine the method used for find the parameters of the model. The value are L for the Maximum Likelihood Estimation, EM for Expectation Maximization method with quasi newton method inside, EMIWRLS for Expectation Maximization method with Iterative Weighted Least Square. |
hessian |
Logical. Indicate if we want calculate the hessian matrix. Default is FALSE.
If the method use is Likelihood, the hessian is calculated by inverting the Information's Fisher Matrix.
To avoid numerically singular matrix we find the pseudo inverse matrix by using the |
itermax |
Integer. Indicate the maximal number of iteration for |
paraminit |
Vector. The vector of initial parameters. By default |
EMIRLS |
Boolean. True if we use EMIRLS method. |
refgr |
Integer. The number of reference group. By default is 1. |
Value
return a object of class Trajectory.NL
beta - vector of the parameter beta.
sigma - vector of the parameters sigma.
delta - vector of the parameter delta. Only if we use time covariate.
theta - vector with the parameter theta if there exist a covariate X that modify the probability or the probability of group membership.
sd - vector of the standard deviation of the parameters.
tab - a matrix with all the parameters and standard deviation.
Model - a string with the model used.
groups - a integer with the number of group.
Names - strings with the name of the parameters.
Method - a string with the method used.
Size - a integer with the number of individuals.
Likelihood - a real with the Likelihood obtained by the parameters.
Time - a vector with the first row of time values.
degre - a vector with the degree of the polynomial shape.
Internal function to fit CNORM Model
Description
Internal function to fit CNORM Model
Usage
trajeR.CNORM(
Y,
A,
X,
TCOV,
ng,
nx,
n,
nbeta,
nw,
ntheta,
period,
degre,
theta,
beta,
sigma,
delta,
pi,
Method,
ssigma,
ymax,
ymin,
hessian,
itermax,
paraminit,
EMIRLS,
refgr
)
Arguments
Y |
Matrix. A matrix containing the variables in the model. |
A |
Matrix. A matrix containing the time variable data. |
X |
Matrix. An optional matrix that modify the probability of belong to group. By default its value is a matrix with one column with value 1. |
TCOV |
Matrix. An optional matrix containing the time covariate that influence the trajectory themselves. By default its value is NULL. |
ng |
Integer. The number of groups. |
nx |
Integer. The number of covariates. |
n |
Integer. Number of individuals. |
nbeta |
Vector of integers. Number of beta parameters for each group. |
nw |
Integer. Number of time dependent covariate. |
ntheta |
Vector of integers. Number of theta parameters for each group. |
period |
Integer. |
degre |
Vector of integer. The degree of every polynomial function. |
theta |
Vector of real. The parameter for calculated the group membership probability. |
beta |
Vector of real. The beta parameter. |
sigma |
Vector of real. The sigma parameter. |
delta |
Vector of real. The delta parameter. |
pi |
Vector of real. The group membership probability. |
Method |
String. Determine the method used for find the parameters of the model. The value are L for the Maximum Likelihood Estimation, EM for Expectation Maximization method with quasi newton method inside, EMIWRLS for Expectation Maximization method with Iterative Weighted Least Square. |
ssigma |
Logical. By default its value is FALSE. For the CNORM model, indicate if we want the same sigma for all normal density function. |
ymax |
Real. For the CNORM model, indicate the maximum value of the data. It concern only the model with censored data. By default its value is the maximum value of the data plus 1. |
ymin |
Real. For the CNORM model, indicate the minimum value of the data. It concern only the model with censored data. By default its value is the maximum value of the data minus 1. |
hessian |
Logical. Indicate if we want calculate the hessian matrix. Default is FALSE.
If the method use is Likelihood, the hessian is calculated by inverting the Information's Fisher Matrix.
To avoid numerically singular matrix we find the pseudo inverse matrix by using the |
itermax |
Integer. Indicate the maximal number of iteration for |
paraminit |
Vector. The vector of initial parameters. By default |
EMIRLS |
Boolean. True if we use EMIRLS method. |
refgr |
Integer. The number of reference group. By default is 1. |
Value
return a object of class Trajectory.CNORM
beta - vector of the parameter beta.
sigma - vector of the parameters sigma.
delta - vector of the parameter delta. Only if we use time covariate.
theta - vector with the parameter theta if there exist a covariate X that modify the probability or the probability of group membership.
sd - vector of the standard deviation of the parameters.
tab - a matrix with all the parameters and standard deviation.
Model - a string with the model used.
groups - a integer with the number of group.
Names - strings with the name of the parameters.
Method - a string with the method used.
Size - a integer with the number of individuals.
Likelihood - a real with the Likelihood obtained by the parameters.
Time - a vector with the first row of time values.
degre - a vector with the degree of the polynomial shape.
min - a real with the minimum value for censored data.
max - a real with the maximum value for censored data.
Internal function to fit LOGIT Model
Description
Internal function to fit LOGIT Model
Usage
trajeR.LOGIT(
Y,
A,
X,
TCOV,
ng,
nx,
n,
nbeta,
nw,
ntheta,
period,
degre,
theta,
beta,
delta,
pi,
Method,
hessian,
itermax,
paraminit,
EMIRLS,
refgr
)
Arguments
Y |
Matrix. A matrix containing the variables in the model. |
A |
Matrix. A matrix containing the time variable data. |
X |
Matrix. An optional matrix that modify the probability of belong to group. By default its value is a matrix with one column with value 1. |
TCOV |
Matrix. An optional matrix containing the time covariate that influence the trajectory themselves. By default its value is NULL. |
ng |
Integer. The number of groups. |
nx |
Integer. The number of covariates. |
n |
Integer. Number of individuals. |
nbeta |
Vector of integers. Number of beta parameters for each group. |
nw |
Integer. Number of time dependent covariate. |
ntheta |
Vector of integers. Number of theta parameters for each group. |
period |
Integer. |
degre |
Vector of integer. The degree of every polynomial function. |
theta |
Vector of real. The parameter for calculated the group membership probability. |
beta |
Vector of real. The beta parameter. |
delta |
Vector of real. The delta parameter. |
pi |
Vector of real. The group membership probability. |
Method |
String. Determine the method used for find the parameters of the model. The value are L for the Maximum Likelihood Estimation, EM for Expectation Maximization method with quasi newton method inside, EMIWRLS for Expectation Maximization method with Iterative Weighted Least Square. |
hessian |
Logical. Indicate if we want calculate the hessian matrix. Default is FALSE.
If the method use is Likelihood, the hessian is calculated by inverting the Information's Fisher Matrix.
To avoid numerically singular matrix we find the pseudo inverse matrix by using the |
itermax |
Integer. Indicate the maximal number of iteration for |
paraminit |
Vector. The vector of initial parameters. By default |
EMIRLS |
Boolean. True if we use EMIRLS method. |
refgr |
Integer. The number of reference group. By default is 1. |
Value
return a object of class Trajectory.LOGIT
beta - vector of the parameter beta.
delta - vector of the parameter delta. Only if we use time covariate.
theta - vector with the parameter theta if there exist a covariate X that modify the probability or the probability of group membership.
sd - vector of the standard deviation of the parameters.
tab - a matrix with all the parameters and standard deviation.
Model - a string with the model used.
groups - a integer with the number of group.
Names - strings with the name of the parameters.
Method - a string with the method used.
Size - a integer with the number of individuals.
Likelihood - a real with the Likelihood obtained by the parameters.
Time - a vector with the first row of time values.
degre - a vector with the degree of the polynomial shape.
Internal function to fit Non Linear Model
Description
Internal function to fit Non Linear Model
Usage
trajeR.NL(
Y,
A,
X,
TCOV,
ng,
nx,
n,
nbeta,
nw,
ntheta,
period,
degre,
theta,
beta,
sigma,
pi,
Method,
ssigma,
hessian,
itermax,
paraminit,
EMIRLS,
refgr,
fct,
diffct,
nls.lmiter
)
Arguments
Y |
Matrix. A matrix containing the variables in the model. |
A |
Matrix. A matrix containing the time variable data. |
X |
Matrix. An optional matrix that modify the probability of belong to group. By default its value is a matrix with one column with value 1. |
TCOV |
Matrix. An optional matrix containing the time covariate that influence the trajectory themselves. By default its value is NULL. |
ng |
Integer. The number of groups. |
nx |
Integer. The number of covariates. |
n |
Integer. Number of individuals. |
nbeta |
Vector of integers. Number of beta parameters for each group. |
nw |
Integer. Number of time dependent covariate. |
ntheta |
Vector of integers. Number of theta parameters for each group. |
period |
Integer. |
degre |
Vector of integer. The degree of every polynomial function. |
theta |
Vector of real. The parameter for calculated the group membership probability. |
beta |
Vector of real. The beta parameter. |
sigma |
Vector of real. The sigma parameter. |
pi |
Vector of real. The group membership probability. |
Method |
String. Determine the method used for find the parameters of the model. The value are L for the Maximum Likelihood Estimation, EM for Expectation Maximization method with quasi newton method inside, EMIWRLS for Expectation Maximization method with Iterative Weighted Least Square. |
ssigma |
Logical. By default its value is FALSE. For the CNORM model, indicate if we want the same sigma for all normal density function. |
hessian |
Logical. Indicate if we want calculate the hessian matrix. Default is FALSE.
If the method use is Likelihood, the hessian is calculated by inverting the Information's Fisher Matrix.
To avoid numerically singular matrix we find the pseudo inverse matrix by using the |
itermax |
Integer. Indicate the maximal number of iteration for |
paraminit |
Vector. The vector of initial parameters. By default |
EMIRLS |
Boolean. True if we use EMIRLS method. |
refgr |
Integer. The number of reference group. By default is 1. |
fct |
Function. The definition of the function f in the definition in nonlinear model. |
diffct |
Function. The differential of the function f in the nonlinear model. |
nls.lmiter |
Integer. In the case of non linear model, the maximum number of iterations allowed. |
Value
return a object of class Trajectory.NL
beta - vector of the parameter beta.
sigma - vector of the parameters sigma.
delta - vector of the parameter delta. Only if we use time covariate.
theta - vector with the parameter theta if there exist a covariate X that modify the probability or the probability of group membership.
sd - vector of the standard deviation of the parameters.
tab - a matrix with all the parameters and standard deviation.
Model - a string with the model used.
groups - a integer with the number of group.
Names - strings with the name of the parameters.
Method - a string with the method used.
Size - a integer with the number of individuals.
Likelihood - a real with the Likelihood obtained by the parameters.
Time - a vector with the first row of time values.
degre - a vector with the degree of the polynomial shape.
fct - the definition of the function used int this model.
Internal function to fit poisson Model
Description
Internal function to fit poisson Model
Usage
trajeR.POIS(
Y,
A,
X,
TCOV,
ng,
nx,
n,
nbeta,
nw,
ntheta,
period,
degre,
theta,
beta,
delta,
pi,
Method,
hessian,
itermax,
paraminit,
EMIRLS,
refgr
)
Arguments
Y |
Matrix. A matrix containing the variables in the model. |
A |
Matrix. A matrix containing the time variable data. |
X |
Matrix. An optional matrix that modify the probability of belong to group. By default its value is a matrix with one column with value 1. |
TCOV |
Matrix. An optional matrix containing the time covariate that influence the trajectory themselves. By default its value is NULL. |
ng |
Integer. The number of groups. |
nx |
Integer. The number of covariates. |
n |
Integer. Number of individuals. |
nbeta |
Vector of integers. Number of beta parameters for each group. |
nw |
Integer. Number of time dependent covariate. |
ntheta |
Vector of integers. Number of theta parameters for each group. |
period |
Integer. |
degre |
Vector of integer. The degree of every polynomial function. |
theta |
Vector of real. The parameter for calculated the group membership probability. |
beta |
Vector of real. The beta parameter. |
delta |
Vector of real. The delta parameter. |
pi |
Vector of real. The group membership probability. |
Method |
String. Determine the method used for find the parameters of the model. The value are L for the Maximum Likelihood Estimation, EM for Expectation Maximization method with quasi newton method inside, EMIWRLS for Expectation Maximization method with Iterative Weighted Least Square. |
hessian |
Logical. Indicate if we want calculate the hessian matrix. Default is FALSE.
If the method use is Likelihood, the hessian is calculated by inverting the Information's Fisher Matrix.
To avoid numerically singular matrix we find the pseudo inverse matrix by using the |
itermax |
Integer. Indicate the maximal number of iteration for |
paraminit |
Vector. The vector of initial parameters. By default |
EMIRLS |
Boolean. True if we use EMIRLS method. |
refgr |
Integer. The number of reference group. By default is 1. |
Value
return a object of class Trajectory.Pois
beta - vector of the parameter beta.
delta - vector of the parameter delta. Only if we use time covariate.
theta - vector with the parameter theta if there exist a covariate X that modify the probability or the probability of group membership.
sd - vector of the standard deviation of the parameters.
tab - a matrix with all the parameters and standard deviation.
Model - a string with the model used.
groups - a integer with the number of group.
Names - strings with the name of the parameters.
Method - a string with the method used.
Size - a integer with the number of individuals.
Likelihood - a real with the Likelihood obtained by the parameters.
Time - a vector with the first row of time values.
degre - a vector with the degree of the polynomial shape for the Poisson part.
Internal function to fit ZIP Model
Description
Internal function to fit ZIP Model
Usage
trajeR.ZIP(
Y,
A,
X,
TCOV,
ng,
nx,
n,
nbeta,
nw,
ntheta,
period,
degre,
degre.nu,
theta,
beta,
nu,
delta,
pi,
Method,
hessian,
itermax,
paraminit,
EMIRLS,
refgr
)
Arguments
Y |
Matrix. A matrix containing the variables in the model. |
A |
Matrix. A matrix containing the time variable data. |
X |
Matrix. An optional matrix that modify the probability of belong to group. By default its value is a matrix with one column with value 1. |
TCOV |
Matrix. An optional matrix containing the time covariate that influence the trajectory themselves. By default its value is NULL. |
ng |
Integer. The number of groups. |
nx |
Integer. The number of covariates. |
n |
Integer. Number of individuals. |
nbeta |
Vector of integers. Number of beta parameters for each group. |
nw |
Integer. Number of time dependent covariate. |
ntheta |
Vector of integers. Number of theta parameters for each group. |
period |
Integer. |
degre |
Vector of integer. The degree of every polynomial function. |
degre.nu |
Vector of integer. The degree of all Poisson part for a ZIP model. |
theta |
Vector of real. The parameter for calculated the group membership probability. |
beta |
Vector of real. The beta parameter. |
nu |
Vector of real. The nu parameter. |
delta |
Vector of real. The delta parameter. |
pi |
Vector of real. The group membership probability. |
Method |
String. Determine the method used for find the parameters of the model. The value are L for the Maximum Likelihood Estimation, EM for Expectation Maximization method with quasi newton method inside, EMIWRLS for Expectation Maximization method with Iterative Weighted Least Square. |
hessian |
Logical. Indicate if we want calculate the hessian matrix. Default is FALSE.
If the method use is Likelihood, the hessian is calculated by inverting the Information's Fisher Matrix.
To avoid numerically singular matrix we find the pseudo inverse matrix by using the |
itermax |
Integer. Indicate the maximal number of iteration for |
paraminit |
Vector. The vector of initial parameters. By default |
EMIRLS |
Boolean. True if we use EMIRLS method. |
refgr |
Integer. The number of reference group. By default is 1. |
Value
return a object of class Trajectory.ZIP
beta - vector of the parameter beta.
delta - vector of the parameter delta. Only if we use time covariate.
theta - vector with the parameter theta if there exist a covariate X that modify the probability or the probability of group membership.
nu - vector of the parameters nu.
sd - vector of the standard deviation of the parameters.
tab - a matrix with all the parameters and standard deviation.
Model - a string with the model used.
groups - a integer with the number of group.
Names - strings with the name of the parameters.
Method - a string with the method used.
Size - a integer with the number of individuals.
Likelihood - a real with the Likelihood obtained by the parameters.
Time - a vector with the first row of time values.
degre - a vector with the degree of the polynomial shape for the Poisson part.
degre.nu - a vector with the degree of the polynomial shape for the exceeded zero state.
AIC function to an trajectory object
Description
Calculate the AIC value to an trajectory object.
Usage
trajeRAIC(sol)
Arguments
sol |
Trajectory's object. An object of type trajectory. |
Value
A real.
Examples
data <- read.csv(system.file("extdata", "CNORM2gr.csv", package = "trajeR"))
data <- as.matrix(data)
sol <- trajeR(Y = data[, 2:6], A = data[, 7:11], degre = c(2, 2), Model = "CNORM", Method = "EM")
trajeRAIC(sol)
BIC function to an trajectory object
Description
Calculate the BIC value to an trajectory object.
Usage
trajeRBIC(sol)
Arguments
sol |
Trajectory's object. An object of type trajectory. |
Value
A real.
Examples
data <- read.csv(system.file("extdata", "CNORM2gr.csv", package = "trajeR"))
data <- as.matrix(data)
sol <- trajeR(Y = data[, 2:6], A = data[, 7:11], degre = c(2, 2), Model = "CNORM", Method = "EM")
trajeRBIC(sol)
SH function to an trajectory object
Description
Calculate the Slope Heuristic value to a list of trajectory objects.
Usage
trajeRSH(l)
Arguments
l |
List. A list of objects of type trajectory. |
Value
A vector of real.
Examples
data <- read.csv(system.file("extdata", "CNORM2gr.csv", package = "trajeR"))
data <- as.matrix(data)
degre <- list(c(2, 2), c(1, 1), c(1, 2), c(2, 1), c(0, 0),
c(0, 1), c(1, 0), c(0, 0), c(0, 2), c(2, 0))
sol <- list()
for (i in 1:10) {
sol[[i]] <- trajeR(
Y = data[, 2:6], A = data[, 7:11],
degre = degre[[i]], Model = "CNORM", Method = "EM"
)
}
trajeRSH(sol)