Package {trajeR}

Average Posterior Probability of Assignment

Description

The Average Posterior Probability (AvePP) measures the classification quality. For each group, it is the average of the highest posterior probabilities for all individuals assigned to that group. A value close to 1 indicates a clear classification.

Usage

AvePP(sol, Y, A, X = NULL)

Arguments

Value

A named numeric vector of the same length as the number of groups, containing the AvePP for each group.

Examples

data <- read.csv(system.file("extdata", "CNORM2gr.csv", package = "trajeR"))
data <- as.matrix(data)
# Use drop=FALSE for single-column matrices to preserve dimensions
sol <- trajeR(Y = data[, 2:6], A = data[, 7:11], Risk = data[, 12, drop = FALSE],
              degre = c(2, 2), Model = "CNORM", Method = "EM")
AvePP(sol, Y = data[, 2:6], A = data[, 7:11])

Bootstrap Confidence Intervals for Group Membership Probabilities

Description

Calculates confidence intervals for the estimated group membership probabilities using a parametric bootstrap method. It simulates new theta parameters from a normal distribution based on the estimated theta and their standard errors.

Usage

ConfIntT(sol, Y, A, nb = 10000, alpha = 0.98)

Arguments

Value

A matrix with two rows (lower and upper bounds) and a column for each group, containing the confidence intervals for the estimated probabilities.

Examples

data <- read.csv(system.file("extdata", "CNORM2gr.csv", package = "trajeR"))
sol <- trajeR(Y = data[, 2:6], A = data[, 7:11], degre = c(2, 2), Model = "CNORM", Method = "L")
ConfIntT(sol, Y = data[, 2:6], A = data[, 7:11])

Calculate Posterior Membership Probabilities

Description

GroupProb calculates the posterior probability for each individual to belong to each of the latent groups, based on a fitted trajeR model.

Usage

GroupProb(Obj, Y, A, TCOV = NULL, X = NULL)

Arguments

Value

A matrix of size n x ng (number of individuals by number of groups), where each entry [i, j] is the posterior probability of individual i belonging to group j.

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])

Generate Group Profiles Based on Covariates

Description

This function calculates the mean of specified covariates for each trajectory group. It first assigns each individual to a group based on the highest posterior probability, then computes the average value of each provided covariate for all members of that group.

Usage

GroupProfiles(sol, Y, A, X)

Arguments

Value

A matrix where rows correspond to the covariates in 'X' and columns correspond to the trajectory groups. Each cell contains the mean of a covariate for a specific 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], Risk = data[, 12, drop = FALSE],
  degre = c(2, 2), Model = "CNORM", Method = "L"
)
GroupProfiles(sol, Y = data[, 2:6], A = data[, 7:11], X = data[, 12, drop = FALSE])

Odds of Correct Classification (OCC)

Description

The Odds of Correct Classification (OCC) compares the odds of correct assignment using the model's posterior probabilities against the odds of assignment based on the estimated group proportions alone. A high OCC value suggests that the model provides a much better classification than a random assignment.

Usage

OCC(sol, Y, A)

Arguments

Value

A named numeric vector of the same length as the number of groups, containing the OCC for 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], Risk = data[, 12, drop = FALSE],
              degre = c(2, 2), Model = "CNORM", Method = "EM")
OCC(sol, Y = data[, 2:6], A = data[, 7:11])

Model Adequacy Assessment

Description

Provides a summary table of model adequacy metrics, including estimated group probabilities, confidence intervals, assignment proportions, Average Posterior Probability (AvePP), and Odds of Correct Classification (OCC).

Usage

adequacy(sol, Y, A, nb = 10000, alpha = 0.98)

Arguments

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 = "L")
adequacy(sol, Y = data[, 2:6], A = data[, 7:11])

Compute Confidence Intervals for Predicted Trajectories

Description

Calculates predicted values and confidence intervals for the mean trajectory of each group at specified time points.

Usage

confidenceInt(Obj, newtime, alpha = 0.05)

Arguments

Value

A list of class "Trajectory.predict" containing:

• newtime: The input time points.

• Ypred: Matrix of predicted values for each group at each time point.

• SEYpred: Matrix of standard errors for the predicted values.

• IC.inf: Matrix of the lower bounds of the confidence intervals.

• IC.sup: Matrix of the upper bounds of the confidence intervals.

• groups: Number of groups from the input object.

Examples

data <- read.csv(system.file("extdata", "CNORM2gr.csv", package = "trajeR"))
sol <- trajeR(Y = data[, 2:6], A = data[, 7:11], degre = c(2, 2), Model = "CNORM", Method = "L")
newtime <- seq(0, 1, by = 0.1)
result <- confidenceInt(sol, newtime, alpha = 0.05)
print(result)

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:

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.

Simulated CNORM Dataset

Description

This dataset is a simulated dataset for use with the trajeR.CNORM function, which is an internal function to fit Censored Normal (CNORM) trajectory models. This dataset is likely used to demonstrate the functionality of the trajeR.CNORM model without specific censoring applied, or where censoring is handled implicitly by the model parameters rather than explicitly in the data.

The CNORM model is suitable for continuous outcome variables.

Usage

data_CNORM

Format

Expected to be a data format compatible with the trajeR.CNORM function, typically matrices for the response variable (Y), time variable (A), and potentially covariates (X, TCOV).

Source

Simulated data for illustrative purposes of trajectory analysis using the trajeR.CNORM model.

Simulated Censored CNORM Dataset

Description

This dataset is a simulated dataset specifically designed for use with the trajeR.CNORM function, demonstrating its capabilities with censored data. The trajeR.CNORM function is an internal function to fit Censored Normal (CNORM) models.

Censoring refers to observations where the true value is not precisely known but is known to be above or below a certain threshold. The trajeR.CNORM function supports both ymin (minimum value for censoring) and ymax (maximum value for censoring).

This dataset is expected to contain a response variable (Y), time variable (A), and potentially covariates (X, TCOV) suitable for trajectory analysis using the CNORM model, where some observations in Y are censored.

Usage

data_CNORM_Censored

Format

Expected to be a data format compatible with the trajeR.CNORM function, typically matrices for Y, A, X, and TCOV. The specific structure would be similar to other datasets used with trajeR.CNORM.

Source

Simulated data for illustrative purposes of censored trajectory analysis using the trajeR.CNORM model.

Simulated LOGIT Dataset

Description

This dataset is a simulated dataset for use with the trajeR.LOGIT function, which is an internal function to fit Logistic trajectory models. This dataset is likely used to demonstrate the functionality of the trajeR.LOGIT model.

The LOGIT model is suitable for binary or categorical outcome variables, often representing probabilities or classifications.

Usage

data_LOGIT

Format

Expected to be a data format compatible with the trajeR.LOGIT function, typically matrices for the response variable (Y), time variable (A), and potentially covariates (X, TCOV).

Source

Simulated data for illustrative purposes of trajectory analysis using the trajeR.LOGIT model.

Simulated ZIP Dataset

Description

This dataset is a simulated dataset for use with the trajeR.ZIP function, which is an internal function to fit Zero-Inflated Poisson trajectory models. This dataset is likely used to demonstrate the functionality of the trajeR.ZIP model.

The ZIP model is appropriate for count data that has an excess of zero observations, often found in fields like public health or ecology.

Usage

data_ZIP

Format

Expected to be a data format compatible with the trajeR.ZIP function, typically matrices for the response variable (Y), time variable (A), and potentially covariates (X, TCOV).

Source

Simulated data for illustrative purposes of trajectory analysis using the trajeR.ZIP model.

Differential

Description

Differential

Usage

diffaitbeta(betak, i, t, A, TCOV, fct, diffct)

Arguments

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

Value

real. Compute the value of the function fct for individual i, time t and group k.

Compute Posterior Probabilities and Group Assignments for Multivariate Trajectory Models

Description

Calculates the posterior probabilities of group membership for each individual based on a fitted multivariate trajectory model. It assigns each individual to the most likely joint trajectory group and provides the specific sub-group assignments across all dimensions.

Usage

get_group_probabilities(
  object,
  lY,
  lA,
  Risk = NULL,
  lymin = NULL,
  lymax = NULL,
  lTCOV = NULL,
  ldelta = NULL,
  lnw = NULL
)

Arguments

Value

A list containing the following components:

Plot Multivariate Trajectories

Description

Plots a grid of longitudinal trajectories for a multivariate model. The grid displays each outcome (rows) and each latent group (columns). Individual trajectories are colored by their assigned group and faded, with the specific group highlighted and its average polynomial curve overlaid.

Usage

plot_trajectory_mult(object, lY, lA, assignments, base_colors = NULL)

Arguments

Plot Group Trajectories from a trajeR Model

Description

A generic plotting function for objects of class 'Trajectory.*'. It visualizes both individual and average group trajectories.

Usage

plotrajeR(Obj, ...)

Arguments

Value

This function is called for its side effect of creating a plot. It does not return any value.

Examples

# See examples for specific methods like plotrajeR.Trajectory.CNORM
data <- read.csv(system.file("extdata", "CNORM2gr.csv", package = "trajeR"))
sol <- trajeR(Y = data[, 2:6], A = data[, 7:11], Risk = data[, 12, drop = FALSE],
              degre = c(2, 2), Model = "CNORM", Method = "EM")
plotrajeR(sol)

Plot Method for BETA Trajectory Objects

Description

Plots the trajectories for a Beta model fitted by 'trajeR'.

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

Value

a graphic.

Plot Method for CNORM Trajectory Objects

Description

Plots the trajectories for a Censored Normal model fitted by 'trajeR'.

Usage

## S3 method for class 'Trajectory.CNORM'
plotrajeR(
  Obj,
  plotcov = NULL,
  col = "black",
  Y = NULL,
  A = NULL,
  Risk = NULL,
  mean = FALSE,
  alpha = 1,
  ...
)

Arguments

Value

a graphic.

Plot Method for LOGIT Trajectory Objects

Description

Plots the trajectories for a Logistic model fitted by 'trajeR'.

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

Value

a graphic.

Plot Method for Non-Linear Trajectory Objects

Description

Plots the trajectories for a non-linear model fitted by 'trajeR'.

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

Value

a graphic.

Plot Method for POIS Trajectory Objects

Description

Plots the trajectories for a Poisson model fitted by 'trajeR'.

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

Value

a graphic.

Plot Method for ZIP Trajectory Objects

Description

Plots the trajectories for a Zero-Inflated Poisson (ZIP) model fitted by 'trajeR'.

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

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

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 Method for a 'Trajectory.CNORM' Object

Description

Displays a summary of a censored normal trajectory model fitted by 'trajeR'.

Usage

## S3 method for class 'Trajectory.CNORM'
print(x, ...)

Arguments

Value

Invisibly returns the original object 'x'.

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 Method for a 'Trajectory.LOGIT' Object

Description

Displays a summary of a logistic trajectory model fitted by 'trajeR'.

Usage

## S3 method for class 'Trajectory.LOGIT'
print(x, ...)

Arguments

Value

Invisibly returns the original object 'x'.

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 Method for a 'Trajectory.NL' Object

Description

Displays a summary of a non-linear trajectory model fitted by 'trajeR'.

Usage

## S3 method for class 'Trajectory.NL'
print(x, ...)

Arguments

Value

Invisibly returns the original object 'x'.

Print Method for a 'Trajectory.ZIP' Object

Description

Displays a summary of a zero-inflated Poisson trajectory model fitted by 'trajeR'.

Usage

## S3 method for class 'Trajectory.POIS'
print(x, ...)

Arguments

Value

Invisibly returns the original object 'x'.

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

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

Print Method for a 'trajectory.mult' Object

Description

Displays a summary of a multivariate (joint) trajectory model fitted by 'trajeR_mult'.

Usage

## S3 method for class 'trajectory.mult'
print(x, ...)

Arguments

Value

Invisibly returns the original object 'x'.

Proportion of Individuals Assigned to Each Group

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

Value

A named numeric vector containing the proportion of individuals assigned to 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], Risk = data[, 12, drop = FALSE],
              degre = c(2, 2), Model = "CNORM", Method = "EM")
propAssign(sol, Y = data[, 2:6], A = data[, 7:11])

Fitting longitudinal mixture models

Description

Fitting longitudinal mixture models

Usage

trajeR(
  Y,
  A = NULL,
  Risk = NULL,
  TCOV = NULL,
  data = NULL,
  ng = NULL,
  degre = NULL,
  degre.nu = 0,
  degre.phi = 0,
  Model,
  Method = "L",
  ssigma = FALSE,
  ymax = NULL,
  ymin = NULL,
  hessian = TRUE,
  itermax = 100,
  paraminit = NULL,
  ProbIRLS = TRUE,
  refgr = 1,
  fct = NULL,
  diffct = NULL,
  nbvar = NULL,
  ng.nl = NULL,
  nls.lmiter = 50,
  control = list()
)

Arguments

Value

Returns an object of a class corresponding to the chosen model (e.g., 'Trajectory.CNORM', 'Trajectory.LOGIT').

Returns an object of a class corresponding to the chosen model (e.g., 'Trajectory.CNORM', 'Trajectory.LOGIT'). This object, referred to as a 'Trajectory' object, contains the following elements:

• 'beta': Vector of the final beta parameters for the trajectory shapes.

• 'sigma': Vector of the final sigma parameters (standard deviations), for CNORM and NL models.

• 'nu': Vector of final nu parameters for the zero-inflation part of a ZIP model.

• 'phi': Vector of final phi parameters (precision) for a BETA model.

• 'delta': Vector of the final delta parameters for time-dependent covariates (if any).

• 'theta': Vector of the final theta parameters for group membership probabilities.

• 'sd': Vector of the standard deviations of the estimated parameters.

• 'tab': A data frame with parameter estimates, standard errors, T-values, and p-values.

• 'Model': A string indicating the fitted model (e.g., "CNORM", "LOGIT").

• 'groups': The number of groups.

• 'Names': The names of the parameters.

• 'Method': The estimation method used ("L" for Likelihood or "EM" for Expectation-Maximization).

• 'Size': The number of individuals (observations).

• 'Likelihood': The final log-likelihood value.

• 'Time': The time points for the first individual, or min/max time for ZIP model.

• ‘degre': A vector with the polynomial degrees for each group’s trajectory.

• 'degre.nu': For ZIP models, a vector with the polynomial degrees for the zero-inflation part.

• 'degre.phi': For BETA models, a vector with the polynomial degrees for the precision part.

• 'min', 'max': For CNORM models, the censoring limits used.

• 'fct': For NL models, the non-linear function provided.

• 'varcov': The variance-covariance matrix of the parameters.

• 'convergence': An integer code indicating the convergence status of the optimization algorithm. The meaning depends on the method used.

  • For 'Method = "L"' (using 'ucminf'):

  • '1': Stopped by small gradient ('grtol'). The current iterate is probably a solution.

  • '2': Stopped by small step ('xtol'). Successive iterates are within tolerance.

  • '3': Stopped by function evaluation limit ('maxeval').

  • '4': Stopped by zero step from line search. May be a solution.

  • '-2': Computation did not start: length of parameters is 0.

  • '-4': Computation did not start: 'stepmax' is too small.

  • '-5': Computation did not start: 'grtol' or 'xtol' is not positive.

  • '-6': Computation did not start: 'maxeval' is not positive.

  • '-7': Computation did not start: The provided Hessian was not positive definite.

  • For 'Method = "EM"':

  • '1': Indicates that the EM algorithm has completed its run (convergence is assessed by the user by checking the stability of parameters across iterations).

Internal function to fit Beta Regression Model

Description

Internal function to fit Beta Regression Model

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,
  control
)

Arguments

Value

Returns an object of class 'Trajectory.BETA'.

• 'beta': Vector of final beta parameters (mean).

• 'phi': Vector of final phi parameters (precision).

• 'delta': Vector of final delta parameters (if 'nw > 0').

• 'theta': Vector of final theta parameters for group membership.

• 'sd': Vector of standard deviations of the parameters.

• 'tab': A data frame with parameter estimates and statistics.

• 'Model': The string "BETA".

• 'groups': The number of groups.

• 'Names': The names of the parameters.

• 'Method': The estimation method used.

• 'Size': The number of individuals.

• 'Likelihood': The final log-likelihood value.

• 'Time': The time points for the first individual.

• 'degre': Polynomial degrees for the mean part.

• 'degre.phi': Polynomial degrees for the precision part.

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,
  control
)

Arguments

Value

Returns an object of class 'Trajectory.CNORM'.

• 'beta': Vector of the final beta parameters.

• 'sigma': Vector of the final sigma parameters.

• 'delta': Vector of the final delta parameters (if 'nw > 0').

• 'theta': Vector of the final theta parameters for group membership.

• 'sd': Vector of the standard deviations of the parameters.

• 'tab': A data frame with parameter estimates, standard errors, T-values, and p-values.

• 'Model': The string "CNORM".

• 'groups': The number of groups.

• 'Names': The names of the parameters.

• 'Method': The estimation method used ("L" or "EM").

• 'Size': The number of individuals.

• 'Likelihood': The final log-likelihood value.

• 'Time': The time points for the first individual.

• 'degre': A vector with the polynomial degrees for each group.

• 'min', 'max': The censoring limits used.

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,
  control
)

Arguments

Value

Returns an object of class 'Trajectory.LOGIT'.

• 'beta': Vector of the final beta parameters.

• 'delta': Vector of the final delta parameters (if 'nw > 0').

• 'theta': Vector of the final theta parameters for group membership.

• 'sd': Vector of the standard deviations of the parameters.

• 'tab': A data frame with parameter estimates, standard errors, T-values, and p-values.

• 'Model': The string "LOGIT".

• 'groups': The number of groups.

• 'Names': The names of the parameters.

• 'Method': The estimation method used.

• 'Size': The number of individuals.

• 'Likelihood': The final log-likelihood value.

• 'Time': The time points for the first individual.

• 'degre': A vector with the polynomial degrees for each group.

Internal function to fit a Non-Linear Model

Description

Internal function to fit a 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,
  control
)

Arguments

Value

Returns an object of class 'Trajectory.NL'.

• 'beta': Vector of final beta parameters.

• 'sigma': Vector of final sigma parameters.

• 'delta': Vector of final delta parameters (if 'nw > 0').

• 'theta': Vector of final theta parameters for group membership.

• 'sd': Vector of standard deviations of the parameters.

• 'tab': A data frame with parameter estimates and statistics.

• 'Model': The string "CNORM" (Note: should probably be "NL").

• 'groups': The number of groups.

• 'Names': The names of the parameters.

• 'Method': The estimation method used.

• 'Size': The number of individuals.

• 'Likelihood': The final log-likelihood value.

• 'Time': The time points for the first individual.

• 'degre': A vector with the number of variables for the non-linear function.

• 'fct': The non-linear function provided.

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,
  control
)

Arguments

Value

Returns an object of class 'Trajectory.POIS'.

• 'beta': Vector of final beta parameters.

• 'delta': Vector of final delta parameters (if 'nw > 0').

• 'theta': Vector of final theta parameters for group membership.

• 'sd': Vector of standard deviations of the parameters.

• 'tab': A data frame with parameter estimates and statistics.

• 'Model': The string "POIS".

• 'groups': The number of groups.

• 'Names': The names of the parameters.

• 'Method': The estimation method used.

• 'Size': The number of individuals.

• 'Likelihood': The final log-likelihood value.

• 'Time': The time points for the first individual.

• 'degre': A vector with the polynomial degrees for each group.

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,
  control
)

Arguments

Value

Returns an object of class 'Trajectory.ZIP'.

• 'beta': Vector of final beta parameters (Poisson part).

• 'nu': Vector of final nu parameters (zero-inflation part).

• 'delta': Vector of final delta parameters (if 'nw > 0').

• 'theta': Vector of final theta parameters for group membership.

• 'sd': Vector of standard deviations of the parameters.

• 'tab': A data frame with parameter estimates and statistics.

• 'Model': The string "ZIP".

• 'groups': The number of groups.

• 'Names': The names of the parameters.

• 'Method': The estimation method used.

• 'Size': The number of individuals.

• 'Likelihood': The final log-likelihood value.

• 'Time': A vector with min and max time values.

• 'degre': Polynomial degrees for the Poisson part.

• 'degre.nu': Polynomial degrees for the zero-inflation part.

Akaike Information Criterion (AIC) for a Trajectory Object

Description

Calculates the Akaike Information Criterion (AIC) for a model fitted by 'trajeR'.

Usage

trajeRAIC(sol)

Arguments

Value

A numeric value representing the AIC.

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)

Bayesian Information Criterion (BIC) for a Trajectory Object

Description

Calculates the Bayesian Information Criterion (BIC) for a model fitted by 'trajeR'.

Usage

trajeRBIC(sol)

Arguments

Value

A numeric value representing the BIC.

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)

Slope Heuristic for Trajectory Model Selection

Description

Applies the slope heuristic (from the 'capushe' package) to a list of 'trajeR' models to select the best one.

Usage

trajeRSH(l)

Arguments

Value

An object of class 'DDSE' from the 'capushe' package, containing the selected model and related information.

Examples

data <- read.csv(system.file("extdata", "CNORM2gr.csv", package = "trajeR"))
degre <- list(
 c(2, 2),
 c(1, 1),
 c(1, 2),
 c(2, 1),
 c(2, 0),
 c(0, 2),
 c(3, 2),
 c(3, 1),
 c(2, 3),
 c(1, 3)
)
sol <- list()
for (i in 1:length(degre)) {
  sol[[i]] <- trajeR(
    Y = data[, 2:6], A = data[, 7:11],
    degre = degre[[i]], Model = "CNORM", Method = "EM"
  )
}
trajeRSH(sol)

Fitting Multivariate Longitudinal Mixture Models

Description

Fits a multivariate (joint) group-based trajectory model for multiple longitudinal outcomes.

Usage

trajeR_mult(
  formulas,
  ng,
  models,
  Method = "L",
  Risk = NULL,
  TCOV = NULL,
  data = NULL,
  degre.nu = NULL,
  degre.phi = NULL,
  ssigma = TRUE,
  ymax = NULL,
  ymin = NULL,
  paraminit = NULL,
  control = list(maxit = 100),
  hessian = FALSE
)

Arguments

Value

An object of class trajectory.mult containing the fitted model parameters for each outcome, the interaction parameters (psi), likelihood, and convergence status.