Package 'BEND' reference manual

Title:	Bayesian Estimation of Nonlinear Data (BEND)
Description:	Provides a set of models to estimate nonlinear longitudinal data using Bayesian estimation methods. These models include the: 1) Bayesian Piecewise Random Effects Model (Bayes_PREM()) which estimates a piecewise random effects (mixture) model for a given number of latent classes and a latent number of possible changepoints in each class, and can incorporate class and outcome predictive covariates (see Lamm (2022) <https://hdl.handle.net/11299/252533> and Lock et al., (2018) <doi:10.1007/s11336-017-9594-5>), 2) Bayesian Crossed Random Effects Model (Bayes_CREM()) which estimates a linear, quadratic, exponential, or piecewise crossed random effects models where individuals are changing groups over time (e.g., students and schools; see Rohloff et al., (2024) <doi:10.1111/bmsp.12334>), and 3) Bayesian Bivariate Piecewise Random Effects Model (Bayes_BPREM()) which estimates a bivariate piecewise random effects model to jointly model two related outcomes (e.g., reading and math achievement; see Peralta et al., (2022) <doi:10.1037/met0000358>).
Authors:	Corissa T. Rohloff [aut, cre] , Rik Lamm [aut] , Yadira Peralta [aut] , Nidhi Kohli [aut] , Eric F. Lock [aut]
Maintainer:	Corissa T. Rohloff <[email protected]>
License:	MIT + file LICENSE
Version:	1.0
Built:	2024-11-01 11:16:23 UTC
Source:	CRAN

Bayesian Bivariate Piecewise Random Effects Model (BPREM)

Description

Estimates a Bayesian bivariate piecewise random effects models (BPREM) for longitudinal data with two interrelated outcomes. See Peralta et al. (2022) for more details.

Usage

Bayes_BPREM(
  data,
  id_var,
  time_var,
  y1_var,
  y2_var,
  iters_adapt = 5000,
  iters_burn_in = 1e+05,
  iters_sampling = 50000,
  thin = 15,
  save_full_chains = FALSE,
  save_conv_chains = FALSE,
  verbose = TRUE
)
Bayes_BPREM(
  data,
  id_var,
  time_var,
  y1_var,
  y2_var,
  iters_adapt = 5000,
  iters_burn_in = 1e+05,
  iters_sampling = 50000,
  thin = 15,
  save_full_chains = FALSE,
  save_conv_chains = FALSE,
  verbose = TRUE
)

Arguments

`data`	Data frame in long format, where each row describes a measurement occasion for a given individual. It is assumed that each individual has the same number of assigned timepoints (a.k.a., rows). There can be missingness in the outcomes (`y1_var` and `y2_var`), but there cannot be missingness in time (`time_var`).
`id_var`	Name of column that contains ids for individuals with repeated measures in a longitudinal dataset.
`time_var`	Name of column that contains the time variable. This column cannot contain any missing values.
`y1_var`	Name of column that contains the first outcome variable. Missing values should be denoted by NA.
`y2_var`	Name of column that contains the second outcome variable. Missing values should be denoted by NA.
`iters_adapt`	(optional) Number of iterations for adaptation of jags model (default = 5000).
`iters_burn_in`	(optional) Number of iterations for burn-in (default = 100000).
`iters_sampling`	(optional) Number of iterations for posterior sampling (default = 50000).
`thin`	(optional) Thinning interval for posterior sampling (default = 15).
`save_full_chains`	Logical indicating whether the MCMC chains from rjags should be saved (default = FALSE). Note, this should not be used regularly as it will result in an object with a large file size.
`save_conv_chains`	Logical indicating whether the MCMC chains from rjags should be saved but only for the parameters monitored for convergence (default = FALSE). This would be useful for plotting traceplots for relevant model parameters to evaluate convergence behavior. Note, this should not be used regularly as it will result in an object with a large file size.
`verbose`	Logical controlling whether progress messages/bars are generated (default = TRUE).

Details

For more information on the model equation and priors implemented in this function, see Peralta et al. (2022).

Value

A list (an object of class BPREM) with elements:

`Convergence`	Potential scale reduction factor (PSRF) for each parameter (`parameter_psrf`), Gelman multivariate scale reduction factor (`multivariate_psrf`), and mean PSRF (`mean_psrf`) to assess model convergence.
`Model_Fit`	Deviance (`deviance`), effective number of parameters (`pD`), and Deviance information criterion (`dic`) to assess model fit.
`Fitted_Values`	Vector giving the fitted value at each timepoint for each individual (same length as long data).
`Parameter_Estimates`	Data frame with posterior mean and 95% credible intervals for each model parameter.
`Run_Time`	Total run time for model fitting.
`Full_MCMC_Chains`	If save_full_chains=TRUE, raw MCMC chains from rjags.
`Convergence_MCMC_Chains`	If save_conv_chains=TRUE, raw MCMC chains from rjags but only for the parameters monitored for convergence.

Author(s)

Corissa T. Rohloff, Yadira Peralta

References

Peralta, Y., Kohli, N., Lock, E. F., & Davison, M. L. (2022). Bayesian modeling of associations in bivariate piecewise linear mixed-effects models. Psychological Methods, 27(1), 44–64. https://doi.org/10.1037/met0000358

Examples


# load simulated data
data(SimData_BPREM)
# plot observed data
plot_BEND(data = SimData_BPREM,
          id_var = "id",
          time_var = "time",
          y_var = "y1",
          y2_var = "y2")
# fit Bayes_BPREM()
results_bprem <- Bayes_BPREM(data = SimData_BPREM,
                             id_var = "id",
                             time_var = "time",
                             y1_var = "y1",
                             y2_var = "y2")
# result summary
summary(results_bprem)
# plot fitted results
plot_BEND(data = SimData_BPREM,
          id_var = "id",
          time_var = "time",
          y_var = "y1",
          y2_var = "y2",
          results = results_bprem)


# load simulated data
data(SimData_BPREM)
# plot observed data
plot_BEND(data = SimData_BPREM,
          id_var = "id",
          time_var = "time",
          y_var = "y1",
          y2_var = "y2")
# fit Bayes_BPREM()
results_bprem <- Bayes_BPREM(data = SimData_BPREM,
                             id_var = "id",
                             time_var = "time",
                             y1_var = "y1",
                             y2_var = "y2")
# result summary
summary(results_bprem)
# plot fitted results
plot_BEND(data = SimData_BPREM,
          id_var = "id",
          time_var = "time",
          y_var = "y1",
          y2_var = "y2",
          results = results_bprem)

Bayesian Crossed Random Effects Model (CREM)

Description

Estimates a Bayesian crossed random effects models (CREM) for longitudinal data with dynamic group membership. Four different choices for functional forms are provided: linear, quadratic, exponential, and piecewise. See Rohloff et al. (2024) for more details.

Usage

Bayes_CREM(
  data,
  ind_id_var,
  cross_id_var,
  time_var,
  y_var,
  form = "linear",
  fixed_effects = NULL,
  iters_adapt = 5000,
  iters_burn_in = 50000,
  iters_sampling = 50000,
  thin = 15,
  save_full_chains = FALSE,
  save_conv_chains = FALSE,
  verbose = TRUE
)
Bayes_CREM(
  data,
  ind_id_var,
  cross_id_var,
  time_var,
  y_var,
  form = "linear",
  fixed_effects = NULL,
  iters_adapt = 5000,
  iters_burn_in = 50000,
  iters_sampling = 50000,
  thin = 15,
  save_full_chains = FALSE,
  save_conv_chains = FALSE,
  verbose = TRUE
)

Arguments

`data`	Data frame in long format, where each row describes a measurement occasion for a given individual. It is assumed that each individual has the same number of assigned timepoints (a.k.a., rows). There can be missingness in the outcome (`y_var`), but there cannot be missingness in time (`time_var`).
`ind_id_var`	Name of column that contains ids for individuals with repeated measures in a longitudinal dataset (e.g., students).
`cross_id_var`	Name of column that contains ids for the crossed factor (e.g., teachers).
`time_var`	Name of column that contains the time variable. This column cannot contain any missing values.
`y_var`	Name of column that contains the outcome variable. Missing values should be denoted by NA.
`form`	Name of the functional form. Options include: ‘linear’ (default), ‘quadratic’, ‘exponential’, ‘piecewise’.
`fixed_effects`	(optional) Starting values for the fixed effects parameters.
`iters_adapt`	(optional) Number of iterations for adaptation of jags model (default = 5000).
`iters_burn_in`	(optional) Number of iterations for burn-in (default = 50000).
`iters_sampling`	(optional) Number of iterations for posterior sampling (default = 50000).
`thin`	(optional) Thinning interval for posterior sampling (default = 15).
`save_full_chains`	Logical indicating whether the MCMC chains from rjags should be saved (default = FALSE). Note, this should not be used regularly as it will result in an object with a large file size.
`save_conv_chains`	Logical indicating whether the MCMC chains from rjags should be saved but only for the parameters monitored for convergence (default = FALSE). This would be useful for plotting traceplots for relevant model parameters to evaluate convergence behavior. Note, this should not be used regularly as it will result in an object with a large file size.
`verbose`	Logical controlling whether progress messages/bars are generated (default = TRUE).

Details

For more information on the model equation and priors implemented in this function, see Rohloff et al. (2024).

Note, this function differs from the above reference by estimating the covariances between the random effects parameters. The variance-covariance matrices of the individual and group random effects have a scaled inverse-Wishart prior (see Peralta et al., 2022).

Value

A list (an object of class CREM) with elements:

`Convergence`	Potential scale reduction factor (PSRF) for each parameter (`parameter_psrf`), Gelman multivariate scale reduction factor (`multivariate_psrf`), and mean PSRF (`mean_psrf`) to assess model convergence.
`Model_Fit`	Deviance (`deviance`), effective number of parameters (`pD`), and Deviance information criterion (`dic`) to assess model fit.
`Fitted_Values`	Vector giving the fitted value at each timepoint for each individual (same length as long data).
`Functional_Form`	Functional form fitted.
`Parameter_Estimates`	Data frame with posterior mean and 95% credible intervals for each model parameter.
`Run_Time`	Total run time for model fitting.
`Full_MCMC_Chains`	If save_full_chains=TRUE, raw MCMC chains from rjags.
`Convergence_MCMC_Chains`	If save_conv_chains=TRUE, raw MCMC chains from rjags but only for the parameters monitored for convergence.

Author(s)

Corissa T. Rohloff

References

Rohloff, C. T., Kohli, N., & Lock, E. F. (2024). Identifiability and estimability of Bayesian linear and nonlinear crossed random effects models. British Journal of Mathematical and Statistical Psychology. https://doi.org/10.1111/bmsp.12334

Examples


# load simulated data
data(SimData_PCREM)
# plot observed data
plot_BEND(data = SimData_PCREM,
          id_var = "id",
          time_var = "time",
          y_var = "y")
# fit Bayes_CREM()
results_pcrem <- Bayes_CREM(data = SimData_PCREM,
                            ind_id_var = "id",
                            cross_id_var = "teacherid",
                            time_var = "time",
                            y_var = "y",
                            form="piecewise")
# result summary
summary(results_pcrem)
# plot fitted results
plot_BEND(data = SimData_PCREM,
          id_var = "id",
          time_var = "time",
          y_var = "y",
          results = results_pcrem)


# load simulated data
data(SimData_PCREM)
# plot observed data
plot_BEND(data = SimData_PCREM,
          id_var = "id",
          time_var = "time",
          y_var = "y")
# fit Bayes_CREM()
results_pcrem <- Bayes_CREM(data = SimData_PCREM,
                            ind_id_var = "id",
                            cross_id_var = "teacherid",
                            time_var = "time",
                            y_var = "y",
                            form="piecewise")
# result summary
summary(results_pcrem)
# plot fitted results
plot_BEND(data = SimData_PCREM,
          id_var = "id",
          time_var = "time",
          y_var = "y",
          results = results_pcrem)

Bayesian Piecewise Random Effects Model (PREM) + Extensions

Description

Estimates a Bayesian piecewise random effects model (PREM), with some useful extensions. There are three model options included in this function:

PREM estimates a Bayesian piecewise random effects model with a latent number of changepoints (default). Allows the inclusion of outcome-predictive covariates (CI-PREM).
PREMM estimates a piecewise random effects mixture model for a given number of latent classes and a latent number of possible changepoints in each class.
CI-PREMM estimates a covariate influenced piecewise random effects mixture model for a given number of latent classes and a latent number of possible changepoints in each class. Allows the inclusion of outcome- and/or class-predictive covariates. See Lock et al. (2018) and Lamm (2022) for more details.

Usage

Bayes_PREM(
  data,
  id_var,
  time_var,
  y_var,
  n_class = 1,
  max_cp = 2,
  class_predictive_vars = NULL,
  outcome_predictive_vars = NULL,
  scale_prior = "uniform",
  alpha = 1,
  cp_prior = "binomial",
  binom_prob = 0.5,
  iters_adapt = 1000,
  iters_burn_in = 20000,
  iters_sampling = 30000,
  thin = 15,
  save_full_chains = FALSE,
  save_conv_chains = FALSE,
  verbose = TRUE
)
Bayes_PREM(
  data,
  id_var,
  time_var,
  y_var,
  n_class = 1,
  max_cp = 2,
  class_predictive_vars = NULL,
  outcome_predictive_vars = NULL,
  scale_prior = "uniform",
  alpha = 1,
  cp_prior = "binomial",
  binom_prob = 0.5,
  iters_adapt = 1000,
  iters_burn_in = 20000,
  iters_sampling = 30000,
  thin = 15,
  save_full_chains = FALSE,
  save_conv_chains = FALSE,
  verbose = TRUE
)

Arguments

`data`	Data frame in long format, where each row describes a measurement occasion for a given individual. It is assumed that each individual has the same number of assigned timepoints (a.k.a., rows). There can be missingness in the outcome (`y_var`), but there cannot be missingness in time (`time_var`).
`id_var`	Name of column that contains ids for individuals with repeated measures in a longitudinal dataset.
`time_var`	Name of column that contains the time variable. This column cannot contain any missing values.
`y_var`	Name of column that contains the outcome variable. Missing values should be denoted by NA.
`n_class`	Number of latent classes (default = 1). Note, CI-PREMM only allows for two classes.
`max_cp`	Maximum number of changepoints in each latent class (default = 2).
`class_predictive_vars`	Name(s) of column(s) that contain class-predictive covariates (time-invariant only). Give a vector of names if multiple covariates. Note, there cannot be any missingness in the covariates.
`outcome_predictive_vars`	Name(s) of column(s) that contain outcome-predictive covariates (time-varying or -invariant). Give a vector of names if multiple covariates. Note, there cannot be any missingness in the covariates.
`scale_prior`	Prior for the scale parameter for the hierarchical random effects. Options include: ‘uniform’ (scaled uniform prior; default) or ‘hc’ (scaled half-cauchy prior).
`alpha`	Concentration parameter for Dirichlet prior for latent classes (default = 1). This can be a vector of values corresponding to the number of classes (specified by n_class). Note, this is not used for CI-PGMM.
`cp_prior`	Prior for the number of changepoints in each class. Options include: 'binomial' (default) or 'uniform'.
`binom_prob`	Probability for binomial prior, if specified (default = 0.5).
`iters_adapt`	(optional) Number of iterations for adaptation of jags model (default = 1000).
`iters_burn_in`	(optional) Number of iterations for burn-in (default = 20000).
`iters_sampling`	(optional) Number of iterations for posterior sampling (default = 30000).
`thin`	(optional) Thinning interval for posterior sampling (default = 15).
`save_full_chains`	Logical indicating whether the MCMC chains from rjags should be saved (default = FALSE). Note, this should not be used regularly as it will result in an object with a large file size.
`save_conv_chains`	Logical indicating whether the MCMC chains from rjags should be saved but only for the parameters monitored for convergence (default = FALSE). This would be useful for plotting traceplots for relevant model parameters to evaluate convergence behavior. Note, this should not be used regularly as it will result in an object with a large file size.
`verbose`	Logical controlling whether progress messages/bars are generated (default = TRUE).

Details

For more information on the model equation and priors implemented in this function, see Lamm et al. (2022; CI-PREMM) and Lock et al. (2018; PREMM).

Value

A list (an object of class PREM) with elements:

`Convergence`	Potential scale reduction factor (PSRF) for each parameter (`parameter_psrf`), Gelman multivariate scale reduction factor (`multivariate_psrf`), and mean PSRF (`mean_psrf`) to assess model convergence.
`Model_Fit`	Deviance (`deviance`), effective number of parameters (`pD`), and Deviance information criterion (`dic`) to assess model fit.
`Fitted_Values`	Vector giving the fitted value at each timepoint for each individual (same length as long data).
`Parameter_Estimates`	Data frame with posterior mean and 95% credible intervals for each model parameter.
`Run_Time`	Total run time for model fitting.
`Full_MCMC_Chains`	If save_full_chains=TRUE, raw MCMC chains from rjags.
`Convergence_MCMC_Chains`	If save_conv_chains=TRUE, raw MCMC chains from rjags but only for the parameters monitored for convergence.

Class_Information contains a list with elements:

`class_membership`	Vector of length n with class membership assignments for each individual.
`individ_class_probability`	nxC matrix with each individual’s probabilities of belonging to each class conditional on their class-predictive covariates (when applicable) and growth curve.
`unconditional_class_probability`	This output will differ based on which model was fit. For a PREM or CI-PREM, this will equal 1 as there is only one class. For a PREMM or CI-PREMM with only outcome-predictive covariates, this will be a vector of length C denoting the population probability of belonging to each class. For a CI-PREMM with class-predictive covariates, this will be a vector of length n denoting the probability of each individual belonging to the non-reference class (Class 2) based on their class-predictive covariates only.

Author(s)

Corissa T. Rohloff, Rik Lamm, Eric F. Lock

References

Lamm, R. (2022). Incorporation of covariates in Bayesian piecewise growth mixture models. https://hdl.handle.net/11299/252533

Lock, E. F., Kohli, N., & Bose, M. (2018). Detecting multiple random changepoints in Bayesian piecewise growth mixture models. Psychometrika, 83(3), 733–750. https://doi.org/10.1007/s11336-017-9594-5

Examples


# load simulated data
data(SimData_PREM)
# plot observed data
plot_BEND(data = SimData_PREM,
          id_var = "id",
          time_var = "time",
          y_var = "y")

# PREM ---------------------------------------------------------------------------------
# fit Bayes_PREM()
results_prem <- Bayes_PREM(data = SimData_PREM,
                           id_var = "id",
                           time_var = "time",
                           y_var = "y")
# result summary
summary(results_prem)
# plot fitted results
plot_BEND(data = SimData_PREM,
          id_var = "id",
          time_var = "time",
          y_var = "y",
          results = results_prem)

# CI-PREM ---------------------------------------------------------------------------------
# fit Bayes_PREM()
results_ciprem <- Bayes_PREM(data = SimData_PREM,
                             id_var = "id",
                             time_var = "time",
                             y_var = "y",
                             outcome_predictive_vars = "outcome_pred_1")
# result summary
summary(results_ciprem)
# plot fitted results
plot_BEND(data = SimData_PREM,
          id_var = "id",
          time_var = "time",
          y_var = "y",
          results = results_ciprem)

# PREMM ---------------------------------------------------------------------------------
# fit Bayes_PREM()
results_premm <- Bayes_PREM(data = SimData_PREM,
                            id_var = "id",
                            time_var = "time",
                            y_var = "y",
                            n_class = 2)
# result summary
summary(results_premm)
# plot fitted results
plot_BEND(data = SimData_PREM,
          id_var = "id",
          time_var = "time",
          y_var = "y",
          results = results_premm)


# CI-PREMM ---------------------------------------------------------------------------------
# fit Bayes_PREM()
results_cipremm <- Bayes_PREM(data = SimData_PREM,
                              id_var = "id",
                              time_var = "time",
                              y_var = "y",
                              n_class = 2,
                              class_predictive_vars = c("class_pred_1", "class_pred_2"),
                              outcome_predictive_vars = "outcome_pred_1")
# result summary
summary(results_cipremm)
# plot fitted results
plot_BEND(data = SimData_PREM,
          id_var = "id",
          time_var = "time",
          y_var = "y",
          results = results_cipremm)


# load simulated data
data(SimData_PREM)
# plot observed data
plot_BEND(data = SimData_PREM,
          id_var = "id",
          time_var = "time",
          y_var = "y")

# PREM ---------------------------------------------------------------------------------
# fit Bayes_PREM()
results_prem <- Bayes_PREM(data = SimData_PREM,
                           id_var = "id",
                           time_var = "time",
                           y_var = "y")
# result summary
summary(results_prem)
# plot fitted results
plot_BEND(data = SimData_PREM,
          id_var = "id",
          time_var = "time",
          y_var = "y",
          results = results_prem)

# CI-PREM ---------------------------------------------------------------------------------
# fit Bayes_PREM()
results_ciprem <- Bayes_PREM(data = SimData_PREM,
                             id_var = "id",
                             time_var = "time",
                             y_var = "y",
                             outcome_predictive_vars = "outcome_pred_1")
# result summary
summary(results_ciprem)
# plot fitted results
plot_BEND(data = SimData_PREM,
          id_var = "id",
          time_var = "time",
          y_var = "y",
          results = results_ciprem)

# PREMM ---------------------------------------------------------------------------------
# fit Bayes_PREM()
results_premm <- Bayes_PREM(data = SimData_PREM,
                            id_var = "id",
                            time_var = "time",
                            y_var = "y",
                            n_class = 2)
# result summary
summary(results_premm)
# plot fitted results
plot_BEND(data = SimData_PREM,
          id_var = "id",
          time_var = "time",
          y_var = "y",
          results = results_premm)


# CI-PREMM ---------------------------------------------------------------------------------
# fit Bayes_PREM()
results_cipremm <- Bayes_PREM(data = SimData_PREM,
                              id_var = "id",
                              time_var = "time",
                              y_var = "y",
                              n_class = 2,
                              class_predictive_vars = c("class_pred_1", "class_pred_2"),
                              outcome_predictive_vars = "outcome_pred_1")
# result summary
summary(results_cipremm)
# plot fitted results
plot_BEND(data = SimData_PREM,
          id_var = "id",
          time_var = "time",
          y_var = "y",
          results = results_cipremm)

Plot a BEND Model (PREM, CREM, BPREM)

Description

Generates a "spaghetti plot" of observed longitudinal trajectories for each individual. If the results from a BEND function are supplied, the trajectory defined by the mean parameters is shown in bold. If fitting a mixture (PREMM or CI-PREMM) or bivariate model (BPREM), the mean trajectories for classes or outcomes will be distinguished by color.

Usage

plot_BEND(
  data,
  id_var,
  time_var,
  y_var,
  y2_var = NULL,
  results = NULL,
  xlab = "X",
  ylab = "Y",
  colors = NULL,
  mean_colors = NULL,
  legend_pos = "topright",
  ...
)
plot_BEND(
  data,
  id_var,
  time_var,
  y_var,
  y2_var = NULL,
  results = NULL,
  xlab = "X",
  ylab = "Y",
  colors = NULL,
  mean_colors = NULL,
  legend_pos = "topright",
  ...
)

Arguments

`data`	Data frame in long format, where each row describes a measurement occasion for a given individual. It is assumed that each individual has the same number of assigned timepoints (a.k.a., rows).
`id_var`	Name of column that contains ids for individuals with repeated measures in a longitudinal dataset.
`time_var`	Name of column that contains the time variable.
`y_var`	Name of column that contains the outcome variable.
`y2_var`	(for `BPREM` only) Name of column that contains the second outcome variable.
`results`	The output of `BEND` model to the data. If results=NULL, only a spaghetti plot of the data will be generated.
`xlab`	X-axis label for the generated plot.
`ylab`	Y-axis label for the generated plot.
`colors`	Colors for each class (`PREMM` or `CI-PREMM`) or outcome (`BPREM`). By default, up to 5 colors are provided in the following order: “blue” (class 1 and outcome 1), “red” (class 2 and outcome 2), “green” (class 3), “gold” (class 4), “gray” (class 5).
`mean_colors`	Colors for the trajectory defined by the mean parameters for each class (`PREMM` or `CI-PREMM`) or outcome (`BPREM`). By default, up to 5 colors are provided in the following order: “darkblue” (class 1 and outcome 1), “darkred” (class 2 and outcome 2), “darkgreen” (class 3), “gold4” (class 4), “darkgray” (class 5).
`legend_pos`	(optional) Option to change legend position (default = "topright").
`...`	(optional) Other parameters to pass to the `plot()` function.

Value

No return value, called to generate plot.

Author(s)

Corissa T. Rohloff

Examples

# load simulated data
data(SimData_PREM)
# plot observed data
plot_BEND(data = SimData_PREM,
          id_var = "id",
          time_var = "time",
          y_var = "y")
# load fitted model results
data(results_prem)
# plot fitted results
plot_BEND(data = SimData_PREM,
          id_var = "id",
          time_var = "time",
          y_var = "y",
          results = results_prem)

# load simulated data
data(SimData_PREM)
# plot observed data
plot_BEND(data = SimData_PREM,
          id_var = "id",
          time_var = "time",
          y_var = "y")
# load fitted model results
data(results_prem)
# plot fitted results
plot_BEND(data = SimData_PREM,
          id_var = "id",
          time_var = "time",
          y_var = "y",
          results = results_prem)

Fitted results for a BPREM

Description

Simulated data for a bivariate piecewise random effects model (BPREM) using SimData_BPREM. Included to demonstrate the use of summary.BPREM().

Usage

data(results_bprem)
data(results_bprem)

Format

A list (an object of class BPREM) with fitted model results.

Fitted results for a PCREM

Description

Simulated data for a piecewise crossed random effects model (PCREM) using SimData_CREM. Included to demonstrate the use of summary.CREM().

Usage

data(results_pcrem)
data(results_pcrem)

Format

A list (an object of class CREM) with fitted model results.

Fitted results for a PREM

Description

Fitted results for a piecewise random effects model (PREM) using SimData_PREM. Included to demonstrate the use of plot_BEND() and summary.PREM().

Usage

data(results_prem)
data(results_prem)

Format

A list (an object of class PREM) with fitted model results.

Simulated data for a BPREM

Description

Simulated data for a bivariate piecewise random effects model (BPREM) with 7 timepoints collected on 30 individuals.

Usage

data(SimData_BPREM)
data(SimData_BPREM)

Format

A data frame with 210 rows and 4 variables.

Details

id ID for each individual.
time Timepoints for each individual.
y1 Outcome 1.
y2 Outcome 2.

Simulated data for a PCREM

Description

Simulated data for a piecewise crossed random effects model (PCREM) with 7 timepoints collected on 30 individuals.

Usage

data(SimData_PCREM)
data(SimData_PCREM)

Format

A data frame with 210 rows and 4 variables.

Details

id ID for each individual.
teacherid ID for each teacher.
time Timepoints for each individual.
y Outcome.

Simulated data for a PREM + Extensions

Description

Simulated data for a piecewise random effects model (PREM) and useful extensions (CI-PREM, PREMM, CI-PREMM) with 18 timepoints collected on 30 individuals.

Usage

data(SimData_PREM)
data(SimData_PREM)

Format

A data frame with 540 rows and 6 variables.

Details

id ID for each individual.
time Timepoints for each individual.
y Outcome.
class_pred_1 First class predictive covariate (time-invariant).
class_pred_2 Second class predictive covariate (time-invariant).
outcome_pred_1 Outcome predictive covariate (time-varying).

Summarize the results of a bivariate piecewise random effects model (BPREM)

Description

Provides a summary of a BPREM model, as returned by Bayes_BPREM().

Usage

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

Arguments

`object`	An object of class "BPREM" (returned by `Bayes_BPREM(...)`).
`...`	Additional arguments.

Value

Prints estimates for key parameters in the BPREM. Also returns a list of these values.

Author(s)

Corissa T. Rohloff

Examples

# load fitted model results
data(results_bprem)
# result summary
summary(results_bprem)

# load fitted model results
data(results_bprem)
# result summary
summary(results_bprem)

Summarize the results of a crossed random effects model (CREM)

Description

Provides a summary of a CREM model, as returned by Bayes_CREM().

Usage

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

Arguments

`object`	An object of class "CREM" (returned by `Bayes_CREM(...)`).
`...`	Additional arguments.

Value

Prints estimates for key parameters in the CREM. Also returns a list of these values.

Author(s)

Corissa T. Rohloff

Examples

# load fitted model results
data(results_pcrem)
# result summary
summary(results_pcrem)

# load fitted model results
data(results_pcrem)
# result summary
summary(results_pcrem)

Summarize the results of a piecewise random effects model (PREM)

Description

Provides a summary of a PREM model, as returned by Bayes_PREM().

Usage

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

Arguments

`object`	An object of class "PREM" (returned by `Bayes_PREM(...)`).
`...`	Additional arguments.

Value

Prints estimates for key parameters in the PREM. Also returns a list of these values.

Author(s)

Corissa T. Rohloff

Examples

# load fitted model results
data(results_prem)
# result summary
summary(results_prem)

# load fitted model results
data(results_prem)
# result summary
summary(results_prem)

Package 'BEND'

Help Index

Bayesian Bivariate Piecewise Random Effects Model (BPREM)

Description

Usage

Arguments

Details

Value

Author(s)

References

Examples

Bayesian Crossed Random Effects Model (CREM)

Description

Usage

Arguments

Details

Value

Author(s)

References

Examples

Bayesian Piecewise Random Effects Model (PREM) + Extensions

Description

Usage

Arguments

Details

Value

Author(s)

References

Examples

Plot a BEND Model (PREM, CREM, BPREM)

Description

Usage

Arguments

Value

Author(s)

Examples

Fitted results for a BPREM

Description

Usage

Format

Fitted results for a PCREM

Description

Usage

Format

Fitted results for a PREM

Description

Usage

Format

Simulated data for a BPREM

Description

Usage

Format

Details

Simulated data for a PCREM

Description

Usage

Format

Details

Simulated data for a PREM + Extensions

Description

Usage

Format

Details

Summarize the results of a bivariate piecewise random effects model (BPREM)

Description

Usage

Arguments

Value

Author(s)

Examples

Summarize the results of a crossed random effects model (CREM)

Description

Usage

Arguments

Value

Author(s)

Examples

Summarize the results of a piecewise random effects model (PREM)

Description

Usage