Bayes_PREM {BEND}

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
)

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)