| Title: | Bayesian Understanding for Mediator Selection Framework |
|---|---|
| Description: | A collection of quantitative tools for selecting mediating effects within exploratory Bayesian mediation models. The package accommodates both continuous and dichotomous outcomes, including the dependent variables and the mediators for identifying and analyzing mediation pathways. |
| Authors: | Dingjing Shi [aut, cre], Tansu Celikel [aut], Chih-Chia Hsing [aut], Dexin Shi [aut] |
| Maintainer: | Dingjing Shi <[email protected]> |
| License: | GPL (>= 3) |
| Version: | 0.1.4 |
| Built: | 2026-10-31 11:46:11 UTC |
| Source: | https://github.com/olfactorybulb/buzzmed |
This function selects time-invariant binary mediators using the generalized two-stage exploratory Bayesian mediation model with dichotomous dependent variables.
buzzEBMcatMcatY( model, dataset, my_prior = NULL, advanced = NULL, a.pip.hyperalpha = NULL, a.pip.hyperbeta = NULL, b.pip.hyperalpha = NULL, b.pip.hyperbeta = NULL, direct.coef.mean = NULL, direct.coef.precision = NULL, direct.coef.init = NULL, a.pip.hyperprior.init = NULL, b.pip.hyperprior.init = NULL, n_chains = NULL, n_adapt = NULL, n_burnin = NULL, n_iter = NULL, thin = NULL )buzzEBMcatMcatY( model, dataset, my_prior = NULL, advanced = NULL, a.pip.hyperalpha = NULL, a.pip.hyperbeta = NULL, b.pip.hyperalpha = NULL, b.pip.hyperbeta = NULL, direct.coef.mean = NULL, direct.coef.precision = NULL, direct.coef.init = NULL, a.pip.hyperprior.init = NULL, b.pip.hyperprior.init = NULL, n_chains = NULL, n_adapt = NULL, n_burnin = NULL, n_iter = NULL, thin = NULL )
model |
A character string specifying the mediation model to be
fitted. The model should be specified using the syntax
|
dataset |
A |
my_prior |
Optional |
advanced |
Character. Use |
a.pip.hyperalpha |
Numeric scalar or vector. Alpha hyperparameter of
the Beta prior distribution for the |
a.pip.hyperbeta |
Numeric scalar or vector. Beta hyperparameter of
the Beta prior distribution for the |
b.pip.hyperalpha |
Numeric scalar or vector. Alpha hyperparameter of
the Beta prior distribution for the |
b.pip.hyperbeta |
Numeric scalar or vector. Beta hyperparameter of
the Beta prior distribution for the |
direct.coef.mean |
Numeric scalar or vector. Mean parameter of the
Normal prior distribution for the direct effects ( |
direct.coef.precision |
Numeric scalar or vector. Precision parameter
of the Normal prior distribution for the direct effects ( |
direct.coef.init |
Numeric or |
a.pip.hyperprior.init |
Numeric or |
b.pip.hyperprior.init |
Numeric or |
n_chains |
Integer. Number of MCMC chains. |
n_adapt |
Integer. Number of adaptation iterations. |
n_burnin |
Integer. Number of burn-in iterations. |
n_iter |
Integer. Number of post-burn-in iterations. |
thin |
Integer. Thinning interval. |
Fits a generalized two-stage exploratory Bayesian mediation model, specifically
designed for cases where both the mediators () and the outcome
variable () are binary (0/1).
A matrix of posterior summary statistics for the monitored parameters.
This function is strictly for binary data. For variables with more than two levels, please convert them into dummy variables or ensure they are binary before running.
Shi, D., Shi, D., and Fairchild, A. J. (2023) "Variable Selection for Mediators under a Bayesian Mediation Model" <doi:10.1080/10705511.2022.2164285>
# Binary case: Both M and Y are Binary set.seed(101) n <- 100 toy_data <- data.frame( X = rbinom(n, 1, 0.5), M1 = rbinom(n, 1, 0.3), M2 = rbinom(n, 1, 0.7), Y = rbinom(n, 1, 0.5) ) # Fit the model results <- buzzEBMcatMcatY( model = "Y ~ X | M1 + M2", dataset = toy_data, n_burnin = 200, n_iter = 1000 ) summary(results)# Binary case: Both M and Y are Binary set.seed(101) n <- 100 toy_data <- data.frame( X = rbinom(n, 1, 0.5), M1 = rbinom(n, 1, 0.3), M2 = rbinom(n, 1, 0.7), Y = rbinom(n, 1, 0.5) ) # Fit the model results <- buzzEBMcatMcatY( model = "Y ~ X | M1 + M2", dataset = toy_data, n_burnin = 200, n_iter = 1000 ) summary(results)
This function selects time-invariant binary mediators using the generalized two-stage exploratory Bayesian mediation model with continuous dependent variables.
buzzEBMcatMcontY( model, dataset, my_prior = NULL, advanced = NULL, y.prec.shape = NULL, y.prec.rate = NULL, a.pip.hyperalpha = NULL, a.pip.hyperbeta = NULL, b.pip.hyperalpha = NULL, b.pip.hyperbeta = NULL, direct.coef.mean = NULL, direct.coef.precision = NULL, y.prec.init = NULL, direct.coef.init = NULL, a.pip.hyperprior.init = NULL, b.pip.hyperprior.init = NULL, n_chains = NULL, n_adapt = NULL, n_burnin = NULL, n_iter = NULL, thin = NULL )buzzEBMcatMcontY( model, dataset, my_prior = NULL, advanced = NULL, y.prec.shape = NULL, y.prec.rate = NULL, a.pip.hyperalpha = NULL, a.pip.hyperbeta = NULL, b.pip.hyperalpha = NULL, b.pip.hyperbeta = NULL, direct.coef.mean = NULL, direct.coef.precision = NULL, y.prec.init = NULL, direct.coef.init = NULL, a.pip.hyperprior.init = NULL, b.pip.hyperprior.init = NULL, n_chains = NULL, n_adapt = NULL, n_burnin = NULL, n_iter = NULL, thin = NULL )
model |
A character string specifying the mediation model to be
fitted. The model should be specified using the syntax
|
dataset |
A |
my_prior |
Optional |
advanced |
Character. Use |
y.prec.shape |
Numeric scalar. Shape hyperparameter of the Gamma prior distribution for the outcome residual precision. The default value is 1. |
y.prec.rate |
Numeric scalar. Rate hyperparameter of the Gamma prior distribution for the outcome residual precision. The default value is 0.001. |
a.pip.hyperalpha |
Numeric scalar or vector. Alpha hyperparameter of
the Beta prior distribution for the |
a.pip.hyperbeta |
Numeric scalar or vector. Beta hyperparameter of
the Beta prior distribution for the |
b.pip.hyperalpha |
Numeric scalar or vector. Alpha hyperparameter of
the Beta prior distribution for the |
b.pip.hyperbeta |
Numeric scalar or vector. Beta hyperparameter of
the Beta prior distribution for the |
direct.coef.mean |
Numeric scalar or vector. Mean parameter of the
Normal prior distribution for the direct effects ( |
direct.coef.precision |
Numeric scalar or vector. Precision parameter
of the Normal prior distribution for the direct effects ( |
y.prec.init |
Numeric or |
direct.coef.init |
Numeric or |
a.pip.hyperprior.init |
Numeric or |
b.pip.hyperprior.init |
Numeric or |
n_chains |
Integer. Number of MCMC chains. |
n_adapt |
Integer. Number of adaptation iterations. |
n_burnin |
Integer. Number of burn-in iterations. |
n_iter |
Integer. Number of post-burn-in iterations. |
thin |
Integer. Thinning interval. |
Fits a generalized two-stage exploratory Bayesian mediation model,
specifically designed for cases where the mediators () are
binary (0/1) and the outcome variable () is continuous.
A matrix of posterior summary statistics for the monitored parameters.
Shi, D., Shi, D., and Fairchild, A. J. (2023) "Variable Selection for Mediators under a Bayesian Mediation Model" <doi:10.1080/10705511.2022.2164285>
# Mixed case: Binary M, Continuous Y set.seed(789) n <- 100 toy_data <- data.frame( X = rnorm(n), M1 = rbinom(n, 1, 0.4), M2 = rbinom(n, 1, 0.6), Y = rnorm(n) ) # Fit the model results <- buzzEBMcatMcontY( model = "Y ~ X | M1 + M2", dataset = toy_data, n_burnin = 200, n_iter = 1000 ) summary(results)# Mixed case: Binary M, Continuous Y set.seed(789) n <- 100 toy_data <- data.frame( X = rnorm(n), M1 = rbinom(n, 1, 0.4), M2 = rbinom(n, 1, 0.6), Y = rnorm(n) ) # Fit the model results <- buzzEBMcatMcontY( model = "Y ~ X | M1 + M2", dataset = toy_data, n_burnin = 200, n_iter = 1000 ) summary(results)
This function selects time-invariant continuous mediators using the generalized two-stage exploratory Bayesian mediation model with dichotomous dependent variables.
buzzEBMcontMcatY( model, dataset, my_prior = NULL, advanced = NULL, m.prec.shape = NULL, m.prec.rate = NULL, a.pip.hyperalpha = NULL, a.pip.hyperbeta = NULL, b.pip.hyperalpha = NULL, b.pip.hyperbeta = NULL, direct.coef.mean = NULL, direct.coef.precision = NULL, m.prec.init = NULL, direct.coef.init = NULL, a.pip.hyperprior.init = NULL, b.pip.hyperprior.init = NULL, n_chains = NULL, n_adapt = NULL, n_burnin = NULL, n_iter = NULL, thin = NULL )buzzEBMcontMcatY( model, dataset, my_prior = NULL, advanced = NULL, m.prec.shape = NULL, m.prec.rate = NULL, a.pip.hyperalpha = NULL, a.pip.hyperbeta = NULL, b.pip.hyperalpha = NULL, b.pip.hyperbeta = NULL, direct.coef.mean = NULL, direct.coef.precision = NULL, m.prec.init = NULL, direct.coef.init = NULL, a.pip.hyperprior.init = NULL, b.pip.hyperprior.init = NULL, n_chains = NULL, n_adapt = NULL, n_burnin = NULL, n_iter = NULL, thin = NULL )
model |
A character string specifying the mediation model to be
fitted. The model should be specified using the syntax
|
dataset |
A |
my_prior |
Optional |
advanced |
Character. Use |
m.prec.shape |
Numeric scalar or vector of length equal to the number of mediators. Shape hyperparameter of the Gamma prior distribution for the mediator residual precisions. The default value is 1. |
m.prec.rate |
Numeric scalar or vector of length equal to the number of mediators. Rate hyperparameter of the Gamma prior distribution for the mediator residual precisions. The default value is 0.001. |
a.pip.hyperalpha |
Numeric scalar or vector. Alpha hyperparameter of
the Beta prior distribution for the |
a.pip.hyperbeta |
Numeric scalar or vector. Beta hyperparameter of
the Beta prior distribution for the |
b.pip.hyperalpha |
Numeric scalar or vector. Alpha hyperparameter of
the Beta prior distribution for the |
b.pip.hyperbeta |
Numeric scalar or vector. Beta hyperparameter of
the Beta prior distribution for the |
direct.coef.mean |
Numeric scalar or vector. Mean parameter of the
Normal prior distribution for the direct effects ( |
direct.coef.precision |
Numeric scalar or vector. Precision parameter
of the Normal prior distribution for the direct effects ( |
m.prec.init |
Numeric or |
direct.coef.init |
Numeric or |
a.pip.hyperprior.init |
Numeric or |
b.pip.hyperprior.init |
Numeric or |
n_chains |
Integer. Number of MCMC chains. |
n_adapt |
Integer. Number of adaptation iterations. |
n_burnin |
Integer. Number of burn-in iterations. |
n_iter |
Integer. Number of post-burn-in iterations. |
thin |
Integer. Thinning interval. |
Fits a generalized two-stage exploratory Bayesian mediation model,
specifically designed for cases where the mediators () are continuous
and the outcome variable () is binary (0/1).
A matrix of posterior summary statistics for the monitored parameters.
Shi, D., Shi, D., and Fairchild, A. J. (2023) "Variable Selection for Mediators under a Bayesian Mediation Model" <doi:10.1080/10705511.2022.2164285>
# Mixed case: Continuous M, Binary Y set.seed(456) n <- 100 toy_data <- data.frame( X = rnorm(n), M1 = rnorm(n), M2 = rnorm(n), Y = rbinom(n, 1, 0.5) ) # Fit the model results <- buzzEBMcontMcatY( model = "Y ~ X | M1 + M2", dataset = toy_data, n_burnin = 200, n_iter = 1000 ) summary(results)# Mixed case: Continuous M, Binary Y set.seed(456) n <- 100 toy_data <- data.frame( X = rnorm(n), M1 = rnorm(n), M2 = rnorm(n), Y = rbinom(n, 1, 0.5) ) # Fit the model results <- buzzEBMcontMcatY( model = "Y ~ X | M1 + M2", dataset = toy_data, n_burnin = 200, n_iter = 1000 ) summary(results)
This function selects time-invariant continuous mediators using the generalized two-stage exploratory Bayesian mediation model with continuous dependent variables.
buzzEBMcontMcontY( model, dataset, my_prior = NULL, advanced = NULL, m.prec.shape = NULL, m.prec.rate = NULL, y.prec.shape = NULL, y.prec.rate = NULL, a.pip.hyperalpha = NULL, a.pip.hyperbeta = NULL, b.pip.hyperalpha = NULL, b.pip.hyperbeta = NULL, direct.coef.mean = NULL, direct.coef.precision = NULL, m.prec.init = NULL, y.prec.init = NULL, direct.coef.init = NULL, a.pip.hyperprior.init = NULL, b.pip.hyperprior.init = NULL, n_chains = NULL, n_adapt = NULL, n_burnin = NULL, n_iter = NULL, thin = NULL )buzzEBMcontMcontY( model, dataset, my_prior = NULL, advanced = NULL, m.prec.shape = NULL, m.prec.rate = NULL, y.prec.shape = NULL, y.prec.rate = NULL, a.pip.hyperalpha = NULL, a.pip.hyperbeta = NULL, b.pip.hyperalpha = NULL, b.pip.hyperbeta = NULL, direct.coef.mean = NULL, direct.coef.precision = NULL, m.prec.init = NULL, y.prec.init = NULL, direct.coef.init = NULL, a.pip.hyperprior.init = NULL, b.pip.hyperprior.init = NULL, n_chains = NULL, n_adapt = NULL, n_burnin = NULL, n_iter = NULL, thin = NULL )
model |
A character string specifying the mediation model to be
fitted. The model should be specified using the syntax
|
dataset |
A |
my_prior |
Optional |
advanced |
Character. Use |
m.prec.shape |
Numeric scalar or vector of length equal to the number of mediators. Shape hyperparameter of the Gamma prior distribution for the mediator residual precisions. The default value is 1. |
m.prec.rate |
Numeric scalar or vector of length equal to the number of mediators. Rate hyperparameter of the Gamma prior distribution for the mediator residual precisions. The default value is 0.001. |
y.prec.shape |
Numeric scalar. Shape hyperparameter of the Gamma prior distribution for the outcome residual precision. The default value is 1. |
y.prec.rate |
Numeric scalar. Rate hyperparameter of the Gamma prior distribution for the outcome residual precision. The default value is 0.001. |
a.pip.hyperalpha |
Numeric scalar or vector. Alpha hyperparameter of
the Beta prior distribution for the |
a.pip.hyperbeta |
Numeric scalar or vector. Beta hyperparameter of
the Beta prior distribution for the |
b.pip.hyperalpha |
Numeric scalar or vector. Alpha hyperparameter of
the Beta prior distribution for the |
b.pip.hyperbeta |
Numeric scalar or vector. Beta hyperparameter of
the Beta prior distribution for the |
direct.coef.mean |
Numeric scalar or vector. Mean parameter of the
Normal prior distribution for the direct effects ( |
direct.coef.precision |
Numeric scalar or vector. Precision parameter
of the Normal prior distribution for the direct effects ( |
m.prec.init |
Numeric or |
y.prec.init |
Numeric or |
direct.coef.init |
Numeric or |
a.pip.hyperprior.init |
Numeric or |
b.pip.hyperprior.init |
Numeric or |
n_chains |
Integer. Number of MCMC chains. |
n_adapt |
Integer. Number of adaptation iterations. |
n_burnin |
Integer. Number of burn-in iterations. |
n_iter |
Integer. Number of post-burn-in iterations. |
thin |
Integer. Thinning interval. |
Fits a generalized two-stage exploratory Bayesian mediation model, specifically
designed for cases where both the mediators () and the outcome variable
() are continuous.
A matrix of posterior summary statistics for the monitored parameters.
Shi, D., Shi, D., and Fairchild, A. J. (2023) "Variable Selection for Mediators under a Bayesian Mediation Model" <doi:10.1080/10705511.2022.2164285>
# 1. Create a continuous synthetic dataset set.seed(123) n <- 100 toy_data <- data.frame( X = rnorm(n), M1 = rnorm(n), M2 = rnorm(n), Y = rnorm(n) ) # 2. Fit the model using lavaan-style syntax # We define Y as the outcome, with M1, M2, and X as predictors results <- buzzEBMcontMcontY( model = "Y ~ X | M1 + M2", dataset = toy_data, n_burnin = 500, n_iter = 2000 ) # 3. Check results summary(results)# 1. Create a continuous synthetic dataset set.seed(123) n <- 100 toy_data <- data.frame( X = rnorm(n), M1 = rnorm(n), M2 = rnorm(n), Y = rnorm(n) ) # 2. Fit the model using lavaan-style syntax # We define Y as the outcome, with M1, M2, and X as predictors results <- buzzEBMcontMcontY( model = "Y ~ X | M1 + M2", dataset = toy_data, n_burnin = 500, n_iter = 2000 ) # 3. Check results summary(results)
A modified version of the framing dataset from the
mediation package, originally based on political communication experiments
studying how issue framing (treatment) affects public opinion or policy support
(Brader, Valentino and Suhay, 2008). The dataset includes both original
variables as well as variables recoded from the original framing dataset from
the mediation package (Tingley et al., 2014). framing2 contains 265
observations and 12 variables.
framing2framing2
A data frame with 265 observations and 12 variables:
First treatment; whether the news story is framed positively or negatively.
Second treatment; whether the news story features a Latino or European immigrant.
Product of the two treatment variables. In the original study the authors only find this cell to be significant.
Subjects' age.
Subjects' gender.
Measure of subjects' negative feeling during the experiment. A numeric scale ranging between 3 and 12 where 3 indicates the most negative feeling.
Subjects' perceived harm caused by increased immigration. A numeric scale between 2 and 8.
A four-point scale measuring subjects' attitudes toward increased immigration. Larger values indicate more negative attitudes.
Whether subjects requested sending an anti-immigration message to Congress on their behalf.
Numeric recoding of the original english variable
from the framing dataset. english2 is recoded as
1 = “Strongly Oppose”, 2 = “Oppose”, 3 = “Favor”, and
4 = “Strongly Favor”.
Numeric recoding of the original anx variable
from the framing dataset. anx2 is recoded as
1 = “not anxious at all”, 2 = “a little anxious”,
3 = “somewhat anxious”, and 4 = “very anxious”.
Numeric recoding of the original educ variable
from the framing dataset. educ2 is recoded as
1 = “less than high school”, 2 = “high school”,
3 = “some college”, and 4 = “bachelor's degree or higher”.
Adapted from the framing dataset in the mediation package.
Brader, T., Valentino, N. A., & Suhay, E. (2008). What Triggers Public Opposition to Immigration? Anxiety, Group Cues, and Immigration Threat. American Journal of Political Science, 52(4), 959–978.
This function selects time-varying mediators using the longitudinal Bayesian mediation selection model.
longBMed(model = NULL, data, n.burnin = 3000, n.iter = 6000, thin = 1)longBMed(model = NULL, data, n.burnin = 3000, n.iter = 6000, thin = 1)
model |
Specifies how variables are assigned to the outcome(Y),
predictor(s)(X), and candidate mediator(s) (M).
The format depends on the type of Named list or data frame: A character string of the form
3-D array: A character string of the form |
data |
One of:
|
n.burnin |
Integer. Number of burn-in iterations. Default |
n.iter |
Integer. Number of posterior samples after burn-in.
Default |
thin |
Integer. Thinning interval. Default |
The model supports one or more predictor variables (X), one or more
candidate mediators (M), and exactly one outcome variable (Y). Data may be
supplied as an numeric array, a named list
of matrices, or a data frame in long format.
For a named list or long-format data frame, the model can be specified using
variable names, such as "Y ~ X1 + X2 | M1 + M2".
For a 3-D array, the model can be specified using integer slice indices,
such as "21 ~ 1 | 2:20", where the left side specifies the outcome,
the expression before | specifies the predictor(s), and the
expression after | specifies the mediator(s).
A matrix of posterior summary statistics from
summary(output)$statistics, including posterior means, standard
deviations, and standard errors for ind.joint and ind.p.
This function allows users to customize priors without needing to manually construct complex data frames. It displays current defaults, allows selection of specific parameters to change, and provides a menu of available probabilistic distributions (e.g., Normal, Gamma, Beta).
run_parms_wizard(verbose = TRUE)run_parms_wizard(verbose = TRUE)
verbose |
Logical. If |
Launches an interactive console-based interface to guide users through viewing and modifying Bayesian prior distributions for mediation models.
The wizard handles two main types of customization:
Distribution Selection: Choose from supported probabilistic distributions.
Argument Specification: Set numeric values for hyperparameters (e.g., shape, rate, mean, precision).
For coefficients like and , the wizard will note if they
reference hyperpriors (back-references). It is generally recommended to
modify the shape of the hyperprior rather than the coefficient's distribution
directly to maintain the hierarchical structure.
A data.frame with columns priors, distribution,
and arguments. This dataframe is formatted to be passed directly
to the my_prior argument in related fitting functions.
This function requires an interactive R session. It will return
invisible(NULL) if the user cancels the process.
# Create toy data toy_data <- data.frame( X = rbinom(100, 1, 0.5), M = rbinom(100, 1, 0.3), Y = rbinom(100, 1, 0.5) ) custom_priors <- NULL if (interactive()){ # Launch the wizard custom_priors <- run_parms_wizard() } # Use the resulting object in a model fit <- buzzEBMcatMcatY(model = "Y ~ M | X", dataset = toy_data, my_prior = custom_priors)# Create toy data toy_data <- data.frame( X = rbinom(100, 1, 0.5), M = rbinom(100, 1, 0.3), Y = rbinom(100, 1, 0.5) ) custom_priors <- NULL if (interactive()){ # Launch the wizard custom_priors <- run_parms_wizard() } # Use the resulting object in a model fit <- buzzEBMcatMcatY(model = "Y ~ M | X", dataset = toy_data, my_prior = custom_priors)
The average rate of action potentials over the observation period (i.e. 2500 ms) is provided per neuron (N:20) across repetitions (n: 300), yielding a single average firing rate value for each neuron.
data(singlespikes)data(singlespikes)
A data frame with 300 observations and 21 variables:
Predictor variable. External Current.
Candidate mediator 1. Average action potential of neuron 1.
Candidate mediator 2. Average action potential of neuron 2.
Candidate mediator 3. Average action potential of neuron 3.
Candidate mediator 4. Average action potential of neuron 4.
Candidate mediator 5. Average action potential of neuron 5.
Candidate mediator 6. Average action potential of neuron 6.
Candidate mediator 7. Average action potential of neuron 7.
Candidate mediator 8. Average action potential of neuron 8.
Candidate mediator 9. Average action potential of neuron 9.
Candidate mediator 10. Average action potential of neuron 10.
Candidate mediator 11. Average action potential of neuron 11.
Candidate mediator 12. Average action potential of neuron 12.
Candidate mediator 13. Average action potential of neuron 13.
Candidate mediator 14. Average action potential of neuron 14.
Candidate mediator 15. Average action potential of neuron 15.
Candidate mediator 16. Average action potential of neuron 16.
Candidate mediator 17. Average action potential of neuron 17.
Candidate mediator 18. Average action potential of neuron 18.
Candidate mediator 19. Average action potential of neuron 19.
Outcome variable. Average action potential of neuron 20.
The dataset contains one predictor, nineteen candidate mediators, and one outcome variable.
Time-averaged neural spiking data included with the buzzMed package.
For each neuron across all repetitions, the time series that describe whether or not a neuron generated action potential is provided. This is a subset of the full data matrix where the temporal index starts at 1002 ms and continues until 1026 ms.
data(sublongspikes)data(sublongspikes)
A numeric array with dimensions 300 × 25 × 21:
300 observations.
25 repeated measurements (time points).
21 variables consisting of one predictor (X), 19 candidate mediators (M), and one outcome (Y).
The third dimension stores the variables in the following order:
Slice 1: Predictor (X)
Slices 2–20: Candidate mediators (M)
Slice 21: Outcome (Y)
Longitudinal spiking train data included with the buzzMed package.