tune_temperatures {bggum}

tune_temperatures

Description

Find Optimal Temperatures for the GGUM MCMCMC Sampler

Usage

tune_temperatures(data, n_temps, temp_tune_iterations = 5000,
  n_draws = 2500, K = NULL, proposal_sds = NULL,
  sd_tune_iterations = 5000, theta_prior_params = c(0, 1),
  alpha_prior_params = c(1.5, 1.5, 0.25, 4), delta_prior_params = c(2,
  2, -5, 5), tau_prior_params = c(2, 2, -6, 6))

Arguments

data

An integer matrix giving the response by each respondent to each item

n_temps

How many temperatures to make?

temp_tune_iterations

How many iterations should the temperature tuning algorithm run for each temperature? (default is 5000)

n_draws

How many draws should be used to determine each temperature? (specifying n_draws < temp_tune_iterations will result in an error; default is 2500).

K

(Optional) A numeric vector with an element for each item giving the number of options for the item; if not provided, it is generated by taking the number of unique options observed in the data

proposal_sds

(Optional) A list of length four where is element is a numeric vector giving standard deviations for the proposals; the first element should be a numeric vector with a standard deviation for the proposal for each respondent's theta parameter (the latent trait), the second a vector with a standard deviation for each item's alpha (discrimination) parameter, the third a vector with a standard deviation for each item's delta (location) parameter, and the fourth a vector with a standard deviation for each item's tau (option threshold) parameters. If not given, the standard deviations are all set to 1.0 before any tuning begins.

sd_tune_iterations

A numeric vector of length one; if proposal standard deviations are not given, this provides the number of iterations to use to tune the proposals before the temperature finding algorithm begins (default is 5000)

theta_prior_params

A numeric vector of length two; the mean and standard deviation of theta parameters' prior distribution (where the theta parameters have a normal prior; the default is 0 and 1)

alpha_prior_params

A numeric vector of length four; the two shape parameters and a and b values for alpha parameters' prior distribution (where the alpha parameters have a four parameter beta prior; the default is 1.5, 1.5, 0.25, and 4)

delta_prior_params

A numeric vector of length four; the two shape parameters and a and b values for delta parameters' prior distribution (where the delta parameters have a four parameter beta prior; the default is 2, 2, -5, and 5)

tau_prior_params

A numeric vector of length four; the two shape parameters and a and b values for tau parameters' prior distribution (where the tau parameters have a four parameter beta prior; the default is 2, 2, -6, and 6)

Details

Atchadé, Roberts, and Rosenthal (2011) determine the optimal swap-acceptance rate for Metropolis-coupled MCMC and provide an algorithm for building optimal temperature schedules. We implement this algorithm in the context of the GGUM to provide a temperature schedule that should result in approximately 0.234 swap acceptance rate between adjacent chains.

Please see the vignette (via vignette("bggum")) for a full in-depth practical guide to Bayesian estimation of GGUM parameters.

Value

A numeric vector of temperatures

References

Atchadé, Yves F., Gareth O. Roberts, and Jeffrey S. Rosenthal. 2011. “Towards Optimal Scaling of Metropolis-Coupled Markov Chain Monte Carlo.” Statistics and Computing 21(4): 555–68.

See Also

ggumMCMC, ggumMC3

Examples

## NOTE: This is a toy example just to demonstrate the function, which uses
## a small dataset and an unreasonably low number of sampling interations.
## For a longer practical guide on Bayesian estimation of GGUM parameters,
## please see the vignette ( via vignette("bggum") ).
## We'll simulate data to use for this example:
set.seed(123)
sim_data <- ggum_simulation(100, 10, 2)
## Now we can tune the temperature schedule:
## (for the purposes of example, we use 100 iterations,
## though in practice you would use much more)
temps <- tune_temperatures(data = sim_data$response_matrix, n_temps = 5,
                           temp_tune_iterations = 100, n_draws = 50,
                           sd_tune_iterations = 100)