gpirtMCMC: Gaussian Process IRT MCMC
In duckmayr/gpirt: Tools for a Gaussian Process IRT Model

Description Usage Arguments Value Examples

View source: R/gpirtMCMC.R

Provides posterior samples for the GP-IRT.

gpirtMCMC(
  data,
  sample_iterations,
  burn_iterations,
  vote_codes = list(yea = 1:3, nay = 4:6, missing = c(0, 7:9, NA)),
  beta_prior_means = matrix(0, nrow = 2, ncol = ncol(data)),
  beta_prior_sds = matrix(3, nrow = 2, ncol = ncol(data)),
  beta_proposal_sds = matrix(0.1, nrow = 2, ncol = ncol(data)),
  theta_init = NULL
)

`data`	An object of class `response_matrix`, or an object coercible to class `response_matrix`
`sample_iterations`	An integer vector of length one giving the number of samples to record
`burn_iterations`	An integer vector of length one giving the number of burn in (unrecorded) iterations
`vote_codes`	A named list giving the mapping from recorded responses to -1, 1, NA. An element named "yea" gives the responses that should be coded as 1, an element named "nay" gives the responses that should be coded as -1, and an element named "missing" gives responses that should be NA; only used if `data` must be coerced to a `response_matrix` object
`beta_prior_means`	A numeric matrix of with `ncol(data)` columns and two rows giving the prior means for the items' linear means' intercept and slope; by default, a matrix of zeros
`beta_prior_sds`	A numeric matrix of with `ncol(data)` columns and two rows giving the prior standard deviations for the items' linear means' intercept and slope; by default, a matrix of threes
`beta_proposal_sds`	A numeric matrix of with `ncol(data)` columns and two rows giving the standard deviations for proposals for the items' linear means' intercept and slope; by default a matrix filled with 0.1
`theta_init`	A vector of length `nrow(data)` giving initial values for the respondent ideology parameters; if NULL (the default), the initial values are drawn from the parameters' prior distributions.

A list with elements

theta: The theta parameter draws, stored in a matrix with sample_iterations + 1 rows (initial values are included) and n columns.
beta: The beta parameter draws, stored in an array with 2 rows, m columns, and sample_iterations + 1 slices.
f: The f parameter draws, stored in an array with n rows, m columns, and sample_iterations + 1 slices.
IRFs: Estimated item response functions for the items, with one column per item, or m columns, and 1001 rows. The first row has the probabilities of a 1 response for a theta value of -5.0, the second the probability for each item of a 1 response for a theta value of -4.99, ..., and the last for a theta value of 5.0.

##### Monotonic IRT example ####
## Simulate data
gen_responses <- function(theta, alpha, beta) {
    # Stardard 2PL model
    n <- length(theta)
    m <- length(alpha)
    responses <- matrix(0, n, m)
    for ( j in 1:m ) {
        for ( i in 1:n ) {
            p <- plogis(alpha[j] + beta[j] * theta[i])
            responses[i, j] <- sample(0:1, 1, prob = c(1 - p, p))
        }
    }
    return(responses)
}
set.seed(1234)
n <- 30
m <- 10
theta <- seq(-3, 3, length.out = n) # Respondent ability parameters
alpha <- seq(-2, 2, length.out = m) # Item difficulty parameters
beta  <- runif(m, 0.5, 3)           # Item discrimination parameters
responses <- gen_responses(theta, alpha, beta)

## Check for unanimity and omit any unanimous items
table(apply(responses, 2, function(x) length(unique(x))))
unanimous_items <- which(apply(responses, 2, function(x) length(unique(x))) < 2)
N <- length(unanimous_items)
if ( N == 0 ) unanimous_items <- n + 1 else m <- m - N
responses <- responses[ , -unanimous_items]

## Generate samples
## (We just use 1 iteration for a short-running toy example here;
##  try 500-1000+ to fully demo the sampler's behavior)
samples <- gpirtMCMC(responses, 1, 0, vote_codes = list(yea = 1, nay = 0,
                                                        missing = NA))
str(samples)