Implement the Man and Culpepper (2020) mode-jumping algorithm to factor analyze mixed-type response data. Missing values should be specified as a non-numeric value such as NA.
IFA_Mode_Jumper_MixedResponses(
Y,
M,
gamma,
Ms,
sdMH,
bounds,
burnin,
chain_length = 10000L
)A N by J matrix of mixed-type item responses.
An interger specifying the number of factors.
The value of the mode-jumping tuning parameter. Man and Culpepper (2020) used gamma = 0.5.
model indicator where 0 = "bounded", 1 = "continuous", 2 = "binary", >2 = "ordinal".
A J vector of tuning parameters for the Cowles (1996) Metropolis-Hastings sampler for ordinal data latent thresholds.
A J by 2 matrix denoting the min and max variable values. Note that bounds are only used for variable j if element j of Ms is zero.
Number of burn-in iterations to discard.
The total number of iterations (burn-in + post-burn-in).
A list that contains nsamples = chain_length - burnin array draws from the posterior distribution:
LAMBDA: A J by M by nsamples array of sampled loading matrices on the standardized metric.
PSIs: A J by nsamples matrix of vector of variable uniquenesses on the standardized metric.
ROW_OUT: A matrix of sampled row indices of founding variables for mode-jumping algorithm.
THRESHOLDS: An array of sampled thresholds.
INTERCEPTS: Sampled variable thresholds on the standardized metric.
ACCEPTED: Acceptance rates for mode-jumping Metropolis-Hastings (MH) steps.
MHACCEPT: A J vector of acceptance rates for item threshold parameters. Note that binary items have an acceptance rate of zero, because MH steps are never performed.
LAMBDA_unst: An array of unstandardized loadings.
PSIs_inv_unst: A matrix of unstandardized uniquenesses.
THRESHOLDS_unst: Unstandardized thresholds.
INTERCEPTS_unst: Unstandardized intercepts.
Cowles, M. K. (1996), Accelerating Monte Carlo Markov chain convergence for cumulative link generalized linear models," Statistics and Computing, 6, 101-111.
Man, A. & Culpepper, S. A. (2020). A mode-jumping algorithm for Bayesian factor analysis. Journal of the American Statistical Association, doi:10.1080/01621459.2020.1773833.