Conduct posterior sampling for IRT model ability parameters with normalized power prior.
For the power parameter \(\delta\), a Metropolis-Hastings algorithm with either independence proposal, or a random walk proposal on its logit scale is used.
For the model parameters \(\beta\), a Metropolis-Hastings algorithm with either normal proposal, or uniform proposal is used.
IRTNPP(y, dseq, prior_mu, prior_sd, MCsize, disa, difa1, difa2,
cut, prior_beta, prior_delta, disb, difb1, difb2,
prop_delta, rw_delta, rw_n_beta, rw_u_beta, ind_delta,
prop_beta, n_sample, burnin, thin)A vector consisting of 5 parts: the acceptance rate in MCMC sampling for \(\beta\) and \(\delta\) using Metropolis-Hastings algorithm, the posterior mean of \(\beta\) and \(\delta\), the posterior standard deviation of \(\beta\) and \(\delta\), the posterior median of \(\beta\) and \(\delta\), and the posterior mode of power parameter \(\delta\).
a vector that contains historical data and current data, where the first half consists of historical data and the second half consists of current data.
numeric vector or scalar between 0 and 1. The value of \(\delta\).
the prior mean of each ability parameter \(\beta\).
the prior standard deviation of each ability parameter \(\beta\).
positive integer. Sample size of importance sampling.
a matrix of item discriminability parameters in historical data.
a vector of the first difficulty parameter of items in historical data.
a vector of the second difficulty parameter of items in historical data.
critical value between 0 and 1. If \(\delta\) is less than or equal to this value, select the initial prior of \(\beta\) as the proposed distribution of importance sampling; Otherwise, select the posterior distribution with historical data of \(\beta\) as the proposed distribution.
list. Parameters of normal prior for \(\beta\).
list. Parameters of beta prior for for \(\delta\).
a matrix of item discriminability parameters in current data.
a vector of the first difficulty parameter of items in current data.
a vector of the second difficulty parameter of items in current data.
character. The class of proposal distribution for \(\delta\).
numeric. The stepsize(variance of the normal distribution) for the random walk proposal of logit \(\delta\). Only applicable if prop_delta = 'RW'.
character. The class of proposal distribution for \(\beta\).
numeric vector. Standard deviation of proposed distribution of for \(\beta\).
numeric. rw_u_beta*2 is the interval length of uniform distribution.
numeric vector. Two parameters when the proposed distribution of \(\delta\) is beta distribution.
positive integer. Specifies the number of posterior samples in the output.
positive integer. The output will only show MCMC samples after bunrin.
positive integer. The thinning parameter in MCMC sampling.
Qiang Zhang zqzjf0408@163.com
This function needs three additional R packages: KernSmooth, msm, mvtnorm.
This function needs two additional R functions: makePositiveDefinite, Metro_Hastings.
The outputs include the posterior estimates of the ability parameters of the IRT model and power parameter, as well as the acceptance rates in sampling \(\delta\) and \(\beta\).
Chalmers, R.P. (2012). mirt: A multidimensional item response theory package for the R environment. Journal of Statistical Software 48:1–29.
Matteucci, M., Veldkamp, B. (2015). The approach of power priors for ability estimation in IRT models. Qual Quant 49:917–926.
Han, Z., Zhang, Q., Wang, M., Ye, K., Chen, M.H. (2023). On efficient posterior inference in normalized power prior Bayesian analysis. Biometrical Journal 65:2200194.