mcmcirtkdrob.rd

使用R语言的马尔科夫链蒙特卡洛模拟（MCMC）源代码程序。

\name{MCMCirtKdRob}
\alias{MCMCirtKdRob}
\title{Markov Chain Monte Carlo for Robust K-Dimensional Item Response Theory
  Model}
\description{
  This function generates a posterior sample from a
  Robust K-dimensional item response theory (IRT) model with logistic
  link, independent standard normal priors on the subject
  abilities (ideal points), and independent normal priors on the
  item parameters.  The user supplies data and priors, and a sample
  from the posterior distribution is returned as an mcmc object, which can be
  subsequently analyzed with functions provided in the coda
  package.
}
  
\usage{
MCMCirtKdRob(datamatrix, dimensions, item.constraints=list(),
   ability.constraints=list(), burnin = 500, mcmc = 5000, thin=1,
    interval.method="step", theta.w=0.5, theta.mp=4,
    alphabeta.w=1.0, alphabeta.mp=4, delta0.w=NA, delta0.mp=3,
    delta1.w=NA, delta1.mp=3, verbose = FALSE, seed = NA,
    theta.start = NA, alphabeta.start = NA,
    delta0.start = NA, delta1.start = NA,
    b0 = 0, B0=0, k0=.1, k1=.1, c0=1, d0=1,
    c1=1, d1=1, store.item=TRUE, store.ability=FALSE,
    drop.constant.items=TRUE, ... )  }

\arguments{
    \item{datamatrix}{The matrix of data.  Must be 0, 1, or missing values.  
    It is of dimensionality subjects by items.}

    \item{dimensions}{The number of dimensions in the latent space.}
    
    \item{item.constraints}{List of lists specifying possible equality
    or simple inequality constraints on the item parameters. A typical
    entry in the list has one of three forms: \code{rowname=list(d,c)}
    which will constrain the dth item parameter for the item named
    rowname to be equal to c, \code{rowname=list(d,"+")} which will
    constrain the dth item parameter for the item named rowname to be
    positive, and \code{rowname=list(d, "-")} which will constrain the dth
    item parameter for the item named rowname to be negative. If
    datamatrix is a
    matrix without row names defaults names of ``V1", ``V2", ... , etc
    will be used. In a \eqn{K}{K}-dimensional model,
    the first item parameter for
    item \eqn{i}{i} is the difficulty parameter (\eqn{\alpha_i}{alpha_i}),
    the second item parameter is the discrimation parameter on dimension
    1 (\eqn{\beta_{i,1}}{beta_{i,1}}), the third item parameter is the
    discrimation parameter on dimension 2
    (\eqn{\beta_{i,2}}{beta_{i,2}}), ...,  and the \eqn{(K+1)}{(K+1)}th
    item parameter
    is the discrimation parameter on dimension \eqn{K}{K}
    (\eqn{\beta_{i,K}}{beta_{i,K}}). 
    The item difficulty parameters (\eqn{\alpha}{alpha}) should
    generally not be constrained. 
    }
    
    \item{ability.constraints}{List of lists specifying possible equality
    or simple inequality constraints on the ability parameters. A typical
    entry in the list has one of three forms: \code{colname=list(d,c)}
    which will constrain the dth ability parameter for the subject named
    colname to be equal to c, \code{colname=list(d,"+")} which will
    constrain the dth ability parameter for the subject named colname to be
    positive, and \code{colname=list(d, "-")} which will constrain the dth
    ability parameter for the subject named colname to be negative. If
    datamatrix  is a
    matrix without column names defaults names of ``V1", ``V2", ... , etc
    will be used.}

    \item{burnin}{The number of burn-in iterations for the sampler.}

    \item{mcmc}{The number of iterations for the sampler after burn-in.}

    \item{thin}{The thinning interval used in the simulation.  The number of
    iterations must be divisible by this value.}

  \item{interval.method}{Method for finding the slicing interval. Can
    be equal to either \code{step} in which case the stepping out
    algorithm of Neal (2003) is used or \code{doubling} in which case the
    doubling procedure of Neal (2003) is used. The stepping out method
    tends to be faster on a per-iteration basis as it typically requires few
    function calls. The doubling method expands the initial interval
    more quickly which makes the Markov chain mix somewhat more
    quickly-- at least in some situations. }
  
  \item{theta.w}{The initial width of the slice sampling interval for
    each ability parameter (the elements of \eqn{\theta}{theta})}
  
  \item{theta.mp}{The parameter governing the maximum possible width of
    the slice interval for each ability parameter (the elements of
    \eqn{\theta}{theta}). If \code{interval.method="step"} then the maximum
    width is \code{theta.w * theta.mp}.

    If \code{interval.method="doubling"}
    then the maximum width is \code{theta.w * 2^theta.mp}. } 
  
  \item{alphabeta.w}{The initial width of the slice sampling interval for
    each item parameter (the elements of \eqn{\alpha}{alpha} and
    \eqn{\beta}{beta})}
  
  \item{alphabeta.mp}{ The parameter governing the maximum possible width of
    the slice interval for each item  parameters (the elements of
    \eqn{\alpha}{alpha} and \eqn{\beta}{beta}). If
    \code{interval.method="step"} then the maximum width is
    \code{alphabeta.w * alphabeta.mp}.

    If \code{interval.method="doubling"}
    then the maximum width is \code{alphabeta.w * 2^alphabeta.mp}. } 
  
  \item{delta0.w}{The initial width of the slice sampling interval for
    \eqn{\delta_0}{delta0}}
  
  \item{delta0.mp}{The parameter governing the maximum possible width of
    the slice interval for \eqn{\delta_0}{delta0}. If
    \code{interval.method="step"} then the maximum width is
    \code{delta0.w * delta0.mp}. If \code{interval.method="doubling"}
    then the maximum width is \code{delta0.w * 2^delta0.mp}. }
  
  \item{delta1.w}{The initial width of the slice sampling interval for
    \eqn{\delta_1}{delta1}}
  
  \item{delta1.mp}{The parameter governing the maximum possible width of
    the slice interval for \eqn{\delta_1}{delta1}. If
    \code{interval.method="step"} then the maximum width is
    \code{delta1.w * delta1.mp}. If \code{interval.method="doubling"}
    then the maximum width is \code{delta1.w * 2^delta1.mp}. }

    \item{verbose}{A switch which determines whether or not the progress of
      the sampler is printed to the screen.  If verbose > 0, the
      iteration number with be printed to the screen every verbose'th
      iteration.} 
    
    \item{seed}{The seed for the random number generator.  If NA, the Mersenne
      Twister generator is used with default seed 12345; if an integer is 
      passed it is used to seed the Mersenne twister.  The user can also
      pass a list of length two to use the L'Ecuyer random number generator,
      which is suitable for parallel computation.  The first element of the
      list is the L'Ecuyer seed, which is a vector of length six or NA (if NA 
      a default seed of \code{rep(12345,6)} is used).  The second element of 
      list is a positive substream number. See the MCMCpack 
      specification for more details.}

    \item{theta.start}{The starting values for the ability parameters
      \eqn{\theta}{theta}. Can be either a scalar or a matrix with
      number of rows equal to the number of subjects and number of
      columns equal to the dimension \eqn{K}{K} of the latent space. If
      \code{theta.start=NA} then starting values will be chosen that are
      0 for unconstrained subjects, -0.5 for subjects with negative
      inequality constraints and 0.5 for subjects with positive inequality
      constraints. }
    
    \item{alphabeta.start}{The starting values for the
    \eqn{\alpha}{alpha} and \eqn{\beta}{beta} difficulty and
    discrimination parameters. If \code{alphabeta.start} is set to a
    scalar the starting value for all unconstrained item parameters will
    be set to that scalar. If \code{alphabeta.start} is a matrix of
    dimension \eqn{(K+1) \times items}{(K+1) x items} then the
    \code{alphabeta.start} matrix is used as the starting values (except
    for equality-constrained elements). If \code{alphabeta.start} is set
    to \code{NA} (the default) then starting values for unconstrained
    elements are set to values generated from a series of proportional
    odds logistic regression fits, and starting values for inequality
    constrained elements are set to either 1.0 or -1.0 depending on the
    nature of the constraints. }

    \item{delta0.start}{The starting value for the
      \eqn{\delta_0}{delta0} parameter.}
    
    \item{delta1.start}{The starting value for the
      \eqn{\delta_1}{delta1} parameter.}
    
    \item{b0}{The prior means of the
    \eqn{\alpha}{alpha} and \eqn{\beta}{beta} difficulty and
    discrimination parameters, stacked for all items.
    If a scalar is passed, it
    is used as the prior mean for all items.}
  
  \item{B0}{The prior precisions (inverse variances) of the
    independent Normal prior on the item parameters.
    Can be either a scalar or a matrix of dimension