mixRasch              package:mixRasch              R Documentation

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_D_e_s_c_r_i_p_t_i_o_n:

     This function will estimate a mixture Rasch model using joint
     maximum likelihood estimation (JMLE). The estimation is based on a
     mixture partial credit model. Step parameters can be constrained
     to estimate a mixture rating scale model.

_U_s_a_g_e:

     mixRasch(data, steps, max.iter = 50, conv.crit = 0.001, model = "RSM", 
              n.c = 1, class, metric, info.fit = TRUE, treat.extreme = 0.3, 
              maxchange = 1.5, maxrange = c(-4, 4), as.LCA = FALSE)

_A_r_g_u_m_e_n_t_s:

    data: A rectangular data set (matrix or data frame) to be analyzed. 

   steps: The maximum number of item thresholds to be estimated. Some
          items may have less than the maximum. 

max.iter: Maximum number EM iterations 

conv.crit: Estimation stops when the largest model parameter change is
          smaller than this criterion. 

   model: "RSM" (the default) constrains all step parameters to be
          equal (i.e., estimates a rating scale model).  Assumes all
          items have the same number of steps. "PCM" allows step
          parameters to differ across items (i.e., estimates a partial
          credit model).  The number of steps can differ across items.  

     n.c: Number of latent classes. 

   class: Optional matrix of starting values for latent class
          membership. 

  metric: Not implemented. Will be an optional argument for setting the
          final scale of the Rasch results. 

info.fit: If "True" the information based criteria of fit (AIC, BIC)
          are estimated. 

treat.extreme: Adjustment to perfect response vectors to allow
          estimation of person parameters. Perfect vectors are not used
          during item parameter estimation. 

maxchange: Limits the change to model parameters in a single iteration.
          Helps keep estimates reasonable in the first few iterations. 

maxrange: Admissible range of item difficulties.  

  as.LCA: If TRUE, all person parameters are constrained to equal zero.
          That analysis accomplishes a latent class analysis rather
          than a mixture Rasch model. 

_D_e_t_a_i_l_s:

     The analyzed data should be a rectangular data file. Missing data
     are permitted and handled in the usual JMLE manner. Large amounts
     of missing data will slow down estimation. Basic results on item
     parameters are returned to the screen. When more than one class is
     specified (n.c greater than 1) Rasch model parameters and measures
     of fit are returned in a list, with each class's results returned
     in a separate element of that list. When n.c = 1 a standard Rasch
     model analysis is performed.

_V_a_l_u_e:

LatentClass : One element for each latent class. Each LatentClass
          element is itself a list containing within class results:
          item statistics (i.stat), person parameters and measures of
          person fit (person.par), item parameters and measures of item
          fit (item.par). 

max.change : The largest model parameter change in each class in the
          last iteration of the estimation.

  class : A rectangular matrix of the order number of people by number
          of classes. Values represent the probability that a person
          (row) belongs to a particular class (column).

   iter : The number of completed iterations.

converge.flag : Indicates if convergence was reached.

info.fit: Provides (if requested) AIC, BIC, CAIC, log likelihood,
          number of estimated parameters, and number of persons used in
          the estimation.

  model : Reports which model was estimated.

removed.items: Provides a vector indicating which, if any, items had to
          be removed from estimation for having perfect vectors.

run.time: Reports time elapsed during estimation.

_N_o_t_e:

     Be aware that this function is an early implementation of the
     procedure. Please contact the author if you encounter any bugs or
     if you have questions or suggestions.

_A_u_t_h_o_r(_s):

     John T. Willse

_R_e_f_e_r_e_n_c_e_s:

     Willse, J. T. (2009). Mixture Rasch models with joint maximum
     likelihood estimation. Presented at the National Council on
     Measurement in Education annual meeting. San Diego.

_E_x_a_m_p_l_e_s:

     # Example data included with mixRasch
     data(SimMix)

     test1 <- mixRasch(SimMix,1,50, conv.crit=.0001, n.c=1)
     test2 <- mixRasch(SimMix,1,500, conv.crit=.0001, n.c=2)

     # The 3 class solution may take a while to converge or need
     # to be restarted if it fails to converge.
     test3 <- mixRasch(SimMix,1,1000, conv.crit=.0001, n.c=3)

     # Notice that the AIC and BIC are lowest for the 2 class solution
     rbind(test1$info.fit,test2$info.fit,test3$info.fit)

     # Notice that the two "difficulty" columns are ordered differently
     # The results reflect that the two groups in the data set have a reversed
     # scale from one another.
     test2

