mpt (version 0.3-0)

mptEM: EM Algorithm for Multinomial Processing Tree Models

Description

Applies the EM algorithm to fit a multinomial processing tree model.

Usage

mptEM(theta, data, a, b, c, maxit = 1000, tolerance = 1e-8, 
  stepsize = 1, verbose = FALSE)

Arguments

theta

a vector of starting values for the parameter estimates.

data

a vector of absolute response frequencies.

a

a three-dimensional array representing the model structure.

b

a three-dimensional array representing the model structure.

c

a matrix of structural constants.

maxit

the maximum number of iterations.

tolerance

the convergence criterion; the iterations converge when $logLik - logLik.old < tolerance$.

stepsize

the step size defaulting to 1; slightly larger values may speed up convergence, but may also give errors; use with care.

verbose

logical indicating if output should be produced for each iteration.

Value

• theta
  the vector of parameter estimates.
• loglik
  the log-likelihood at termination of the algorithm.
• pcat
  a vector of predicted probabilities for each response category.
• pbranch
  a vector of predicted branch probabilities.
• iter
  the number of iterations of the algorithm.

Details

Usually mptEM is automatically called by mpt.

The algorithm applies to MPT models where the probabilities of the i-th branch leading to the j-th category take the form $$p_{ij}(\Theta) = c_{ij} \prod_{s = 1}^S \theta_s^{a_{ijs}} (1 - \theta_s)^{b_{ijs}},$$ where $\Theta$ is the parameter vector.

See Hu and Batchelder (1994) and Hu (1999) for details on the algorithm.

References

Hu, X., & Batchelder, W.H. (1994). The statistical analysis of general processing tree models with the EM algorithm. Psychometrika, 59, 21--47.

Hu, X. (1999). Multinomial processing tree models: An implementation. Behavior Research Methods, Instruments, & Computers, 31, 689--695.

See Also

mpt.