| mptEM {mpt} | R Documentation |
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
|
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. |
Details
Usually, mptEM is automatically called by mpt.
A prerequisite for the application of the EM algorithm is that 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 \vartheta_s^{a_{ijs}} (1 - \vartheta_s)^{b_{ijs}},
where \Theta = (\vartheta_s) is the parameter vector, a_{ijs}
and b_{ijs} count the occurrences of \vartheta_s and
1 - \vartheta_s in a branch, respectively, and c_{kj} is a
nonnegative real number. The branch probabilities sum up to the total
probability of a given category, p_j = p_{1j} + \dots + p_{Ij}. This
is the structural restriction of the class of MPT models that can be
represented by binary trees. Other model types have to be suitably
reparameterized for the algorithm to apply.
See Hu and Batchelder (1994) and Hu (1999) for details on the algorithm.
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. |
References
Hu, X. (1999). Multinomial processing tree models: An implementation. Behavior Research Methods, Instruments, & Computers, 31(4), 689–695. doi: 10.3758/BF03200747
Hu, X., & Batchelder, W.H. (1994). The statistical analysis of general processing tree models with the EM algorithm. Psychometrika, 59(1), 21–47. doi: 10.1007/bf02294263
See Also
mpt.
Examples
## Fit storage-retrieval model to data in Riefer et al. (2002)
mpt(mptspec("SR2"), c(243, 64, 58, 55), method = "EM")