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OpenMx (version 2.3.1)

mxExpectationBA81: Create a Bock & Aitkin (1981) expectation

Description

When a two-tier covariance matrix is recognized, this expectation automatically enables analytic dimension reduction (Cai, 2010).

Usage

mxExpectationBA81(ItemSpec, item = "item", ..., qpoints = 49L, qwidth = 6,
  mean = "mean", cov = "cov", verbose = 0L, weightColumn = NA_integer_,
  EstepItem = NULL, debugInternal = FALSE)

Arguments

ItemSpec
a single item model (to replicate) or a list of item models in the same order as the column of ItemParam
item
the name of the mxMatrix holding item parameters with one column for each item model with parameters starting at row 1 and extra rows filled with NA
...
Not used. Forces remaining arguments to be specified by name.
qpoints
number of points to use for equal interval quadrature integration (default 49L)
qwidth
the width of the quadrature as a positive Z score (default 6.0)
mean
the name of the mxMatrix holding the mean vector
cov
the name of the mxMatrix holding the covariance matrix
verbose
the level of runtime diagnostics (default 0L)
weightColumn
the name of the column in the data containing the row weights (default NA)
EstepItem
a simple matrix of item parameters for the E-step. This option is mainly of use for debugging derivatives.
debugInternal
when enabled, some of the internal tables are returned in $debug. This is mainly of use to developers.

Details

The standard Normal distribution of the quadrature acts like a prior distribution for difficulty. It is not necessary to impose any additional Bayesian prior on difficulty estimates (Baker & Kim, 2004, p. 196).

References

Bock, R. D., & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm. Psychometrika, 46, 443-459.

Cai, L. (2010). A two-tier full-information item factor analysis model with applications. Psychometrika, 75, 581-612.

Seong, T. J. (1990). Sensitivity of marginal maximum likelihood estimation of item and ability parameters to the characteristics of the prior ability distributions. Applied Psychological Measurement, 14(3), 299-311.

See Also

http://cran.r-project.org/package=rpf{RPF}