restrictions2Mathomatic: Format Equations for Mathomatic
In FAiR: Factor Analysis in R

Description Usage Arguments Details Value Author(s) References Examples

This function exports a system of equations that can be read by the program Mathomatic by George J. Gesslein II.

1 2	restrictions2Mathomatic(object, file = "") restrictions2mathomatic(object, file = "")

`object`	An object of `restrictions-class` or `FA-class`.
`file`	Character string giving the path to the export file. This argument is passed to `cat`, so by default the file is printed to the screen (and may be wrapped incorrectly).

restrictions2mathomatic is just an alias for restrictions2Mathomatic, which “symbolically” multiplies the correlation matrix among primary factors from the left and right by the primary pattern matrix and equates the lower triangle (exclusive of the diagonal) of this reduced covariance matrix to the lower triangle of the population covariance matrix. The resulting system of equations is exported in a format suitable for reading into Mathomatic, which is a lightweight program that can solve systems of nonlinear equations symbolically. Thus, one can use Mathomatic to verify that a factor analysis model is identified in the sense that (if the model holds exactly) the free parameters can be expressed solely in terms of the population covariances. See, for example, Steiger (2002) illustrations, although Factanal should automatically avoid the specific problems that Steiger (2002) is most concerned with.

You have to manually add equations to the system that reflect the constraints imposed on the model; doing so is trivial at the Mathomatic prompt. However, for a variety of reasons, actually solving the system of equations in Mathomatic may involve more work and frustration than one might expect. For example, if you have more than n = 14 manifest variables, then you have to recompile Mathomatic changing #define N_EQUATIONS in Mathomatic/am.h to some number bigger than 100 to hold all 0.5 * n * (n - 1) equations implied by the factor analysis model, plus equations for the constraints.

Nothing is returned. A file is written to file.

Ben Goodrich

Mathomatic is licensed under LGPL 2.1 and is available in source and binary forms from http://mathomatic.orgserve.de/math/.

Steiger, J. H. (2002) When constraints interact: A caution about reference variables identification constraints, and scale dependencies in structural equation modeling. Psychological Methods, 7, 210–227.

    man <- make_manifest(covmat = ability.cov)
    beta <- matrix(NA_real_, nrow = nrow(cormat(man)), ncol = 2)
    rownames(beta) <- rownames(cormat(man))
    free <- is.na(beta)
    beta <- new("parameter.coef.SEFA", x = beta, free = free, num_free = sum(free))

    Phi  <- diag(2)
    free <- lower.tri(Phi)
    Phi  <- new("parameter.cormat", x = Phi, free = free, num_free = sum(free))
    res  <- make_restrictions(manifest = man, beta = beta, Phi = Phi,
                              discrepancy = "MLE")

    restrictions2Mathomatic(res, file = "") # file printed to screen