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 |

`file` |
Character string giving the path to the export file. This
argument is passed to |

`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.

1 2 3 4 5 6 7 8 9 10 11 12 13 | ```
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
``` |

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