^MML^
^Structured^

# Single-Factor Analysis by
Minimum Message Length Estimation

### Journal of the Royal Statistical Society.
Series B (Methodological),
Vol. 54,
No. 1.
(1992),
pp. 195-209.

**Summary**:
The minimum message length (MML) technique is applied to the
problem of estimating the parameters of a multivariate Gaussian model in
which the correlation structure is modelled by a single common factor.
Implicit estimator equations are derived and compared
with those obtained from a maximum likelhood (ML) analysis.
Unlike ML, the MML estimators remain consistent when used to estimate both
the factor loadings and the factor scores.
Tests on simulated data show the MML estimates
to be on average more accurate than the ML estimates when the former exist.
If the data show little evidence for a factor,
the MML estimate collapses.
It is shown that the condition for the existence
of an MML estimate is essentially that the log-likelihood ratio
in favour of the factor model exceeds the value expected
under the null (no-factor) hypothesis.

**Keywords**:
Consistency, estimation, factor analysis, minimum message length,
multivariate analysis, niosance.

The paper is available
[here (click)]
at Jstor [4/'01].

Also download the
[Factor Snob]
program, or see
[Multiple-Factor Analysis].

L. Allison
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