A new lease of life for Thomson's bonds model of intelligence.

Modern factor analysis is the outgrowth of Spearman's original "2-factor" model of intelligence, according to which a mental test score is regarded as the sum of a general factor and a specific factor. As early as 1914, Godfrey Thomson realized that the data did not require this interpretation and he demonstrated this by proposing what became known as his "bonds" model of intelligence. Van der Maas et al. (2006) have recently drawn attention to what they perceive as difficulties with both models and have proposed a 3rd model. Neither alternative requires the general factor that was at the core of Spearman's idea. Although Thomson's model has been largely forgotten, the authors show that it merits further consideration because it can compete, statistically and biologically, on equal terms with Spearman's model. In particular, they show that it is impossible to distinguish statistically between the 2 models. There are also lessons to be learnt from the way in which Thomson arrived at his model and from the subsequent debate between Spearman and Thomson. The extent to which the recent proposal by van der Maas et al. may offer any advantage over Spearman's and Thomson's models is unclear and requires further investigation.

The origin of factor scores: Spearman, Thomson and Bartlett.

The indeterminacy of factor scores has been a perennial source of debate since the time of Spearman. The main purpose of this paper is to show that, in spite of his inadequate tools and concepts, Sir Godfrey Thomson's approach of 70 years ago was on the right lines. His thinking was constrained by the primitive state of his statistical understanding but it is illuminated by his substantial exchange of the correspondence with M. S. Bartlett in the 1930s, most of which has survived in the Godfrey Thomson archive at the University of Edinburgh. In order to justify our claim and clarify the issues, we have found it necessary to fill in some of the gaps in the original derivations of Spearman, Thomson and Bartlett and to express their work in terms which are intelligible today. The opportunity is taken to relate this earlier work to contemporary debates.

A goodness of fit test for sparse 2p contingency tables.

When a model is fitted to data in a 2p contingency table many cells are likely to have very small expected frequencies. This sparseness invalidates the usual approximation to the distribution of the chi-squared or log-likelihood tests of goodness of fit. We present a solution to this problem by proposing a test based on a comparison of the observed and expected frequencies of the second-order margins of the table. A chi2 approximation to the sampling distribution is provided using asymptotic moments. This can be straightforwardly calculated from the expected cell frequencies. The new test is applied to several previously published examples relating to the fitting of latent variable models, but its application is quite general.