Correspondence analysis used complementary to loglinear analysis

Loglinear analysis and correspondence analysis provide us with two different methods for the decomposition of contingency tables. In this paper we will show that there are cases in which these two techniques can be used complementary to each other. More specifically, we will show that often correspondence analysis can be viewed as providing a decomposition of the difference between two matrices, each following a specific loglinear model. Therefore, in these cases the correspondence analysis solution can be interpreted in terms of the difference between these loglinear models. A generalization of correspondence analysis, recently proposed by Escofier, will also be discussed. With this decomposition, which includes classical correspondence analysis as a special case, it is possible to use correspondence analysis complementary to loglinear analysis in more instances than those described for classical correspondence analysis. In this context correspondence analysis is used for the decomposition of the residuals of specific restricted loglinear models.     

Iterative least squares estimates of communality: Initial estimate need not affect stabilized value

A common criticism of iterative least squares estimates of communality is that method of initial estimation may influence stabilized values. As little systematic research on this topic has been performed, the criticism appears to be based on cumulated experience with empirical data sets. In the present paper, two studies are reported in which four types of initial estimate (unities, squared multiple correlations, highestr, and zeroes) and four levels of convergence criterion were employed using four widely available computer packages (BMDP, SAS, SPSS, and SOUPAC). The results suggest that initial estimates have no effect on stabilized communality estimates when a stringent criterion for convergence is used, whereas initial estimates appear to affect stabilized values employing rather gross convergence criteria. There were no differences among the four computer packages for matrices without Heywood cases.     

Symmetry and transitivity of conditional relations in monkeys (Cebus apella) and pigeons (Columba livia)

In Experiment 1 six monkeys were tested with discriminative relations that were backward relative to their training in a 0-second conditional (“symbolic”) matching procedure. Although there was some indication of backward associations, the evidence was generally weak, and statistical evaluations did not reach conventional significance levels. Unlike children, who show backward associations to the point of symmetry, monkeys and pigeons display at best only weak and transient backward associations. In Experiment 2 associative transitivity was assessed across two sets of conditional matching tasks. All four monkeys tested demonstrated strong transitivity. In contrast, in Experiment 3 there was no evidence of transitivity in three pigeons tested under conditions closely comparable to those of Experiment 2. These results may identify some key features of interspecies differences and contribute to analyses of serial learning in animals.