PERCEPTUAL ANALYSIS OF 2-WAY 2-MODE FREQUENCY DATA - PROBABILITY MATRIX DECOMPOSITION AND 2 ALTERNATIVES

A perceptual mapping technique for the analysis of two-way two-mode fr equency data is presented: probability matrix decomposition. The techn ique is compared, both theoretically and empirically, to two alternati ve techniques: latent class analysis by the binomial model and corresp ondence analysis. From a theoretical perspective the most salient diff erence is that probability matrix decomposition (PMD) allows for testi ng several decision rules, each of which constitutes a different model of the psychological process assumed to give rise to the data, This d istinguishes PMD from both correspondence analysis and latent class an alysis, which can be considered tools for 'data reduction' without any underlying theory. when PMD models adequately reflect the underlying decision process, the technique is expected to lead to a more accurate representation of the data, The empirical comparison was based on a s et of judgments obtained from 50 consumers concerning the appropriaten ess of 11 attributes for 41 sandwich fillings. Applying each of the th ree techniques to the binary judgments aggregated across respondents s howed that PMD had the best fit in representing the data and also had the largest predictive power with respect to the preferences of consum ers for the sandwich fillings. These findings support the hypothesis t hat modelling the underlying process may lead to a more accurate repre sentation. Regarding the interpretability of the resulting perceptual maps, there also was an advantage for PMD. When considering the ease o f data analysis however, correspondence analysis seems to be superior. (C) 1997 Elsevier Science B.V.