Perceptual analysis of two-way two-mode frequency data: probability matrix decomposition and two alternatives

A perceptual mapping technique for the analysis of two-way two-mode frequency data is presented: probability matrix decomposition. The technique is compared, both theoretically and empirically, to two alternative techniques: latent class analysis by the binomial model and correspondence analysis. From a theoretical perspective the most salient difference is that probability matrix decomposition (PMD) allows for testing several decision rules, each of which constitutes a different model of the psychological process assumed to give rise to the data. This distinguishes PMD from both correspondence analysis and latent class analysis, 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 set of judgements obtained from 50 consumers concerning the appropriateness of 11 attributes for 41 sandwich fillings. Applying each of the three techniques to the binary judgements aggregated across respondents showed that PMD had the best fit in representing the data and also had the largest predictive power with respect to the preferences of consumers for the sandwich fillings. These findings support the hypothesis that modelling the underlying process may lead to a more accurate representation. Regarding the interpretability of the resulting perceptual maps, there also was an advantage for PMD. When considering the ease of data analysis however, correspondence analysis seems to be superior.