Analysis of objective and subjective data using fuzzy coding and multiple correspondence analysis: principle and example in a sitting posture study

Fuzzy coding vs. crisp coding and then local coding vs. global coding is proposed to transform a quantitative scale into a category scale. Such a transformation technique is seen as the most general one to investigate either heterogeneous but quantitative variables or variables with different scale models (both quantitative and qualitative). A major point of fuzzy coding is that space modalities can be built very early in the statistical analysis process and from a discussion between several specialists. The multiple correspondence analysis (MCA) is proposed to investigate a table where the data come from fuzzy coding; the table rows corresponding to the empirical situations and the columns to the space modalities of the respective variables. Two examples are considered. First, a didactic data set is designed in order to compare the principal component analysis, the MCA with crisp coding and the MCA with fuzzy coding. Second, an example about a sitting posture study is considered in order to show the possibility of achieving relationships between objective and subjective data. The empirical situations correspond to adjustment combinations of the seat, the table and the backrest; the variables are posture indicators and subjective assessments. The main result is that the subjective variables have a much more consistent evolution with the adjustments than the objective ones. Consequently, there is a poor connection between these two sets of variables. The backrest is the furniture setting with the highest influence. From the interpretation of the MCA factor planes, it is possible to find the best and the worst adjustment combinations.