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    Multiple Correspondence Analysis (MCA)

    On March 6th 2004, I made a Multiple Correspondence Analysis (MCA) with the data collected since the last modification of the french version of the test. I then had a total of 271 subjects collected since November 13th 2003. I used the demonstration version of XLSTAT.

    The MCA is a statistical technique used to highlight correspondences between qualitative variables describing a population. These correspondences emphasize independent "latent factors" whose interpretation is the responsibility of the analyst.
    The assumption was to find significant factors which represent the dominant sensory modality of the subjects.

    This analysis emphasized 20 independent factors whose importance is distributed according to the graph below in eigenvalue of the variance. These 20 factors can be attached a priori to anything: psychological dimensions, age, sex, profession, taste for macaronis...

    Multiple Correspondence Analysis

    The coordonates graph of the modalities acording to the factors F1 and F2 is given below. This graph indicates the positioning of the items (30 possible answers) according to the factors F1 and F2.

    correspondence analysis

    Each Mi point represents the method M of question i: In red: the items K, in green: the V, in blue: the A. We see that the F1 axis very clearly constitutes an axis (non-K) /(K) since all the K items are beyond a value of 0.2 and that none is before.
    We also see arising a bottom upwards orientation A/V for the non-K on the F2 axis except for items v5 and v7 which are apart from the "V cloud".

    We can thus say that the assumption is confirmed. The distribution of the items in clouds on the graph of the principal factors constitutes a validation of the questionnaire. Only the items a7/v7 and a5/v5 present an inversion of their supposed interpretation. The items a3/v3 have quasi no discriminating capacity.

    The distribution of the subjects is given in the graph below:


    Each subject is represented in yellow on a scale expressed in a number of standard deviation, this graph makes it possible to visualize its distance with each item in projection to the (F1, F2) plan.

    Critics of the method:

    The MCA method makes it possible to emphasize quantitative latent factors. The fact of seeking correspondences according to two axes for variables with three modalities can bring a bias. I know no technique to emphasize qualitative latent factors with three modalities.

    With any questionnaire of 10 questions of 3 modalities, we would always find a certain number of latent factors, the ideal for an assumption with three modalities is to find two quantitative factors which are distinguished significantly from the others by their relative percentage of the variance. From this point of view our AFCM is not conclusive: although being most significant, the F1 and F2 factors explain only 16,74% of the variance.

    On the other hand, it is not at all obvious a priori that the items are found ordered on the axes according to their supposed interpretation. From this point of view our analysis is very conclusive.

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