page_title: Factor analysis of mixed data
section_title: Example
hierarchical_section_title: Factor analysis of mixed data / Example
caption_attribution_description: English: MFA. Test data. Representation of variables.
context_page_description: In statistics, factor analysis of mixed data, or factorial analysis of mixed data, is the factorial method devoted to data tables in which a group of individuals is described both by quantitative and qualitative variables. It belongs to the exploratory methods developed by the French school called Analyse des données founded by Jean-Paul Benzécri.
  The term mixed refers to the simultaneous presence, as active elements, of quantitative and qualitative variables. Roughly, we can say that FAMD works as a principal components analysis for quantitative variables and as a multiple correspondence analysis for qualitative variables.
context_section_description: A very small data set (Table 1) illustrates the operation and outputs of the FAMD . Six individuals are described by three quantitative variables and three qualitatives variables. Data were analyzed using the R package function FAMD FactoMineR .
  In the relationship matrix, the coefficients are equal to  (quantitative variables),  (qualitative variables) or  (one variable of each type).
  The matrix shows an entanglement of the relationships between the two types of variables.
  The representation of individuals (Figure 1) clearly shows three groups of individuals. The first axis opposes individuals 1 and 2 to all others. The second axis opposes individuals 3 and 4 to individuals 5 and 6.
  The representation of variables (relationship square, Figure 2) shows that the first axis () is closely linked to variables ,  and  . The correlation circle (Figure 3) specifies the sign of the correlation between ,  and ; the representation of the categories (Figure 4) clarifies the nature of the relationship between  and . Finally individuals 1 and 2, individualized by the first axis, are characterized by high values of  and  and by the categories  of  as well.
  This example illustrates how the FAMD simultaneously analyses of quantitative and qualitative variables. Thus, it shows, in this example, a first dimension based on the two types of variables.
caption: Figure3. FAMD. Test example. Correlation circle.
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