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Multiple factor analysis (MFA) is a factorial method devoted to the study of tables in which a group of individuals is described by a set of variables (quantitative and / or qualitative) structured in groups. It may be seen as an extension of: * Principal component analysis (PCA) when variables are quantitative, * Multiple correspondence analysis (MCA) when variables are qualitative, * Factor analysis of mixed data (FAMD) when the active variables belong to the two types. == Introductory example == Why introduce several groups of variables active in the same factorial analysis? '' data'' Let us consider the case of quantitative variables, that is to say, within the framework of the PCA. An example of data from ecological research provides a useful illustration. There are, for 72 stations, two types o f measurements. # The abundance-dominance coefficient of 50 plant species (coefficient ranging from 0 = the plant is absent, to 9 = the species covers more than three-quarters of the surface). The whole set of the 50 coefficients defines the floristic profile of a station. # Eleven pedological measurements (Pedology = soil science): particle size, physical, chemistry, etc. The set of these eleven measures defines the pedological profile of a station. '' Three possible analyses'' '' PCA of flora (pedology as supplementary)'' This analysis focuses on the variability of the floristic profiles. Two stations are close one another if they have similar floristic profiles. In a second step, the main dimensions of this variability (i.e. the principal components) are related to the pedological variables introduced as supplementary. '' PCA of pedology (flora as supplementary)'' This analysis focuses on the variability of soil profiles. Two stations are close if they have the same soil profile. The main dimensions of this variability (i.e. the principal components) are then related to the abundance of plants. '' PCA of the two groups of variables as active'' One may want to study the variability of stations from both the point of view of flora and soil. In this approach, two stations should be close if they have both similar flora'' 'and similar soils. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Multiple factor analysis」の詳細全文を読む スポンサード リンク
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