|
In statistics, factor analysis of mixed data (FAMD) (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 (PCA) for quantitative variables and as a multiple correspondence analysis (MCA) for qualitative variables. ==Scope == When data include both types of variables but the active variables being homogeneous, PCA or MCA can be used. Indeed, it is easy to include supplementary quantitative variables in MCA by the correlation coefficients between the variables and factors on individuals (a factor on individuals is the vector gathering the coordinates of individuals on a factorial axis); the representation obtained is a correlation circle (as in PCA). Similarly, it is easy to include supplementary categorical variables in PCA.〔Escofier Brigitte & Pagès Jérôme (2008). Analyses factorielles simples et multiples. Dunod. Paris. 318 p. p. 27 et seq.〕 For this, each category is represented by the center of gravity of the individuals who have it (as MCA). Thus the presence of supplementary variables having a type different from the one of active variable does not pose any particular problem. When the active variables are mixed, the usual practice is to perform discretization on the quantitative variables (e.g. usually in surveys the age is transformed in age classes). Data thus obtained can be processed by MCA. This practice reaches its limits: * When there are few individuals ( less than a hundred to fix ideas ) in which case the MCA is unstable ; * When there are few qualitative variables with respect to quantitative variables (one can be reluctant to discretize twenty quantitative variables to take into account a single qualitative variable). 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「Factor analysis of mixed data」の詳細全文を読む スポンサード リンク
|