PRINCIPAL COMPONENTS, FACTOR ANALYSIS, CORRESPONDENCE ANALYSIS and SCALING

It is usual in statistical work have many variables measured or observed in a collection of individuals and pretend to study them together, for which usually go to the multivariate statistical data analysis of data. Then there are a variety of techniques and select the most appropriate data and scientific objective. Many variables on a sample is presumable that a part of the collected information may be redundant or be excessive, in which case the multivariate dimension reduction...
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It is usual in statistical work have many variables measured or observed in a collection of individuals and pretend to study them together, for which usually go to the multivariate statistical data analysis of data. Then there are a variety of techniques and select the most appropriate data and scientific objective. Many variables on a sample is presumable that a part of the collected information may be redundant or be excessive, in which case the multivariate dimension reduction methods (principal components, factor analysis, correspondence analysis and multidimensional scaling) try to eliminate it. These methods combine many observed variables to get few fictitious variables representing them with the minimum loss of information.Principal components and factor analysis are a techniques of multivariate statistical analysis that ranks among the methods of interdependence. They are a multivariate method of simplification or reduction of the dimension and that applies when there is a large set of variables with quantitative data correlated each other chasing get fewer variables, linear combination of primitives and incorrelacionadas, that are called principal components or factors, which summarizes as well as possible to the variable initials with the minimum loss of information, and whose subsequent interpretation will allow a simpler analysis of the studied problem. This reduction in many variables to few components can simplify application on the latter's other multivariate techniques (regression, cluster, etc.). If the variables were qualitative variables, it would result in the correspondence analysis.The multidimensional scaling allows the researcher to determine the relative image perceived from a set of objects (companies, products, ideas or other objects on which individuals develop perceptions). it provides a representation graph in a geometric space of few dimensions (perceptual map) which allows to understand how individuals perceive objects and which patterns, usually hidden, are behind that perception (in this sense can also be considered the multidimensional scaling as a dimension reduction technique). In these spaces, objects take the form of points and the proximity between them reflects the analogy existing between them.