Factor Analysis and Component Analysis

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    Can you please explain with example where to use Factor Analysis and principal Component analysis



    The goal of principle components analysis (PCA) is to arrive at a smaller number of components that will extract the most amount of variance from a larger number of observed variables, whereas the goal of factor analysis (FA) is to explain common variance shared by the observed variables.
    In PCA, the components are a linear combination of the observed variables weighted by eigenvectors.
    In FA, the observed variables are linear combinations of the underlying and unique factors.
    In most scenarios, they tend to yield very similar results. Having stated that, there is much debate between “mathematical statisticians” and  “research psychologists” as to which procedure should be used on a regular basis.
    A simple example would be developing a measure of depression (“latent” construct) based on a large pool of “manifest” items/variables assessing behaviors/emotions such as crying, feelings of guilt, suicidal thoughts, etc. You could use these procedures to (1) reduce the number of items/variables needed to measure depression and to (2) detect structure between the “manifest” items/variables.

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