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Unformatted text preview: Factor Analysis The factor analysis model assumes that there is a smaller set of uncorrelated variables (underlying factors or underlying characteristics) that will give a better understanding of the data being analyzed. Objectives: 1) To determine whether a smaller set of uncorrelated variables exists that will explain the relationships that exist among the original variables 2) To determine the number of underlying variables (unobservable or latent random quantities called factors) . 3) Interpretation of the new variables. 4) To evaluate the score of experimental units on these new variables 5) To use these new variables in further analyses. Criticism: no unique FA solutions and subjectivity in determining the number of underlying factors, in how they are created, in interpretation.. More pros and cons: Is a powerful and useful multivariate technique for extracting information from high dimensional data in large data sets. Extracts relationships not usually visible directly from viewing the data. Can be used to develop measures (latent factors) capable of representing a number of observed variables. Is complex and has many techniques with associated controversy as to which technique is best. Incorporates a high degree of subjectivity in deciding the number of factors, factor rotations to use and factor interpretation. Has reliability issues that are unresolved Small changes in a data set can lead to big changes in the form of the latent factors computed. Provides no guarantee of the validity, stability or plausibility of results. Factor Analysis Lecture notes.doc 1 Charles Edward Spearman (18631945) and Karl Pearson (18571936) (1904) General Intelligence, Objectively Determined and Measured Spearman speculated that all intellective functioning was underpinned by an overall mental ability accompanied by specific abilities for differing mental tasks. One of the great achievements of psychology evolved from Spearman's efforts to make his theory operational. The statistical procedure we now know as 'factor analysis'. Classics 1 0.83 0.78 0.70 0.66 0.63 French 0.83 1 0.67 0.67 0.65 0.57 Eng 0.78 0.67 1 0.64 0.54 0.51 Math 0.70 0.67 0.64 1 0.45 0.51 Discr 0.66 0.65 0.54 0.45 1 0.40 Music 0.63 0.57 0.51 0.51 0.40 1 Classics= + f 1 French= + f 1 Eng= + f 1 Math= + f 1 Discr= + f 1 Music= + f 1 Factor Analysis Lecture notes.doc 2 How Factor Analysis (FA) differs from PCA: Purpose: Only FA may be used to identify the factor structure underlying a set of variables. FA deals with latent factors that are responsible for the structure of the variancecovariance matrix or the correlation matrix. Principal components versus common factors: In FA the factors are not assumed to be linear combinations of the observed variables (as in the case of PC). FA assumes that the observed variables are a linear combination of the underlying factors....
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This note was uploaded on 12/26/2010 for the course CPSC 499 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.
 Spring '08
 Staff

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