Factor Analysis

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Factor Analysis
Factor analysis is a data and variable reduction technique that attempts to partition a given set of variables into groups (called factors) or maximally correlated variables.

1. Factor Analysis Characteristics
i. Interdependence  Technique
* Dependent Variable – None
* More than one Variable – metric
ii. Factor analysis is subjective and creative
2. Factor Analysis Output
i. Data reduction from large number of variables to smaller number of factors

ii. Factors are a smaller number of variables that capture as much information as possible from the original data set iii. Fk = w1S1 + w2S2 + . . . + wiSi
iv. Factor loading matrix, indicating the number of factors created from the data.  The number of factors can range from 1 to n - the number of variables originally included in the data set.  Factor loadings may be positive or negative. v. Typically, the factors will be independent.  The correlation between two factors is zero and there is no overlap of information vi. Achieved communality is the proportion of variance accounted for by all the extracted factors vii. The eigenvalue of any factor is the total standardized variance accounted for by that factor. Therefore, typically factors with an eigenvalue less than one are not retained. viii. Factors are combinations of variables.  The factors must be interpreted and labeled by the researcher. 3. Hypotheses

i. Formal hypotheses are typically not used for factor analysis ii. The implied null hypothesis is:
iii. H0:  the variables in the data set cannot be meaningfully reduced to a smaller set of combined variables iv. The implied alternative hypothesis is:
v. Ha:  the variables in the data set can be meaningfully reduced to a smaller set of combined variables vi. The factor can meaningfully replace two or more variables in the data set.  Meaningful factors can be created when at least some of the variables are correlated...
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