FACTOR ANALYSIS (Hair, 2013)

• Factor analysis is an interdependence technique whose primary purpose is to define the underlying structure among the variables in the analysis. 

• Broadly speaking, factor analysis provides the tools for analyzing the structure of the interrelationships (correlations) among a large number of variables (e.g., test scores, test items, questionnaire responses) by defining sets of variables that are highly interrelated, known as factors. 

• Factor analytic techniques can achieve their purposes from either an exploratory or confirmatory perspective. 

FACTOR ANALYSIS DECISION PROCESS

(Nguồn: Hair, 2009)

(Nguồn: Hair, 2009)

Factor analysis provides the researcher with two distinct, but interrelated, outcomes: data summarization and data reduction. 

• In summarizing the data, factor analysis derives underlying dimensions that, when interpreted and understood, describe the data in a much smaller number of concepts than the original individual variables. 

• Data reduction extends this process by deriving an empirical value (factor score) for each dimension (factor) and then substituting this value for the original values.

DATA SUMMARIZATION

• The fundamental concept involved in data summarization is the definition of structure. Through structure, the researcher can view the set of variables at various levels of generalization, ranging from the most detailed level (individual variables themselves) to the more generalized level, where individual variables are grouped and then viewed not for what they represent individually, but for what they represent collectively in expressing a concept.

• The goal of data summarization is achieved by defining a small number of factors that adequately represent the original set of variables

• Structure is defined by the interrelatedness among variables allowing for the specification of a smaller number of dimensions (factors) representing the original set of variables. 

DATA REDUCTION

• Factor analysis can also be used to achieve data reduction by 
• (1) identifying representative variables from a much larger set of variables for use in subsequent multivariate analyses, 

• or (2) creating an entirely new set of variables, much smaller in number, to partially or completely replace the original set of variables. 

• In both instances, the purpose is to retain the nature and character of the original variables, but reduce their number to simplify the subsequent multivariate analysis. 

Data summarization makes the identification of the underlying dimensions or factors ends in themselves. Thus, estimates of the factors and the contributions of each variable to the factors (termed loadings) are all that is required for the analysis. 

Data reduction relies on the factor loadings as well, but uses them as the basis for either identifying variables for subsequent analysis with other techniques or making estimates of the factors themselves (factor scores or summated scales), which then replace the original variables in subsequent analyses. 

Nguồn: 

• Hair, J. F. (2009). Multivariate data analysis.