Factor analysis is a collection of methods used to examine how underlying constructs influence the responses on a number of measured variables. Factor analyses are performed by examining the pattern of correlations between the observed measures. Measures that are highly correlated (either positively or negatively) are likely influenced by the same factors, while those that are relatively uncorrelated are likely influenced by different factors.
There are basically two types of factor analysis:
Exploratory factor analysis (EFA) :-
The primary objectives of an EFA are to determine
1. The number of common factors influencing a set of measures.
2. The strength of the relationship between each factor and each observed measure
Uses of EFA :
· Identify the nature of the constructs underlying responses in a specific content area.
· Determine what sets of items are together in a questionnaire.
· Demonstrate the dimensionality of a measurement scale.
· Determine what features are most important when classifying a group of items.
· Generate factor scores representing values of the underlying constructs for use in other analyses.
Confirmatory factor analysis (CFA)
The primary objective of a CFA is to determine the ability of a predefined factor model to fit an
observed set of data.
Uses of CFA:
· Establish the validity of a single factor model.
· Compare the ability of two different models to account for the same set of data.
· Test the significance of a specific factor loading.
· Test the relationship between two or more factor loadings.
· Test whether a set of factors are correlated or uncorrelated.
· Assess the convergent and discriminant validity of a set of measures.
Types of factoring
Principal component analysis (PCA): The most common form of factor analysis, PCA seeks a linear combination of variables such that the maximum variance is extracted from the variables. It then removes this variance and seeks a second linear combination which explains the maximum proportion of the remaining variance, and so on. This is called the principal axis method and results in uncorrelated factors.
Common factor analysis: It is also called principal factor analysis (PFA) or principal axis factoring (PAF), seeks the least number of factors which can account for the common variance (correlation) of a set of variables.
Factor analysis is an interdependence technique. The complete set of interdependent relationships is examined. There is no specification of dependent variables, independent variables, or causality. Factor analysis assumes that all the rating data on different attributes can be reduced down to a few important dimensions. This reduction is possible because the attributes are related. The rating given to any one attribute is partially the result of the influence of other attributes. The statistical algorithm deconstructs the rating (called a raw score) into its various components, and reconstructs the partial scores into underlying factor scores. The degree of correlation between the initial raw score and the final factor score is called a factor loading. There are two approaches to factor analysis: "principal component analysis" (the total variance in the data is considered); and "common factor analysis" (the common variance is considered).
Author- Anusha Pant