Factor Analysis : Introduction
Factor analysis is a collection of methods used to examine how underlying constructs influence the responses on a number of measured variables.
There are basically two types of factor analysis: exploratory and confirmatory..
1>Exploratory factor analysis (EFA) attempts to discover the nature of the constructs influencing a set of responses.
2>Confirmatory factor analysis (CFA) tests whether a specified set of constructs is influencing responses in a predicted way.
Both types of factor analyses are based on the Common Factor Model, illustrated in figure 1.1. This model proposes that each observed response (measure 1 through measure 5) is influenced partially by underlying common factors (factor 1 and factor 2) and partially by underlying unique factors (E1 through E5). The strength of the link between each factor and each measure varies, such that a given factor influences some measures more than others. This is the same basic model as is used for LISREL analyses.
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.
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.
Some common uses of EFA are to
Ø Identify the nature of the constructs underlying responses in a speci¯c content area.
Ø Determine what sets of items \hang together" in a questionnaire.
Ø Demonstrate the dimensionality of a measurement scale. Researchers often wish to develop scales that respond to a single characteristic.
Ø Determine what features are most important when classifying a group of items.
Ø Generate \factor scores" representing values of the underlying constructs for use in other analyses.
Miscellaneous notes on EFA:
1>To have acceptable reliability in your parameter estimates it is best to have data from at least 10 subjects for every measured variable in the model. This number should be increased if you expect that the influence of the common factors is relatively weak. You should also have measurements from at least three variables for every factor that you want to include in your model.
2> You should endeavour to have a wide variety of measurements for your EFA. The more accurately that your selection of measurements properly represents the population" of measurements that could be taken, the more generality you will have in your findings.
3> EFA can be performed in SAS using proc factor. Principal component analysis can be performed in SAS using proc princomp, while it can be performed in SPSS using the Analyze/Data reduction/Factor analysis menu selection. EFA cannot actually be performed in SPSS (despite the name of menu item used to perform PCA).
confirmatory factor analysis
Confirmatory factor analysis (CFA) is a special form of factor analysis. It is used to test whether measures of a construct are consistent with a researcher's understanding of the nature of that construct (or factor).
CFA is commonly used in social research. CFA is frequently used when developing a test, such as a personality test, intelligence test, or survey. CFA is also frequently used as a first step to assess the proposed measurement model in a structural equation model. Many of the rules of interpretation regarding assessment of model fit and model modification in structural equation modeling apply equally to CFA. CFA is distinguished from structural equation modeling by the fact that in CFA, there are no directed arrows between latent factors.[clarification needed] In the context of SEM ,the CFA often is called 'the measurement model', while the relations between the latent variables (with directed arrows) are called 'the structural model'
No comments:
Post a Comment