1.1 Objectives
The primary objectives of an EFA are to determine
1. The number of common factors infuencing a set of measures.
2. The strength of the relationship between each factor and each observed measure.
Some common uses of EFA are to
1. Identify the nature of the constructs underlying responses in a specific content area.
2. Determine what sets of items hang together in a questionnaire.
3. Demonstrate the dimensionality of a measurement scale. Researchers often wish to develop scales that respond to a single characteristic.
4. Determine what features are most important when classifying a group of items.
5. Generate \factor scores" representing values of the underlying constructs for use in other analyses.
1.2 Performing EFA
There are seven basic steps to performing an EFA:
1.Collect measurements. You need to measure your variables on the same (or matched) experimental units.
2. Obtain the correlation matrix. You need to obtain the correlations (or covariances) between each of your variables.
3. Select the number of factors for inclusion. Sometimes you have a specifc hypothesis that will
determine the number factors you will include, while other times you simply want your final model
to account for as much of the covariance in your data with as few factors as possible. If you have k
measures, then you can at most extract k factors. There are a number of methods to determine the
optimal" number of factors by examining your data. The Kaiser criterion states that you should use
a number of factors equal to the number of the eigen values of the correlation matrix that are greater than one. The Scree test states that you should plot the eigenvalues of the correlation matrix in descending order, and then use a number of factors equal to the number of eigenvalues that occur prior to the last major drop in eigen value magnitude.
4. Extract your initial set of factors. You must submit your correlations or covariance into a computer program to extract your factors. This step is too complex to reasonably be done by hand. Thereare a number of different extraction methods, including maximum likelihood, principal component,and principal axis extraction. The best method is generally maximum likelihood extraction, unless you seriously lack multivariate normality in your measures.
5. Rotate your factors to a final solution. For any given set of correlations and number of factors
there are actually an infinite number of ways that you can define your factors and still account for the same amount of covariance in your measures. Some of these definitions, however, are easier to interpret theoretically than others. By rotating your factors you attempt to and a factor solution that is equal to that obtained in the initial extraction but which has the simplest interpretation.
There are many diferent types of rotation, but they all try make your factors each highly responsive
to a small subset of your items (as opposed to being moderately responsive to a broad set). There
are two major categories of rotations, orthogonal rotations, which produce uncorrelated factors, and oblique rotations, which produce correlated factors. The best orthogonal rotation is widely believed to be Varimax. Oblique rotations are less distinguishable, with the three most commonly used being Direct Quartimin, Promax, and Harris-Kaiser Orthoblique.
6. Interpret your factor structure. Each of your measures will be linearly related to each of your
factors. The strength of this relationship is contained in the respective factor loading, produced by
your rotation. This loading can be interpreted as a standardized regression coefficient, regressing the factor on the measures. You define a factor by considering the possible theoretical constructs that could be responsible for the observed pattern of positive and negative loadings. To ease interpretation you have the option of multiplying all of the loadings for a given factor by -1. This essentially reverses the scale of the factor, allowing you, for example, to turn an unfriendliness factor into a friendliness factor.
7. Construct factor scores for further analysis. If you wish to perform additional analyses using
the factors as variables you will need to construct factor scores. The score for a given factor is a
linear combination of all of the measures, weighted by the corresponding factor loading. Sometimes factor scores are idealized, assigning a value of 1 to strongly positive loadings, a value of -1 to strongly negative loadings, and a value of 0 to intermediate loadings. These factor scores can then be used in analyses just like any other variable, although you should remember that they will be strongly collinear with the measures used to generate them.
Posted By:
Deepika Gnanasekar,
12075,
Marketing Batch
Source: “http://www.stat-help.com/factor.pdf”
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