1. Chapter_19 Factor Analysis
Factor Analysis is a general name denoting a class of procedures primarily used for data reduction and summarization.
It is an interdependence technique in that an entire set of interdependent relationships is examined.
Area of Factor Analysis:
To identify underlying dimensions or factors.
To identify a new, smaller set of uncorrelated variables.
To identify a smaller set of salient variables from a larger set.
Naresh K. Malhotra
Marketing Research-an applied orientation, 4th ed.

2. Factor Analysis
Model:
Where,

3. Conducting Factor Analysis
It is a eight-step process:
Formulate the problem
Construct the correlation matrix
Determine the method of factor Analysis
Rotate the factors
Interpret the factors
Calculate the factor scores
Select the surrogate variables
Determine the model fit

4. Conducting Factor Analysis
Formulate the problem
Objectives of factor analysis should be identified.
The variables to be included in the factor analysis should be specified based on past research, theory and judgment of the researcher.
The variables be appropriately measured on an interval or ratio scale.

5. Conducting Factor Analysis
Conduct the correlation matrix
For the factor analysis to be appropriate, the variables must be correlated.
If the correlations between all the variables are small, factor analysis may not be appropriate.
Determine the method of factor analysis
Principal component analysis
Total variance in the data is considered.
Common factor analysis
Estimates the factors based only on the common variance.

6. Conducting Factor Analysis
Determine the method of factor analysis
A Priori determination
Determination based on Eigenvalues
Determination based on Scree Plot
Determination based on Percentage of Variance
Determination based on Split-Half Reliability
Determination based on Significance Test

7. Conducting Factor Analysis
Rotate Factors
The factor matrix contains the coefficients used to express the standardized variables in terms of the factors. These coefficients, the factor loadings, represent the correlations between the factors and the variables. A coefficient with a large absolute value indicates that the factor and the variable are closely related.
Although the initial or unrotated factor matrix indicates the relationship between the factors and individual variables, it seldom results in factors that can be interpreted, because the factors are correlated with many variables. If the variables is found in 2 factors then through rotation, the factor matrix is transformed into a simpler one that is easier to interpret.

8. Conducting Factor Analysis
Interpret factors
The factor can then be interpreted in terms of the variables that load high on it.
On the other hand, variables at the end of an axis are those that have high loadings on only that factor, and hence describe the factor. Variables near the origin have small loadings on both the factors.

9. Conducting Factor Analysis
Calculate factor scores
If the goal of factor analysis is to reduce the original set of variables to a smaller set of composite variables (factors) for use in subsequent multivariate analysis, it is useful to compute factor scores for each respondent.
A factor is simply a linear combination of the original variables.
The weights, or factor score coefficients, used to combine the standardized variables are obtained from the factor score coefficient matrix.

10. Conducting Factor Analysis
Select surrogate variables
Instead of computing factor scores, the researcher wishes to select surrogate variables. Selection of substitute or surrogate variables involves singling out some of the original variables for use in subsequent analysis.
If the researcher thinks that the factor which is important not important as his prior knowledge then he reject the variable and selecting the variable is called surrogate variable. Obviously the rejected variable will be replaced with the another variable with the highest factor loadings of the next one.

11. Conducting Factor Analysis
Determine the model fit
The difference between the observed correlations (correlation matrix) and the reproduced correlations can be examined to determine the model fit.
These differences are called residuals. If there are many large residuals (value more than 0.05), the factor model does not provide a good fit to the data and the model should be reconsidered.

12. Conducting Factor Analysis: SPSS Windows
Result of Principal component analysis
Analyze > Data Reduction > Factor
Descriptive > Coefficients, KMO and Bartlett’s test of spericity, and Reproduced
Extraction > Method > Principal Components, Correlation Matrix and Eigenvalues over 1
Rotation > check on varimax