Examples Of Factor Analysis

Factor Analysis Assignment

1.
The principal component analysis is the approach that is used for data reduction and creation of one or more than one index variables from the large number of variables. This happens with the use of linear combination of variables. The index variable that is created from this analysis is called components.
While, the Factor Analysis is the approach that is used for data reduction in different way than principal component analysis. It is the measurement model of latent variable. This cannot be measured directly with one variable rather, it is observed through the relationship between x and y variables.
2.
The general approach (Kaiser) is to retain factors with eigenvalue ≥ 1 and eliminate factors with eigenvalue

3 components extracted.
Interpret the factors extracted.
Bartlett's Test of Sphericity shows the value of significance sig=.000 which reflects the strong correlation between household behavior and shopping behavior and rejects the null hypothesis.
In the communalities table, the initial is by definition, always equals to 1. While in the extraction column, variables with high values are well represented in the common factor space. In the above table of communalities, all variables have high values, near to 1, and thus are well represented.
The screen plot graphs the eigenvalue against the component number. You can see these values in the first two columns of the table immediately above. From the third component on, you can see that the line is almost flat, meaning the each successive component is accounting for smaller and smaller amounts of the total variance. In general, we are interested in keeping only those principal components whose eigenvalues are greater than 1. Components with an eigenvalue of less than 1 account for less variance than did the original variable and so are of little use. In the case of above table, three principal components; 1, 2 and 3 are kept.
Explain the model

The value >3 reflects a good model fit while a value >6 indicates a permissible and average fit model. In the above table, the value of chi-square=5.5 indicates that the model of average fit for the data.
Please solve the following problems on the Nike data. Consider only the following variables: awareness, attitude, preference, intention, and loyalty toward Nike.
4-1. Analyze the Nike data using principal components analysis, using the varimax rotation procedure.
Factor