Common Factor Analysis Assignment
Factor Analysis Assignment
1. “What is the major difference between principal components analysis and common factor analysis?”
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. “Explain
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3 components extracted.
3-2. 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 does not approve the null hypothesis.
• In the communalities table, the initial is by definition, always equals to 1. While in the extraction column, the high value variables are represented in a well way 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. It can be seen that the values which are in the first two columns are consistently high. Below and including the third row, a flat line can be seen which means that every successive row is accounting for smaller value of gross variance. Generally, the principal components with eigenvalues greater than 1 are kept. The components which have eigenvalue <1 are accounted for less variance as compared to the original variable are thus are less used. In the case of above table, three principal components; 1, 2 and 3 are kept.
3-3. Explain the model
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The value of chi-square from the first table indicates the model fit, either it is good or average. 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.
4. “Please solve the following problems on the Nike data. Consider only the following variables: awareness, attitude, preference, intention, and loyalty toward
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