First you have to do a pre-calculation, select the menu in the analysis - dimensionality reduction - factor analysis, the main panel pops up, the variables you want to analyze the variable box, and then click OK. At this point there will be only one or two charts in the output window. One of the charts is the variance contribution of the principal components. In this chart you need to find two adjacent columns (the third and fourth columns, I think), where the first column refers to the contribution to the variance of the individual factors, and the second one is the cumulative contribution of the factors. This means that the values in the first column add up to 100, and the values in the second column increase, with the last one equaling 100. If the first column is 60,30,10, then the second column is 60,90,100. There is a sum between the two columns. Once you have found these two columns, you need to find the number that makes the cumulative contribution eighty percent. The first column of the table is 1,2,3, etc., which represents the first factor. For example, the row that 3 refers to includes the variance contribution of the third factor and the cumulative variance contribution of the third factor. You have to find the cumulative to eighty percent of that factor is the first factor, and then just calculate by extracting a few factors.

After you know how many factors to extract by precomputation, you start the formal calculation. Open the main panel of factor analysis again, in the rightmost a **** there are five options, respectively, description, extraction, rotation, score, options. These five weren't used in pre-calculation, but they're going to be used now. Tap Continue.

Click on the description, in the dialog box, select the initial variable analysis, kmo statistic and bartlett spherical test of the two options, (note that the kmo and bartlett is an option, the option name is very long) this step is used to determine whether the variable is suitable for factor analysis.

Click on the extraction, the top of the dialog box, select the method of principal components, the analysis of the correlation matrix, the output of the unrotated factor solution and gravel plot two options, the extraction of a fixed number of factors, in the factor to be extracted, fill in the factor number of factors calculated in the pre-calculation of the pre-calculation of the number of factors. Tap Continue.

Rotation, select the maximum variance method, and output the rotated solution. Continue.

Save as a variable in Score, select Regression as the method, and check the box to display the factor score coefficient matrix. Continue.

OK.

Then you can analyze the results.

First look at the results of kmo and bartlett, the closer the kmo statistic is to 1, the stronger the variable correlation, the better the factor analysis. Usually more than 0.7 for general, 0.5 or less unacceptable, is not suitable for factor analysis. bartlett test from the test correlation matrix, if the p-value, that is, sig, is relatively small, generally considered less than 0.05, of course, the smaller the better, it is suitable for factor analysis.

If these two tests are qualified, only then can go to write the factor model.

For the sake of description, let's say we have two factors f1, f2,

The rotated and transformed factor loading matrix will tell you the coefficients of each variable expressed in terms of factors. For example, variable x1 = factor 1*f1 + factor 2*f2, variable 2 and so on.

The factor score coefficients matrix will tell you the weights that each variable accounts for in each factor, for example f1 = coefficient 1*x1 + coefficient 2*x2+.

Based on this we can figure out the factor scores.

Because we chose to save the factor as a new variable before, spss will directly save the two factor scores as two new variables.

And then don't we have a formula for this

Total Score = Variance Contribution of Factor 1 * Score of Factor 1 + Variance Contribution of Factor 2 * Score of Factor 2 +...

Just calculate it according to this formula.

Use either spss or Excel.

I hope it can help you Oh.

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