Help Manual


Sigma Magic Help Version 15

Factor Analysis - Exploratory


Factor analysis is a useful tool to investigate variable relationships for complex concepts such as socioeconomic status. It allows us to investigate concepts that are not easily measured directly by collapsing a large number of variables that are measured into a few interoperable underlying factors (which may not be directly measured). For example, if you want to analyze product positioning in the market, you may do a survey in the market of the attributes customers use to evaluate products. Let's say there are ten variables. Factor analysis can help you identify which set of variables are similar and can be grouped so that you will have a smaller number of resulting factors to analyze and interpret your data. The key concept is that multiple observed variables can have a similar pattern of responses because they are all associated with a key latent variable. Once the underlying factors are identified, they can be used for product positioning maps to make business decisions. This analysis performs both Principal Factor Analysis (PCA) and Exploratory Factor Analysis (EFA).

This functionality is provided by the R software using the function fa from package psych. Note that this functionality requires that R Script software be installed on your computer and linked to the Sigma Magic software within the options menu. Exploratory Factor Analysis worksheet can be added to your active workbook by clicking on Analytics and then selecting Exploratory Factor Analysis.


Click on Analysis Setup to open the menu options for this tool. A sample screenshot of the menu is shown below.
menu 1
Num Factors: Specify the number of factors to extract from the data set. If this value is set to Auto, then the system will determine an appropriate number of clusters from the analysis.
MomentsUse the method of moments for the estimation of parameters.
Max. LikelihoodUse maximum likelihood estimates for the estimation of parameters.
Algorithm: Specify the algorithm to use for this analysis. The following options are available:
AutoUses the Principal Component Analysis as the default.
Least SquaresUses the Least Squares Method for identification of factors.
Max LikelihoodUses the maximum likelihood estimator for the identification of factors.
Principle ComponentsUses the principal component analysis for the identification of factors.
Rotation: Specify the method to rotate the factors. The goal of factor rotation is to obtain a simpler factor loading pattern that is easier to interpret than the original factor pattern. Rotation of factors results in minimizing the variables needed. Orthogonal rotation methods include Equamax, Orthomax, Quartimax, and Varimax. Quartimax orthogonal rotation seeks to maximize the sum of all loadings raised to the power of 4, which minimizes the number of factors needed to explain a variable. Varimax orthogonal rotation tries to maximize the variance of the squared loadings in each factor. Hence, each factor has only a few variables with large loadings by factor. Equamax orthogonal rotation can be seen as a method of sharpening some properties of varimax. In contrast, oblique rotation methods assume that the factors are correlated.
AutoUses the Oblimin transformation as the default.
NoneDo not use any rotation.
BifactorIt is an orthogonal transformation that uses one general factor and the remaining group factors.
EquamaxA rotation method that is a combination of the varimax method and the quartimax method.
ObliminIt is an oblique transformation that minimizes a certain criterion.
PromaxIt is an oblique transformation
OrthomaxIt is an orthogonal rotation that maximizes the variance across the rows of the factor matrix by raising the loadings to the fourth power; the effect is to make large loadings especially large and small loadings especially small.
QuartimaxRotation method that simplifies the variables.
VarimaxIt is an orthogonal transformation that simplifies the factors. It tries to maximize the variance of the squared loadings in each factor.
VariminVarimin gives variables of an analysis an optimal opportunity to manifest functional interrelations underlying correlational observations.
Scores: Specify the method to calculate the scores. The following options are available.
AutoUses the Regression as the default.
AndersonUses Anderson algorithm.
BartlettUses Bartlett algorithm.
RegressionEstimate factor scores using regression.
tenBergePreserves correlation.
ThurstonUses simple regression.
Sort: You can sort the variables such that all related variables are grouped together in order for you to easily identify the grouping
Cutoff: In order to help you select the grouping of variables into factors, sometimes, it helps to suppress variables that don't have a large impact on the factors. Only those values are displayed that are above the specified cutoff value.
Additional Options: This field is optional. You can specify any additional options for the R software program directly by typing it here.
Help Button: Click on the Help Button to view the help documentation for this tool.
Cancel Button: Click on the Cancel Button to discard your changes and exit this menu.
OK Button: Click on the OK Button to save your changes and try to execute the program. Note that you will need to specify the required data in order to complete the analysis and generate outputs. If there are any missing data, then the software will remind you to specify the data and click on Compute Outputs to generate analysis results.


If you click on the Data button, you will see the following dialog box. Here you can specify the data required for this analysis. Data
Search Data: The available data displays all the columns of data that are available for analysis. You can use the search bar to filter this list and to speed up finding the right data to use for analysis. Enter a few characters in the search field and the software will filter and display the filtered data in the Available Data box.
Available Data: The available data box contains the list of data available for analysis. If your workbook does not have any data in tabular format, this box will display "No Data Found". The information displayed in this box includes the row number, whether the data is Numeric (N) or Text (T), and the name of the column variable. Note that the software displays data from all the tables in the current workbook. Even though data within the same table have unique column names, columns across different tables can have similar names. Hence, it is important that you not only specify the column name but also the table name.
Add or View Data: Click on this button either to add more data into your workbook for analysis or to view more details about the data listed in the available data box. When you click on this button, it opens up the Data Editor dialog box where you can import more data into your workbook, or you can switch from the list view to a table view to see the individual data values for each column.
Required Data: The code for the required data specifies what data can be specified for that box. An example code is N: 2-4. If the code starts with an N, then you will need to select only numeric columns. If the code starts with a T, then you can select both numeric and text columns. The numbers to the right of the colon specify the min-max values. For example, if the min-max values are 2-4, then you need to select a minimum of 2 columns of data and a maximum of 4 columns of data in this box. If the minimum value is 0, then no data is required to be specified for this box.
Select Button: Click on this button to select the data for analysis. Any data you select for the analysis is moved to the right. To select a column, click on the columns in the Available Databox to highlight them and then click on the Select Button. A second method to select the data is to double click on the columns in the list of Available Data. Finally, you can also drag and drop the columns you are interested in by holding down the select columns using your left mouse key and dragging and dropping them in one of the boxes on the right.
Selected Data: If the right amount of data columns has been specified, the list box header will be displayed in the black color. If sufficient data has not been specified, then the list box header will be displayed in the red color. Note that you can double-click on any of the columns in this box to remove them from the box.
View Selection: Click on this button to view the data you have specified for this analysis. The data can be viewed either in the tablular format or you can view a graphical summary of the data selected.


If you click on the Program button, the software will display the program code - an example screenshot is shown in the figure below. Pre-Process Inputs 3
R Program: You can view the R program that will be executed here. This program is usually automatically generated from the options you have specified in the setup earlier. This is the program that will be executed by the R program to generate analysis outputs. If you like, you can edit this program.
Auto Mode: If the radio button is selected as Auto, then the software will automatically update this code based on any changes you make in the input dialog box. We recommend that you use this option to generate the R program so that all your input settings are used to generate analysis results.
Manual Mode: If you use the Manual option, then you will be allowed to edit the R program before the program is executed. Make sure that you specify a syntactically correct program; otherwise, the R program may report errors.


If you click on the Verify button, the software will perform some checks on the data you have entered. A sample screenshot of the data is shown in this figure. Pre-Process Inputs 4
Verify Checks: The objective of this analysis as well as any checks that are performed are listed in this dialog box. For example, the software may check if you have correctly specified the input options and if you have specified the data correctly for analysis.
Check Status: The results of the analysis checks are listed here. If the checks are passed, then they are shown as a green-colored checkmark. If the verification checks fail, then they are shown as a red-colored cross. If the verification checks result in a warning, they are shown in the orange color exclamation mark and finally, any checks that are required to be performed by the user are shown as blue info icons.


Click on Compute Outputs to update the results on the worksheet. A sample screenshot of the worksheet is shown below.
EFA Example
Notes Section: The notes section provides a summary of the input data, and the analysis results section shows the results of the factor analysis, which highlights how many components to include in the factor analysis. Next, the factor analysis results are displayed along with the standardized loadings for each variable, the number of observations within each cluster and the sum of squares within the cluster, and overall.
Graph Section: The graph section shows the reduction in eigenvalues with the number of components. Pick the number of components which show an inflection point. The factor loadings are shown on the right, which will help determine which variables to combine into the selected factors. In this analysis, the number of factors that show a significant reduction in eigenvalues is "3". The factor outputs are sorted and displayed together in the output column. For this analysis, the variables "gear", "am", "drat", "cyl", "disp", and "wt" vary together as one factor, while "wt", "hp" and "carb" are sort of related variables for another factor.


Here are a few pointers regarding this analysis:
  • This analysis requires that the R software needs to be installed on your computer. Further, you will need to provide a link to the RScript executable file under Sigma Magic Options so that the software can use the R software to generate analysis results.


Following examples can be found in the Examples folder.
  • For the data given in the file, determine which variables can be grouped together using factor analysis (Exploratory Factors 1.xlsm)


For more information on this topic, please refer to the following articles. Do note that if any external links are mentioned below, they are for reference purposes only.