Help Manual


Sigma Magic Help Version 17

Factor Analysis - Exploratory


Factor analysis is useful for investigating variable relationships for complex concepts such as socioeconomic status. It allows us to investigate concepts not easily measured directly by collapsing many variables that are measured into a few interoperable underlying factors (which may not be directly measured). For example, to analyze product positioning, you may survey the market for 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. It can be grouped so that you will have fewer 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, the system will determine an appropriate number of clusters from the analysis.
1-100Number of factors to extract from the data set.
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. Factor rotation aims to obtain a simpler factor loading pattern that is easier to interpret than the original factor pattern. The 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 for you to identify the grouping easily
Cutoff: Sometimes, it helps to suppress variables that don't have a large impact on the factors to help you select the grouping of variables into factors. Only those values that are above the specified cutoff value are displayed.
Additional Options: This field is optional. By typing it here, you can specify any additional options for the R software program.
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. You must specify the required data to complete the analysis and generate outputs. If there are any missing data, the software will remind you to specify the data and click on Compute Outputs to generate analysis results.


You will see the following dialog box if you click the Data button. 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 speed up finding the right data 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 has no 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 crucial that you not only specify the column name but also the table name.
Add or View Data: Click on this button to add more data to 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 the Data Editor dialog box, where you can import more data into your workbook. You can also 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, you must select only numeric columns. If the code begins with a T, you can select 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, you must select a minimum of 2 columns of data and a maximum of 4 columns 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 choose 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 choose the data is to double-click on the columns in the list of Available Data. Finally, you can 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: The list box header will be displayed in black if the right number of data columns is specified. If sufficient data has not been specified, then the list box header will be displayed in 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 specified for this analysis. The data can be viewed in a tabular format or a graphical summary of the selected data.


If you click the Verify button, the software will perform some checks on the data you 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, they are shown as a green checkmark. If the verification checks fail, they are shown as a red cross. If the verification checks result in a warning, they are shown in the orange exclamation mark. Finally, any checks that are required to be performed by the user are shown as blue info icons.
Overall Status: The overall status of all the checks for the given analysis is shown here. The overall status check shows a green thumps-up sign if everything is okay and a red thumps-down sign if any checks have not passed. Note that you cannot proceed with generating analysis results for some analyses if the overall status is not okay.


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 factor analysis results, 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.
Graph Section: The graph section shows the reduction in eigenvalues with the number of components. Pick the number of elements that 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" is 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.


The following examples are in the Examples folder.
  • For the data given in the file, determine which variables can be grouped using factor analysis (Exploratory Factors 1.xlsx)


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.

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