Factor Analysis
In many scientific fields, notably psychology and other social sciences, the user is often interested in quantities, such as intelligence or social status, that are not directly measurable. However, it is often possible to measure other quantities that reflect the underlying variable of interest. Factor analysis is an attempt to explain the correlations between observable variables in terms of underlying factors which are themselves not directly observable. For example, measurable quantities, such as performance on a series of tests, can be explained in terms of an underlying factor, such as intelligence.
To perform factor analysis
Choose Statistics Multivariate
Factor Analysis. The dialog shown below appears.
Model page
In the Factor Analysis dialog, the Model page has the following options:
Data
Data Set
Select a data set from the dropdown list or type the name of a data set. You can also type into the Data Set edit field any expression that evaluates to a data set.
Enter an S-PLUS expression that identifies the rows to use in the analysis. To use all the rows in the data set, leave this field blank.
Select this box to omit from the analysis any rows in the data set that contain missing values for any of the variables in the model.
Use Covariance List as Input
Select this to use a covariance list as model input, instead of a data set. Selecting this enables the Covariance List field. Selecting this enables the Covariance List field and makes the other Data fields and Formula fields unavailable.
Covariance List
Enter the name of a covariance list to be used as alternative model input. This list must have the form of a list returned by cov.wt and cov.mve. Components must include center and cov. A cor component is not used; however, an n.obs component is used if present.
Formula
Factor Analysis Formula
Select from the Variable field to enter variables into the Formula field.
Model
Number of Factors
Enter the number of factors to fit. The default is to fit 1 factor.
Method
Choose either maximum likelihood (mle) or principal factor estimation (principal). The default is maximum likelihood estimation.
Rotation
Choose a rotation to use; the default is varimax rotation.
In the Save As field, enter the name for the object in which to save the results of the analysis. If an object with this name already exists, its contents are overwritten. The model object can be used in later functions such as plotting.
Options page
In the Factor Analysis dialog, the Options page has the following options:
Model Options
Type of Score
Select the type of factor score to compute; the default is regression.
Starting Values
Enter the name of a matrix of starting values for the maximum likelihood estimation procedure.
Maximum Iteration
Enter a numeric value specifying the maximum number of iterations to perform for the maximum likelihood estimation procedure. If convergence has not been reached after this number of iterations, the procedure stops. The default value appears in the field.
Uniqueness Tolerance
Enter a positive number giving the tolerance for the change in uniqueness. If no uniqueness changes by more than this value from one iteration to the next, convergence is declared. The default is 0.0001.
Results page
In the Factor Analysis dialog, the Results page has the following options:
Short Output for Factor Analysis
Display a summary of the model results in the designated output window. Printed results include sums of squares of the factor loadings, the size of the data, the names of the components in the fitted model object, and the call that created the model object.
Component Importance
Select this to include the importance of each factor in the printed results.
Loadings
Select this to include the loadings matrix with the printed results.
Loading Options
In the Cutoff Loading Value field enter a number giving the cutoff for printing the loadings. Elements of the loadings matrix whose absolute value is smaller than the cutoff value appear as blanks. This field is only enabled when Loadings is selected.
Plots page
In the Factor Analysis dialog, the Plots page has the following options:
Plot
Loadings Plot
Select this to display a barplot of the factor loadings for each factor (Factor Analysis) or of the components loadings (Principal Components Analysis).
Biplot
Select this to produce a biplot between two factors of the fitted model (Factor Analysis) or of the component loadings (Principal Analysis). The biplot shows the relation of the factors to both the original variables and the original data. This field is enabled only when the number of factors to be fitted is greater than one.
Biplot Options
Biplot Which Scores Enter the two factors or components to be plotted in the form c(factor1, factor2). By default, a biplot of the first two factors is created. This field is enabled only when Biplot is selected.
Predict page
In the Factor Analysis dialog, the Predict page has the following options:
New Data
Enter the name of a matrix or data set to use for computing predictions. It must contain the same names as the terms in the right side of the formula for the model. If omitted, the original data are used for computing predictions.
Enter the name of a data set in which a part of the analysis, such as fitted values and residuals, predictions, confidence intervals, or standard errors, is saved.
Predictions
Select this to save predictions to the data set specified in Save In.
Related S-Plus language functions for Factor Analysis
factanal, factanal.object, factanal.fit.mle, factanal.fit.principal, factanal.mle.control, factanal.start.mle, predict.factanal, fitted.factanal, rotate.factanal, biplot.factanal
Other related S-Plus language functions
princomp