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 __image\ebd_ebd75.gif Multivariate __image\ebd_ebd76.gif Factor Analysis. The dialog shown below appears.

Model page

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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.

Subset Rows

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.

Omit Rows with Missing Values

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.

Save Model Object

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

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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

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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

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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

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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.

Save In

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