Factor Analysis Model Fit Options

After submitting the Model Launch, the model results appear. The following options are available from the Factor Analysis report’s red triangle menu.

Prior Communality

An initial estimate of the communality for each variable. For a given variable, this estimate is the squared multiple correlation coefficient (SMC), or RSquare, for a regression of that variable on all other variables.

Note: The Prior Communality Estimates table only appears if the Common Factor Analysis (diagonals = SMC) option is selected.

Prior Communality Estimates

Eigenvalues

Shows the eigenvalues of the reduced correlation matrix and the percent of the common variance for which they account. The reduced correlation matrix is the correlation matrix with its diagonal entries replaced by the communality estimates. The eigenvalues indicate the common variance explained by the factors. The Cum Percent can exceed 100% because the reduced correlation matrix is not necessarily positive definite and can have negative eigenvalues.

Note that the table indicates the number of factors retained for analysis.

The Eigenvalues option is available only when the Prior Communality option is set to Common Factor Analysis (diagonals = SMC). The communality estimates are the SMC (square multiple correlation) values.

Eigenvalues of the Reduced Correlation Matrix indicates that the first two factors account for 100% of the common variance. This pattern suggests that you might not need more than two factors to model your data.

Eigenvalues of the Reduced Correlation Matrix

Unrotated Factor Loading

Shows the factor loading matrix before rotation. Factor loadings measure the influence of a common factor on a variable. Because the unrotated factors are orthogonal, the factor loading matrix is the matrix of correlations between the variables and the factors. The closer the absolute value of a loading is to 1, the stronger the effect of the factor on the variable.

Use the slider and value to Suppress Absolute Loading Values Less Than the specified value in the table. Suppressed values appear dimmed according to the setting specified by Dim Text.

Use the Dim Text slider and value to control the table’s font transparency gradient for factor values less in absolute value than the specified Suppress Absolute Loading Values Less Than value.

Note: The Suppress Absolute Loading Values Less Than value and Dim Text value are the same values used in the Rotated Factor Loading table. Changes to one loading table’s settings changes the settings in the other loading table.

Unrotated Factor Loading

Note: The Unrotated Factor Loading matrix is re-ordered so that variables associated with the same factor appear next to each other.

Rotation Matrix

Shows the calculations used for rotating the factor loading plot and the factor loading matrix.

Rotation Matrix

Target Matrix

Shows the matrix to which the varimax factor pattern is rotated. This option is available only for the Promax rotation.

Target Matrix

Factor Structure

Shows the matrix of correlations between variables and common factors. This option is available only for oblique rotations.

Factor Structure

Final Communality Estimates

Estimates of the communalities after the factor model has been fit. When the factors are orthogonal, the final communality estimate for a variable equals the sum of the squared loadings for that variable.

Final Communality Estimates

Standard Score Coefficients

Lists the multipliers used to convert factor values when saving rotated components as factors to the source data table.

Standard Score Coefficients

Variance Explained by Each Factor

Gives the variance, percent, and cumulative percent, of common variance explained by each rotated factor.

Variance Explained by Each Factor

Significance Test

If you select Maximum Likelihood as the factoring method, the results of two Chi-square tests are provided.

The first test is for H0: No common factors. This null hypothesis indicates that none of the common factors are sufficient to explain the intercorrelations among the variables. This test is Bartlett’s Test for Sphericity, whose null hypothesis is that the correlation matrix of the factors is an identity matrix (Bartlett, 1954).

The second test is for H0: N factors are sufficient, where N is the specified number of factors. Rejection of this null hypothesis indicates that more factors might be required to explain the intercorrelations among the variables (Bartlett, 1954).

The tests in Significance Test indicate that the common factors already included in the model explain some of the intercorrelations, but that more factors are needed.

Note: The Significance Test table only appears if the Maximum Likelihood factoring method option is selected.

Significance Test

Rotated Factor Loading

Shows the factor loading matrix after rotation. If the rotation is orthogonal, these values are the correlations between the variables and the rotated factors.

Use the slider and value to Suppress Absolute Loading Values Less Than the specified value in the table. Suppressed values appear dimmed according to the setting specified by Dim Text.

Use the Dim Text slider and value to control the table’s font transparency gradient for factor values less in absolute value than the specified Suppress Absolute Loading Values Less Than value.

Note: The Suppress Absolute Loading Values Less Than value and Dim Text value are the same values used in the Unrotated Factor Loading table. Changes to one loading table’s settings changes the settings in the other loading table.

Rotated Factor Loading

Note: The Rotated Factor Loading matrix is re-ordered so that variables associated with the same factor appear next to each other.

Factor Loading Plot

The plot of the rotated loading factors.

Factor Loading Plot

Note that in the Factor Loading Plot, Factor 1 relates to the Carbon Tetrachloride-Chloroform-Benzene-Hexane cluster of variables, and Factor 2 relates to the Ether–1-Octanol cluster of variables. See the matrix of Rotated Factor Loading for details.

Score Plot

The Score Plot graphs each factor’s calculated values in relation to the other adjusting each value for the mean and standard deviation.

Score Plot

Score Plot with Imputation

Imputes any missing values and creates a score plot. This option is available only if there are missing values.

Display Options

Enables you to show or hide arrows on all plots that can display arrows.

Save Rotated Components

Saves the rotated components to the data table, with a formula for computing the components. The formula cannot evaluate rows with missing values.

Save Rotated Components with Imputation

Imputes missing values, and saves the rotated components to the data table. The column contains a formula for doing the imputation, and computing the rotated components. This option appears after the Factor Analysis option is used, and if there are missing values.

Remove Fit

Removes the fit model results from the Factor Analysis Fit Model report. This option enables you to change the Model Launch configuration for a new report.