Interpret all statistics and graphs for Factor Analysis

Interpretation

Examine the loading pattern to determine the factor that has the most influence on each variable. Loadings close to -1 or 1 indicate that the factor strongly influences the variable. Loadings close to 0 indicate that the factor has a weak influence on the variable. Some variables may have high loadings on multiple factors.

Unrotated factor loadings are often difficult to interpret. Factor rotation simplifies the loading structure, and often makes the factors more clearly distinguishable and easier to interpret. However, one method of rotation may not work best in all cases. You may want to try different rotations and use the one that produces the most interpretable results. You can also sort the rotated loadings to more clearly assess the loadings within a factor.

Interpretation

Examine the communality values to assess how well each variable is explained by the factors. The closer the communality is to 1, the better the variable is explained by the factors. You can decide to add a factor if the factor contributes significantly to the fit of certain variables.

Interpretation

Examine the variance for each factor. The higher the variance, the more that the factor explains the variability in the data. If you do not know how many factors to extract in the analysis, you can first use the principal components method of extraction, without rotation, using the default number of factors (which extracts the maximum number of factors) as a preliminary assessment. Then define the important factors as those with a variance (eigenvalue) greater than a certain value. For example, one criteria is to include any factors with an eigenvalue of at least 1. Another method is to visually evaluate the eigenvalues on the scree plot to determine at what point the eigenvalues show little change and approach 0. For more information, see the topic on the Scree plot.

Interpretation

Examine the % Var value for each factor. Higher values of % Var indicate that a factor explains more of the variability. Therefore, you can use the % Var values to determine which factors are most important.

The communality value for % Var indicates the total variation explained by all the factors in the analysis. Use this value to help determine whether the number of factors used in the analysis explains a sufficient amount of total variation in the data.

Interpretation

Interpretation

Use the scree plot to select the number of factors to use based on the size of the eigenvalues. The ideal pattern is a steep curve, followed by a bend, and then a straight line. Use the factors in the steep curve before the first point that starts the line trend.

Interpretation

If the first two factors account for most of the variance in the data, you can use the score plot to assess the data structure and detect clusters, outliers, and trends. Groupings of data on the plot may indicate two or more separate distributions in the data. If the data follow a normal distribution and no outliers are present, the points are randomly distributed about the value of 0.

Interpretation

Use the loading plot to identify which variables have the largest effect on the factors. Loadings can range from -1 to 1. Loadings close to -1 or 1 indicate that the variable strongly influences the factor. Loadings close to 0 indicate that the variable has a weak influence on the factor. Evaluating the loadings can also help you characterize each factor in terms of the variables. After selecting the number of factors, try different rotations so you can more easily interpret the factor loadings.

Interpretation

Use the biplot to assess the data structure and the loadings of the first two factors on one graph. Minitab plots the second factor scores versus the first factor scores, as well as the loadings for both factors.