Exploratory Factor Analysis
Presented by: Dawn Huber at the COE Faculty Research Center
Detecting Multivariate Outliers
Analyze
à Regression
à Linear
Highlight subno and click it over to the Dependent box:
Highlight all items (44 of them) and click them over to the Independent(s) box:
Click Statistics
Click Collinearity diagnostics
Click Continue
Click Save
Under Distances, click Mahalanobis
Click Continue
Click OK
To detect if a variable is a multivariate outlier, one must know the critical value for which the Mahalanobis distance must be greater than. Using the criterion of a = 0.001 with 44 df (number of variables), the critical C2 = 78.75.
Due to the large number of variables to examine, an easy way to analyze all the Mahalanobis distance values for the 44 items is to go to
Data
à Sort Cases
Scroll down the variable list to the last variable and highlight the Mahalanobis Distance variable (MAH_1) and click it over to the Sort by: box
Then under Sort Order, click Descending
Click OK
The values under the Mahalanobis (MAH_1) column will then be arranged in descending order – from highest to lowest values.
On the Data View page, examine the top values and determine how many cases meet the criteria for a multivariate outlier (i.e., > 78.75).
For this set of data – we are opting to delete the outlying cases. To delete the cases, highlight the gray numbers (on the left of the screen) then click the Delete key.
Save As the modified data set, “FACTORMINUSMVOUTLIERS”
Missing Data
To check for missing data, go to
Analyze
à Descriptive Statistics
à Frequencies
Click over all the items to Variable(s): (except Subno and MAH_1)
De-select Display frequency tables
This will produce a warning message, simply click OK
Click OK
Normality
Normality among single variables is assessed by skewness and kurtosis – and as such, the distributions of the 44 variables need to be examined for skewness and kurtosis.
To obtain the skewness and kurtosis of the 44 variables one would first go to
Analyze
à Descriptive Statistics
à Frequencies
Click over all 44 items to Variable(s): box
Click Statistics
Under Dispersion, click on all of the options
Under Central Tendency, click on all of the options
Under Distribution, click on all of the options
Click Continue
Click Charts
Click Histograms
Click With normal curve
Click Continue
De-select Display frequency tables
Click OK
Linearity
Multivariate normality implies linearity – and as such, can be assessed through inspection of scatterplots. To spot check for linearity, we will examine Loyal (with strong negative skewness) and Masculin (with strong positive skewness).
To create a scatterplot, select
Graphs
à Scatter
Click Simple
Click Define
Highlight Masculin, and click it over to the Y-Axis:
Highlight Loyal and click it over to the X-Axis:
Click OK
Conducting a Principal Factor Analysis
Analyze
à Data Reduction
à Factor
Highlight all 44 items and click them over to the Variable(s): box.
Click Descriptives
Under Statistics
Click Univariate descriptives
Click Initial solution (default)
Under Correlation Matrix
Click Coefficients
Click Determinant
Click KMO and Bartlett’s test of sphericity
Click Continue
Click Extraction
Change Method to Principal axis factoring
Under Display
Click Unrotated factor solution (default)
Click Scree plot
Click Continue
Click OK
Creating 4 factors:
Analyze
à Data Reduction
à Factor
Click Reset
Highlight all 44 items and click them over to the Variable(s): box.
Click Extraction
Change Method to Principal axis factoring
Under Display
Click Unrotated factor solution (default)
Under Extract
Click Number of factors:
Type in 4 (four)
Click Continue
Click Rotation
Under Method
Click Varimax
Click Continue
Click OK
Internal Consistency of Factors
Analyze
à Scale
à Reliability Analysis
Click over the 44 items under the Items: box
Under the Model: box – be sure that Alpha is selected
Click OK
For each FACTOR (Scale)
Analyze
à Scale
à Reliability Analysis
Click over the items for that factor under the Items: box
Under the Model: box – be sure that Alpha is selected
Click OK
Repeat this separately for each factor (scale)
Exploratory Factor Analysis
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