Factor Analysis

What is Factor Analysis?

Factor is a set of variables that are highly interrelated.

Factor analysis...

is a statistical method used to describe variability among observed variables.
explains the interrelationships among a set of observed variables.
is a technique that is used to reduce a large number of variables into fewer numbers of factors.

Exploratory Factor Analysis (EFA)

EFA explores the data & provides information about how many constructs are needed to represent the data.

EFA is an exploratory technique applied to a set of observed variables that seeks to find underlying factors.

The constructs are derived from statistical results, not from theory, & so the constructs can only be named/labelled after the EFA.

EFA is data driven.

Confirmatory Factor Analysis (CFA)

CFA is theory driven.

Prior to CFA, the researcher MUST:

Specify the number of constructs that exist within a set of items.
Specify at which construct each item will load highly on.
Assign items to construct based on theory. CFA does not assign them to construct.

Common Criteria

Factor Loading >0.50 (depending on number of sample, Refer book by Hair et al. (2014) pg.115)
Communality >0.50
Keiser-Meyer-Olkin (KMO) sampling of adequacy >0.50
Bartlet Test of Sphericity is significant; p<0.05
% Variance explained >50%
Eigen Value >1

Exercise

Comparing EFA and CFA. Please download a dataset here.

Exploratory Factor Analysis (EFA)

Step 1: At the Analyze Tab, Select Dimension Reduction, and Factor.

Step 2: At the Factor Analysis dialog box, transfer all variables to the right box labelled as Variables

Step 3: Tick the required Statistics and Correlation Matrix. Continue.

Step 4: Define Factor Analysis extraction method. Continue.

Please refer here, to differentiate between Principal Component and Principal Axes Factoring.

Step 5: Select Rotation method. Continue.

Refer here to differentiate between the rotation methods.

Step 6: Select the options. Continue, and OK.

Confirmatory Factor Analysis (CFA)

Here, factor analysis MUST be done in every single pre-defined constructs. The items belongs to one construct will not be allowed to extract to another construct.

Step 1: At the Analyze Tab, Select Dimension Reduction, and Factor.

Step 2: At the Factor Analysis dialog box, transfer items belongs to each construct to the right box labelled as Variables

Step 3: Tick the required Statistics and Correlation Matrix. Continue.

Step 4: Define Factor Analysis extraction method. Fixed numbers of factors to 1. Continue.

Step 5: Select the options. Here, we should define the minimum value of factor loading for the extraction. Continue, and OK.

The minimum value of factor loading is defined based on number sample. Refer to the following (Hair et al., 2014. pg. 115):

Examples of Reporting Styles

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