Confirmatory Factor Analysis (CFA)

Oftentimes our questionnaire is based on an existing theoretical framework that consists of various constructs in some proposed relationships. For example, the Theory of Planned Behavior (TPB) proposes that Attitude, Subjective Norm, and Perceived Behavioral Control are the factors of Intention, which in turn affects Behavior.

The Attitude, Subjective Norm, … etc. are the constructs or factors in this model. For each construct / factor we have a number of questionnaire items that collect data about that construct / factor (in contrast to the case of linear regression where we have only one variable for each construct). For example:

[Factor 1] Attitude:

• Q1: xxxx

• Q2: xxxx

• Q3: xxxx

[Factor 2] Subjective Norm:

• Q4: xxxx

• Q5: xxxx

…

This categorization usually comes from theories developed in other previous studies. But how do we know if this categorization is consistent with our data? How do we know if Q1, Q2, Q3 really measure the same factor (however it is named), and Q4, Q5,... really measure another factor, etc.?

To answer this question, we conduct a Confirmatory Factor Analysis (CFA) to confirm that the items measure their corresponding factors.

Note #1: Attitude, Subjective Norm, …, etc. are also called latent variables here because we do not measure these directly, but instead we measure them through Q1, Q2, Q3, …, etc.

Note #2: Desirably, the Q1, Q2, … should be continuous numbers. But it is a common practice to accept ordinal variables as well if we have multiple items under each construct / factor.

Note #3: Read more about CFA here: https://towardsdatascience.com/confirmatory-factor-analysis-theory-aac11af008a6.