FACTOR ANALYSIS- INTRODUCTION, TYPES AND ASSUMPTIONS

A lot of candidates fear statistics as most of the time it is equated with complicated mathematical operations and difficult formulae. But it remains essential to note that the topics of statistics in competitive exams of Psychology (such as UGC NET and GATE) require an in-depth understanding of the theoretical basis of the concepts. It is only after having clarity of the theory that one may proceed and apply the same while answering questions. This blog is dedicated specifically to the topic of factor analysis covering its explanation, basic assumptions and other allied concepts and terms.

1. WHAT IS FACTOR ANALYSIS

Factor analysis is a statistical technique which helps in decreasing and grouping a large set of variables (which share an association among each other) into smaller and more manageable underlying factors.

 Factors can be inferred only as they are latent and cannot be directly observed. Each factor explains a group of variables. We may understand this with the help of an example. Suppose a test includes items such as “Do you look forward to going to your workplace each day?” , ” Do you feel your inputs are valued”, and “How often do you think about quitting the job?”, one may assume that the test might be measuring the levels of job satisfaction at work. Here, we inferred this from the items of the test since it wasn’t directly observable. This job satisfaction here becomes the factor.

2. TYPES OF FACTOR ANALYSIS

Factor analysis is mainly of two main types that have been explained below-

1. Exploratory Factor Analysis (EFA)

As the name suggests, we use this when we do not have a predetermined factor structure or theory on the basis of which we study or conduct factor analysis. The aim herein is to identify the factor structures. EFA is mainly used when researchers are developing a new test.

2. Confirmatory Factor Analysis (CFA)

This type of factor analysis is used by researchers when they already have some hypothesis about the number of factors that is guiding their research. It is used when a theoretical model already exists, that’s why the name, confirmatory factor analysis.

ASSUMPTIONS OF FACTOR ANALYSIS

Now that we know what a factor is and what factor analysis means, let us look at the assumptions of Factor analysis, which makes an important topic from an examination point of view.

1.  Adequate Sample Size

Since Factor Analysis studies correlations among variables that are observable to study hidden structures (factors), it remains an important topic to make sure that the sample size isn’t too small. That increases the risk of spurious correlations. To choose an adequate sample size, the Kaiser-Meyer-Olkin (KMO) Measure of Sampling Adequacy is used. A KMO value above 0.5 is an indication that the sample is adequate.

2.  Sufficient Correlation

We have established in the  beginning that factor analysis studies observed variables and then infers an underlying factor, therefore, it is important to find out if sufficient correlation exists among those variables. If not, there won’t be a case of grouping variables under a single factor since each would be dissimilar and uncorrelated. To check whether or not an adequate correlation exists among variables, we use the Bartlett’s Test of Sphericity. Hence, if the result of this test is statistically significant (typically p < 0.05), it is a  confirmation that meaningful correlations exist among the variables and we can move ahead with carrying out factor analysis.

3. No Multicollinearity

In the previous point, we have discussed how an adequate correlation among variables should exist if one is to proceed with factor analysis. But here comes another important assumption- the correlation among the variables should not be too high that is, multicollinearity should not exist. This is because a very high correlation distorts results by producing redundant data and can hamper the research. In simple terms , we can say that if the variables share a very high correlation they are essentially measuring the same thing, therefore it would be better to remove one of them in that case.

4. Linearity

Researchers have to make sure that the relationships between the variables that are observed, as well as the factors, must be linear, since the entire technique of factor analysis is built on Pearson correlations.

5. No Significant Outliers

Outliers can heavily distort the correlations and ultimately impact the factor structure, thereby impacting the entire process.

Understanding these topics not only helps gain clarity about the concept of factor analysis but also aids in tackling questions related to this topic which show up quite frequently in competitive exams like UGC NET and GATE.