The Why and What of Factor Analysis

This topic was chosen with the expectation that our students participating in management courses at the B-school and research scholars seeking PhDs in various fields would be exposed to statistical analysis which will help them to complete their respective assignments and research. A practical approach is used to assist the readers on the concept and step-by-step instructions on performing the factor analysis.

This blog is the first in a proposed series of blogs on statistical analysis and writing high-quality academic articles/research papers.

A brief on the data set used

The data set used as part of this blog, to demonstrate the technique of factor analysis, was collected by the author of this blog. The sample respondents were collected using a Google survey form from the PGDM students studying in the B-school. In order to ensure data privacy and anonymity of the respondents, the data set does not include any personal information about the students. The same data set is also used in the class to teach students how to perform a series of measures including pre-checks, data entry in SPSS, descriptive statistics, factor analysis and further for doing inferential statistical analysis as well as structural equation modelling (SEM). Anyone requiring the data set for practice purposes should request the author of this blog by sending an email.

What is factor analysis?

Factor analysis is a technique used for data reduction. Let me take an example to explain this concept. The behavioral intent to use mobile banking can be measured by asking respondents to evaluate mobile banking app (and the transactions they have made using the app) on a series of questions on a Likert scale (or also known as items). These items or questions can be used to determine what factors are to be considered part of the study to determine the behavioral intent of using mobile banking.

While performing factor analysis, no distinction is made between the predictor or independent variable and the criterion or dependent variable. Hence this method is known as an interdependence technique in which the entire set of interdependent relationship is examined [1].

Factor analysis is used to determine the number of factors that explain the correlations among a set of variables [1]. I will continue to explain this concept with the help of mobile banking data set. A total of 20 numbers of questions or statements was used to measure the behavioral intent of mobile banking using the Likert scale. The questions relate to the perceived usefulness, perceived ease of use, trust and habit of using the app for making financial transaction or for obtaining non-financial information.

Factor analysis requires a larger sample size and is based on the correlation matrix of the variables involved, and correlations usually need a large sample size before they stabilize. As a rule of thumb, the recommended sample size is 4 to 10 times the number of items used in the study [2].

The criteria for determining the number of factors include determination based on eigenvalue (represents the total variance explained by each factor), a priori, scree plot, split-half reliability method or based on the percentage of variance.

Which software can be used for performing factor analysis?

Some of the software that can be used for performing factor analysis are SPSS, SAS, R and SmartPLS. For explaining the concept in this blog, the author has used SPSS to determine the number of factors using the mobile banking data set.

Pre-checks before performing factor analysis

1.      Subsequent to collecting the data from respondents, ensure to utilize the data preparation technique such as consistency check for data out of range, assigning missing values, discarding unsatisfactory responses, removing duplicate records and those showing zero or little variance.

2.      Perform Reliability analysis (Cronbach Alpha) and remove any items with low item-to-item correlation.

Step-by-step procedure to perform factor analysis

3.      Determine the method of factor analysis – principal component analysis (PCA) a recommended method that accounts for maximum variance in the data (for use in subsequent multivariate analysis). The second method is principal axis factoring in which the factors are estimated based only on the common variance.

4.      The test statistic, Bartlett's test of sphericity is an identity matrix and is used to examine the hypothesis that the variables are uncorrelated in the population.

5.      The Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy is appropriate, that is between 0.5 and 1.0. KMO is an index used to examine the appropriateness of factor analysis. Hence, values below 0.5 imply that factor analysis may not be appropriate as the correlations between pairs of variables cannot be explained by other variables.[2]

6.      Choose the method to rotate the factors – Varimax (an orthogonal method of rotation) or Promax (an oblique method of rotation when the axes are not maintained at right angles).

7.      Resolve any issues related to items cross-loading on multiple factors or items with low factor score. As a rule of thumb, 0.7 or higher factor loading represents that the factor extracts sufficient variance from that variable [2]. Factor loading is the variance explained by the variable on that particular factor.

Using the mobile banking data set, the factor analysis was performed as follows:

Step 1 – A total 65 usable sample was obtained after removing duplicate records, unengaged response (zero variance).

Step 2 – For 65 respondents in the data set, the results obtained for Cronbach alpha are .946 for a total of 20 items and PU (.894), PEOU (.907), HB (.90), TR (.937), BI (.89) for individual factors.

Step 3 – Extraction Method: Principal Component Analysis, a priori 5 factors (as it is an adapted scale [3] with a pre-determined number of factors).

Step 4 – Bartlett's Test of Sphericity, approx. Chi-square (901.632), df (136), Significance (.00)

Step 5 – KMO (.811)

Step 6 – Rotation Method: Varimax with Kaiser Normalization.

Step 7 – 3 items (PU1, HB4, BI2) were removed due to cross-loading with other factors.

The result obtained from the above step is detailed in Table 1 – Rotated Component Matrix.

What are the applications of factor analysis?

There are various domains that have found the factor analysis to be useful including marketing, human resource and other management domains, psychology etc. As mentioned earlier, factor analysis is a statistical procedure or interdependence technique, primarily used for data reduction. In marketing research, the various applications of factor analysis include market segmentation, determine brand attributes in product research, media consumption habits in advertising studies or determining the characteristics of price-sensitive customers.

This blog, along with other proposed blogs on research design and writing quality research papers, will assist students, research scholars and academicians in publishing research articles in good journals. This blog can also be used as a class activity, to publish assignment, evidence of students learning over time and effectively implement them in a classroom. So stay tuned and keep an eye out for future blogs to learn more about this topic of statistical analysis and writing quality research papers.

References

[1] Malhotra, N. K., & Dash, S. (2019). Marketing research: An applied orientation. Pearson India.

[2] Hair, J.F., Black, W.C., Babin, B.J. and Anderson, R.E. (2010), Multivariate Data Analysis, 7th ed., Upper Saddle River, NJ: Pearson Prentice Hall.

[3] Sankaran, R. and Chakraborty, S. (2021), Factors impacting mobile banking in India: empirical approach extending UTAUT2 with perceived value and trust, IIM Kozhikode Society & Management Review, Vol. ahead-of-print, doi.org/10.1177/2320206820975219.