Factor Analysis in Research

 

 Factor Analysis in Research

Definition

Factor Analysis is a statistical technique used to identify underlying relationships between a large number of observed variables by reducing them to a smaller set of unobserved variables, known as factors.

These factors represent latent constructs that influence the patterns of correlations among the observed variables.

 Purpose of Factor Analysis

·         To reduce data dimensionality (data simplification)

·         To identify latent constructs or factors not directly measured (e.g., attitude, intelligence, perception)

·         To detect structure in the relationships between variables

·         To develop and validate questionnaires or scales (common in social science and finance studies)

 Key Concepts

Term

Explanation

Observed Variables

Measurable items from surveys or tests (e.g., Q1, Q2, Q3 on risk perception)

Latent Variables (Factors)

Unobserved dimensions (e.g., Risk Aversion, Financial Literacy)

Factor Loading

Correlation coefficient between observed variable and factor

Eigenvalue

Indicates how much variance in the data a factor explains

Communality

Proportion of each variable’s variance explained by the factors

Rotation

Adjusting the factors to improve interpretation (Varimax is most common)

Types of Factor Analysis

Type

Description

When to Use

Exploratory Factor Analysis (EFA)

Identifies possible factor structure when you don't have predefined expectations

Early-stage research; developing new scales

Confirmatory Factor Analysis (CFA)

Tests hypotheses about factor structure; part of structural equation modeling (SEM)

Validating established theories or models

 Steps in Factor Analysis

1.      Define the problem and collect data

o    Use structured items (Likert scale) for measurable variables.

2.      Assess data suitability

o    KMO (Kaiser-Meyer-Olkin) > 0.6 and Bartlett’s Test of Sphericity (significant) indicate suitability.

3.      Extract initial factors

o    Principal Component Analysis (PCA) or Principal Axis Factoring (PAF) are common methods.

4.      Determine the number of factors

o    Use Eigenvalues > 1, Scree Plot, or Parallel Analysis.

5.      Rotate the factors

o    Orthogonal (e.g., Varimax) or Oblique (e.g., Promax) to enhance clarity.

6.      Interpret factors

o    Label factors based on variables with high loadings.

7.      Validate the results

o    If needed, perform Confirmatory Factor Analysis on a separate sample.

 Example (Finance Research)

Study Topic: Factors influencing personal financial behavior of working professionals.

Questionnaire Items (Likert scale):

·         Q1: I plan a monthly budget.

·         Q2: I avoid unnecessary expenses.

·         Q3: I prefer long-term investments.

·         Q4: I keep track of my bank transactions.

·         Q5: I am confident in making investment decisions.

Result from EFA:

·         Factor 1 (Financial Discipline): Q1, Q2, Q4

·         Factor 2 (Investment Confidence): Q3, Q5

 Output Interpretation

Variable

Factor 1 (Discipline)

Factor 2 (Confidence)

Communality

Q1

0.80

0.10

0.66

Q2

0.77

0.20

0.65

Q3

0.15

0.82

0.70

Q4

0.72

0.22

0.60

Q5

0.18

0.79

0.68

 Advantages

·         Reduces data complexity

·         Reveals latent structures or dimensions

·         Improves questionnaire design and scale validity

·         Useful for index construction

 Limitations

·         Requires large sample size (minimum: 5–10 respondents per variable)

·         Results can be sensitive to sample or method used

·         Interpretation can be subjective if variables load on multiple factors

 Applications in Finance and Social Science

·         Grouping items into constructs like risk tolerance, financial literacy, consumer trust

·         Developing valid survey instruments

·         Segmenting market data or investor profiles

·         Analyzing customer satisfaction dimensions in financial services

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