factor analysis new

8/3/2019 Factor Analysis New

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EF 5303 (DR SEE KIN HAI)

(Factor Analysis)

1. Factor analysis is a data reduction technique to reduce a large number of variables

to a smaller number of factors which account for many of the original variables.

2. Used to see the pattern of responses of people in closed-ended questionnaires withitems measuring similar things identified. An exploratory technique where you

can summaries the structure of a set of variables.

3. Seven methods of factor extraction: 1. Principal Components (PC), 2.Unweighted Least Square, 3. Generalised Least Squares, 4. Maximum Likelihood,

5. Principal-Axis Factoring (PAF), 6. Alpha Factorring, 7. Image Factoring

3 steps in factor analysis procedure

1. Computation of Correlation Matrix - to see the appropriateness of factor analytic

model

2. Factor Extraction to determine the number off factors needed to represent thedata

3. Rotation to make the factor structure more interpretable can bee 1 Orthogonal(factors uncorrelated with one another); 2 oblique (factors are correlated) etc

Conditions needed to use Factor Analysis

1. Sample size min 5 persons per variable, 100 subjects acceptable, 200+

preferable

2. Correlation matrix correlation value > 0.3, Bartletts test of sphericity is large andsig and Kaiser-Meyer-Olkin measure > 0.6

Example:

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Four Steps are needed

1. Create a correlation matrix

2. Extract factors = computer select a combination of indep vars whose sharescorrelations explain the greatest amount of total variance that contribute to dep

var (Factor 1), then extract a second factor (Factor 2) etc. Factor = 1; eigenvalue

= 5.13312 ( show the proportion of variance accounted for by each factor;therefore 1st eigenvalue largest as it explains with greatest amount of total

variance)

3. Select and Rotate factors = Decide which factors to retain for analysis having facevalidity or theoretical validity. Eigenvalue > 1.0 selected use a Scree plot to

select. Now Rotate the factors for interpretation with factor loadings from -1.0 to

1.0 showing the strength of the ind var with the Factor (correlation). > 0.6 = high

loading as correlation.

The unrotated and rotated structure shown above for simple representation. Varimaxrotations (orthogonal) axes at 90o to each other. Other rotations Oblimin/ Promax are

difficult to interprete at this stage.

4. Interpret results= Factors with high loading (> 0.5) have good face validity andappear to measure some underlying construct. This will lead to Construct

Validity.

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factor analysis new

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