Chapter 21 Factor Analysis

Question 1

Communality

Answer 1

Variability in an item explained by all the identified factors within a solution

Question 2

Eigenvalue

Answer 2

Measure of the total variance in the variables accounted for by one factor

Question 3

Factor analysis (FA)

Answer 3

Method of extracting factors which account for correlations (technically co-variances) between several variables (e.g. items on psychological scales, experimental tests)

Question 4

Exploratory factor analysis

Answer 4

Use of factor analysis to identify latent (underlying) factors which explain the variance in correlations. Usually performed in a conceptual area where there is as yet no known well-supported factor structure.

Question 5

Confirmatory factor analysis

Answer 5

Factor analysis performed to support an already identified factor structure. Might be with a larger data set or on a different population from the original.

Question 6

Factor extraction

Answer 6

Stage in factor analysis when an initial set of factors is developed to explain the correlations between variables

Question 7

Factor loading

Answer 7

Degree to which an item is associated with a factor in the analysis. A form of partial correlation.

Question 8

Factor matrix

Answer 8

Table produced by SPSS showing loadings of each factor on each item/variable.

Question 9

Factor rotation

Answer 9

Adjustment of the factor solution so that factors tie up more closely with the original variables. Can be orthogonal or oblique.

Question 10

Initial solution

Answer 10

This is obtained in the first of two major steps in a factor analysis. This will provide the information needed for data checking and for deciding on the number of factors to extract.

Question 11

Oblique factors

Answer 11

Factors which are allowed to correlate with each other.

Question 12

Orthogonal factors

Answer 12

Factors which are not allowed to correlate with each other; geometrically at right angles to one another.

Question 13

Pattern matrix

Answer 13

Table provided by SPSS which shows the loadings, after rotation, of each factor on each item.

Question 14

Principal component’s analysis (PCA)

Answer 14

A method of data reduction, which can be used to identify groups of indicators (e.g., items on a scale or experimental tests) that are correlated but are not expected to be caused by an underlying factor. Thus, PCA does not find ‘latent’ factor structure.

Question 15

Scree test/plot

Answer 15

Plot of factors against their eigenvalues that can be used to assist with identifying the number of factors to extract

Question 16

Structure matrix

Answer 16

Table provided by SPSS which shows the correlations of factors with items