14-15 Factor Analysis: a simple introduction

Question 1

How was factor analysis originally developed?

Answer 1

Factor analysis was originally developed by psychometrician Charles Spearman as a method to uncover the structure of mental abilities (Spearman’s G)

Question 2

Is factor analysis one particular method of analysis?

Answer 2

No, it’s an umbrella term that refers to a number of advanced multivariate statistical techniques that are used to uncover the hidden (latent) structure/construct (dimensions) from a set of observed (manifest, measured) attributes

Question 3

What is FA used for?

Answer 3

FA is used to condense a large number of observed attributes into a much smaller, yet meaningful, set of grouping constructs, called factors (or components)

Question 4

What is the purpose of FA?

Answer 4

To explore the underlying variance structure of a set of correlation coefficients. Thus, factor analysis is useful for exploring and verifying patterns in a set of correlation coefficients.

Question 5

What are the two major types of factor analysis?

Answer 5

1. Exploratory factor analysis –what are the factors?

2. Confirmatory factor analysis –do the hypothesised factors exist?

Question 6

What is exploratory factor analysis (EFA)?

Answer 6

EFA is used when one is interested in identifying a (potentially) hidden structure/construct

Question 7

What is the most commonly used type of EFA used in psychology?

Answer 7

Principal components analysis (PCA)

Question 8

How does principal components analysis work?

Answer 8

Factor weights are computed in order to extract the maximum possible variance, with successive factoring continuing until there is no further meaningful variance left. The factor model must then be rotated for analysis.

Question 9

What does principal components analysis assume?

Answer 9

That ALL the variance in the items can be explained by some hidden structure/construct

Question 10

What is confirmatory factor analysis?

Answer 10

Confirmatory factor analysis is used when looking to confirm an already hypothesised, theorised or empirically identified structure/construct.

Question 11

What is an item in FA?

Answer 11

An observed element of an attribute, e.g. a question in a questionnaire or a response in a single task

Question 12

What is factorability in FA?

Answer 12

The suitability of an item (or data set) to be included in an FA model.

Question 13

On what does factorability depend?

Answer 13

On the degree of numerical association between items. Items with very low .90 correlations need to be considered with caution.

Question 14

What does Bartlett’s Test of Sphericity test?

Answer 14

It assesses the factorability of a dataset. Specifically, whether the item correlation matrix is significantly different from a matrix with zero correlations. A significant result is desirable.

Question 15

What is Simple Structure?

Answer 15

A pattern of loadings where items load most strongly on one factor, and much more weakly on the other factors. In other words, they form distinct groups based on the degree of their association.

Question 16

A highly factorable dataset has ________ within-group correlations and ________ between-group correlations

Answer 16

A highly factorable dataset has high within-group correlations and low to none between-group correlations

Question 17

In a simple structure items form highly ___________ dimensions.

Answer 17

In a simple structure items form highly independent dimensions.

Question 18

What is a factor in FA?

Answer 18

A latent dimension that is made up of a group of related items.

Question 19

For a factor to be meaningful, what two conditions must be fulfilled?

Answer 19

The items attached to the factor must be related both in a qualitative (conceptual) and quantitative (numerical) sense

Question 20

What are orthogonal factors or components?

Answer 20

Dimensions that are considered to be independent of each other. E.g. Neuroticism and Extraversion are seen as orthogonal dimensions of personality

Question 21

What are oblique factors or components?

Answer 21

Dimensions that are considered to be related to a degree to each other (e.g. Gf and Gc intelligence factors)

Question 22

What is factor loading?

Answer 22

The correlation between an item and a factor.

Question 23

Above what loading is an item considered to “belong” to or make up a factor?

Answer 23

When an item has a loading of >.40 (as a rule of thumb)

Question 24

What does rotation do?

Answer 24

It geometrically transforms the factors (latent space) in order to generate a model that contains a simpler structure

Question 25

What is Varimax (orthogonal) rotation?

Answer 25

When you rotate orthogonal factors in such a way that it maximises the variance each of them explains

Question 26

What is Oblimin (oblique) rotation?

Answer 26

A rotation that is used for oblique (related) factors.

Question 27

What are the pros and cons of Oblimin rotation?

Answer 27

Pro: It gives you a clearer picture of the underlying constructs

Con: It dangerously distorts the conceptual space

Question 28

What is an eigenvalue?

Answer 28

An eigenvalue for a given factor measures the variance in all the variables which is accounted for by that factor. If a factor has a low eigenvalue, then it is contributing little to the explanation of variances in the variables and may be ignored as redundant with more important factors. Eigenvalues measure the amount of variation in the total sample accounted for by each factor.

Question 29

In selecting number of factors, what is the Kaiser criterion?

Answer 29

Retain any factor that has an eigenvalue equal to or greater than one. I.e. retain factors that can explain the variance in at least a single item

Question 30

What is the “Little Jiffy” technique in factor analysis?

Answer 30

Consider eigenvalues greater than 1, then do varimax rotation

Question 31

What is Catell’s (1958) scree plot rule?

Answer 31

The Cattell scree test plots the components as the X axis and the corresponding eigenvalues as the Y-axis. As one moves to the right, toward later components, the eigenvalues drop. When the drop ceases and the curve makes an elbow toward less steep decline, Cattell’s scree test says to drop all further components after the one starting the elbow.

Question 32

In EFA, what is the “variance explained” rule?

Answer 32

To keep all factors that can collectively account for 80%-90% of the variance.

Question 33

In EFA, what is the Joliffe criterion?

Answer 33

Retain all factors with eigenvalues greater than or equal to .70

Question 34

In EFA, what is the comprehensibility rule?

Answer 34

Retain all factors that are meaningful and clearly interpretable within the context of a given study