Factor Analysis

Question 1

Define FA. What is its aim?

Answer 1

A family of statistical techniques used to examine the r/ships between a set of Vs & identify groups of highly correlated Vs. The aim is to simplify a set of inter-related measures without losing important info

Question 2

What are factors?

Answer 2

Underlying, hypothesised constructs which are developed to account for correlations between Vs

Question 3

Define & distinguish between CFA & EFA

Answer 3

EFA describes a set of correlations between Vs (i.e. a correlation matrix) using a smaller no. of common factors with minimal cross-loadings. CFA tests the goodness of fit of a dataset to a pre-specified model of factors (a nonsig fit is desired). Differences: descriptive (no p value given) vs. inferential (p value given)

Question 4

Give 3 uses of FA with specific e.g.s

Answer 4

1) theory development: to identify the no. and nature of factors required to account for inter-correlations (EFA), 2) theory evaluation e.g. the cross-cultural applicability of a theory (CFA) & 3) data simplification

Question 5

The final stage of FA is to give the factors ___

Answer 5

Names

Question 6

Why is mathematical FA preferred to handwritten FA? 2 reasons

Answer 6

1) Because it is difficult to interpret factors from complex inter-correlation matrices
2) Because it allows us to specify what contribution each V makes to a factor I.e. the loading

Question 7

Define a V’s loading

Answer 7

The extent to which it correlates with a factor

Question 8

The product of V1 and V2’s loadings on to factor A equals the…

Answer 8

Correlation between V1 & V2 which can be attributed to factor A

Question 9

Define the residual correlation between V1 and V2

Answer 9

The correlation between the two Vs which remains after removing the proportion of the V1-V2 correlation which can be explained by factor A

Question 10

If residual correlations are low, this means that we don’t need to…

Answer 10

Add more factors to account for the remaining intercorrelation

Question 11

So the residual correlation matrix contains correlations of ___ ___ size

Answer 11

Diminished absolute

Question 12

What is one way of deciding which factor loadings are worth keeping?

Answer 12

Use correlation coefficient significance levels

Question 13

Because FA is usually designed to extract factors which explain as much of the variance of ___ of the Vs, then cross-loadings are quite common. To remove these moderate loadings and ensure high or low loadings onto factors, ___ is necessary

Answer 13

All. Rotation

Question 14

A h2 value is generated for each variable. This is a measure of that variable’s communality. What is communality? It can take any value from ___ to ___. If h2 was 0 this would mean that this V…

Answer 14

The amount of variance in the variable which is explained by all of the factors extracted or the sum of squares of factor loading for that V. From 0 to 1. Shared no variance in common with any of the extracted factors

Question 15

The sum of squares of factor loadings for each factor tells us…. A value of 2.24 means that ___ of the variance of all Vs is explained by that factor. N.B. unlike in multiple regression, the % of variance explained is not the variance explained after…

Answer 15

How much of the total V each factor accounts for. 22.4%. Controlling for the variance explained by all other factors

Question 16

Unrotated factor matrices are difficult to interpret because they displays lots of ___ factors with ___-loadings

Answer 16

Overlapping. Cross

Question 17

Factors are represented graphically by lines at right angles because they are ___

Answer 17

Orthogonal

Question 18

Varimax rotation attempts to ___ & ___ loadings on each factor so that they approach 0 and 1

Answer 18

Maximise, minimise

Question 19

What changes after rotation: commonalities for each V &/or the sum of squares of factor loadings for each factor? Does the total variance explained by all factors change?

Answer 19

Commonalities stay the same. Total loadings for each factor change. No

Question 20

Oblique rotation allows the factors to be non-orthogonal/ correlated & this is sometimes appropriate e.g….. The advantage is it may account….. The disadvantage is…..

Answer 20

Aggression towards family (F1) may be correlated with aggression towards authority (F2). For a larger % of the variance. A lack of clarity in the factor model (I.e. factors may need to be re-FA I.e. the point of FA is defeated) with loadings above 1

Question 21

Name 3 methods of factor extraction. Which does psychology use by tradition?

Answer 21

PCA, canonical factoring, alpha factoring. PCA

Question 22

Name 4 methods used to decide how many factors to keep

Answer 22

1) Kaiser criterion, 2) Scree method (where does the line on the “factor no. against % variance explained” graph change direction), 3) Factor interpretability, 4) Theoretical reasons

Question 23

Give 2 problems with FA. All we can do is…

Answer 23

1) The factor solution reached is under the control of the experimenter
2) There is no definitely correct way to FA
….rule out factor structures which do not fit the data

Question 24

What is cognitive failure? How many factors were expected by Broadbent? What were they? How many factors were actually found? These discrepancies & ultimate reliance on theory to determine how many factors are present causes some to see FA as an ___ rather a science

Answer 24

A person’s failure to complete a task which he/she is normally capable of completing. 3: memory slips, attention slips & psychomotor slips. Just 1 but modern research has found more (2, 4 & 5). Art

Question 25

What is the advantage of CFA? What is it used for? What is CFA’s full name?

Answer 25

It’s more scientific because it depends less on judgement & experimenter decision. To cross-validate factor structures in different samples I.e. test their applicability. Confirmatory maximum likelihood factor analysis

Question 26

How does CFA work? This contrasts with EFA which assumes that all Vs will…. So EFA is ___ & CFA is theoretical in as much in CFA the ___ between pre-specified factors & the data is tested

Answer 26

Loadings are pre-specified/ restricted to hypothesised values based on previous EFAs. Load onto all factors. Atheoretical. Linkage

Question 27

In CFA we test whether unexpected, inappropriate links (e.g. between neuroticism traits & extraversion) have weights of ___. CFA finds that ___ factors fit cognitive failure questionnaire (CFQ) responses best

Answer 27

Zero. 4 (memory for names is the 4th)