Purposes of FA/ PCA

Question 1

What is the aim of factor analysis?

Answer 1

To uncover patterns of relationships between observed variable, and attempt to describe/ explain those relationships with a smaller number of factors.

Are there patterns that are systematically related?

Uncover latent factors that CAUSE the responses in observed variables

Examines ONLY the shared variance across the observed variables

FA to figure out the optimal weights of variables

e.g. social anxiety

Question 2

What is exploratory factor analysis used for?

Answer 2

exploratory, decisions made during FA are determined by the analysis outcome.

Can be used to:

1) Explore the number of factors that might be present in the dataset.
2) Uncover the meaning and importance of factors (by looking at how much variance in the observed variables they account for)
3) Theory testing (although this is normally CFA).
4) reducing variables required in an analysis.
5) Testing replicaibility of factor solution across samples.

Question 3

Principal component analysis (PCA)

Answer 3

Used as a data summary technique.

To create an index variable from a set of measurable variables (called a component).

Figure out the optimal number of components, and the optimal weights of these.

ALL of the observed variance is analysed

Question 4

Confirmatory factor analysis (CFA)

Answer 4

A theory driven model is tested by placing constraints on relationships between observed variables and latent factors, and between latent factors

Question 5

Possible issue with FA

Answer 5

:( it relies heavily on the decision making of the researcher

:( often used as last ditch attempt to ‘save’ a dataset

Question 6

FA or PCA?

Answer 6

FA when you have a theoretical basis for expecting factors that cause responses (if factors have been hypothesised)

PCA to extract linear composites to use on further analyses (reducing data down)

Question 7

Steps for FA and PCA

Answer 7

1) practical issues and assumptions
2) extraction
3) rotation
4) interpretation

Question 8

How can you instantly tell in PCA or FA (principal axis factoring) has been done?

Answer 8

Look at initial commonalities, if these are all 1s it is PCA.

Look at the correlation matrix, if the diagonals are all 1s it is PCA (because it looks at unique and error variance too)

This diagonal for FA is the squared multiple correlations (SMC)- this is the correlation between each variable and ALL other variables .