L3 Factor Analysis

Question 1

What is principal factor and component an analysis of?

Answer 1

Interdependence

Question 2

What does factor analysis involve?

Answer 2

Reducing a number of variables down to a fewer number of underlying factors

Question 3

Determine whether development, GDP, life expectancy, and technological development are variables or factors?

Answer 3

Development is a factor

The rest are all variables that can be attributed towards development as an underlying factor

Question 4

What needs to have been identified in order to carry out factor analysis?

Answer 4

We need to have identified a number of significantly strong correlations between the variables that are within our sample

Question 5

What needs to be maximised and what needs to be minimised in order to optimise the factor analysis?

Answer 5

Maximise the common variance and minimise the residual variance. Think of the diagram

Question 6

What is factor loading?

Answer 6

Term given to explain the relative connections of each of the original variables upon the underlying factor i.e. the variables that are controlled by the underlying factor all load on to it

Question 7

What are the 3 possible purposes of factor analysis?

Answer 7

1. Assess the degree to which items are tapping in to the same concept
2. Reduce large datasets down to smaller ones so that they can be understood better
3. Improve clarity of complex phenomenon by reducing number of factors

Question 8

What are the two types of factor analysis?

Answer 8

1. Exploratory - detecting and identifying groups of functionally related variables
2. Confirmatory - testing hypothesis

Question 9

What are the 3 main steps involved in a factor analysis?

Answer 9

1. Correlation matrix
2. Principal component or principal factor analysis
3. Rotation

Question 10

What is a correlation matrix?

Answer 10

A table/matrix that displays the different variables and their correlations with each other as well as the associated statistical significance.

Question 11

How do we determine that statistical significance of the correlation between two variables in SPSS?

Answer 11

Look at the number of asterix that the box has within it

Question 12

How many individuals did Gorsuch (1983) propose was necessary per analysis?

Answer 12

100

Question 13

What are the 3 types of variance that make up the total variance?

Answer 13

1. common variance - shared between variables
2. specific/unique variance - specific to one variable
3. error variance - fluctuations that result inevitably from measuring something

Question 14

What is the main difference between principal component analysis and principal axis factoring?

Answer 14

the way they deal with specific/unique variance

Question 15

Outline the format of principal axis factoring

Answer 15

Estimating the common and specific variance across all variables to produce two specific values - working forwards

Question 16

Outline the format of principal component analysis?

Answer 16

Assume there is total common variance between the variables, therefore the value = 1. Later we determine what is not common and so deduct away from the common variance - working backwards

Question 17

When are PCA and PAF used?

Answer 17

PCA - when we have limited information about the variance of the sample so we have to work backwards from a base assumption
PAF - when we have sufficient prior knowledge regarding the sample

Question 18

What is the initial assumption we make when undertaking principal component analysis?

Answer 18

Commonality = 1 i.e. all the variables share something in common

Question 19

When undertaking principal component analysis in SPSS, what does the communalities table include?

Answer 19

the first column shows the initially assumed common variance and the % of the variance for that variable that is explained by some underlying factor.

Question 20

When undertaking principal component analysis in SPSS, what does the Total variance explained table include?

Answer 20

The % of variance column shows how much that ‘component’ explain of the variance, and next to it shows the cumulative % of variance explained by all of the factors identified.

Question 21

What is the Kaiser Criterion? How does it work?

Answer 21

A method used to extract a certain number of components/factors from the sample in SPSS. It extracts the components that have an eigen value greater or equal to 1 and excludes the ones which do not. This means that a number of components can be identified.

Question 22

What problem with the Kaiser Criterion led to other methods for extracting specific factors?

Answer 22

It would exclude factors that had an eigen value of 0.99 which means their importance is ignored

Question 23

What is the scree test?

Answer 23

An alternative method to extracting components that uses a graph. Where there is a significant kink in the line that marks the last component that is used to explain the sample variance

Question 24

What is the name of the point which marks the major kink in the line during a scree test?

Answer 24

Inflexion point

Question 25

What is a component matrix, not a correlation matrix, and why is it useful?

Answer 25

It shows the correlations of each of the initial variables to the extracted factors (the loading) to determine which variables are explained by which underlying factors/components

Question 26

What is a rotation and when are they necessary?

Answer 26

When variables correlate/load on to more than 1 factor quite well - this means that we cannot attribute this variables to a specific factor. Rotation involves rotating the component factors so that their relationship to the variables becomes closer or further away thereby meaning that one will explain that variance best

Question 27

What is the purpose of rotations?

Answer 27

To make sure that the variables only align strongly with one of the factors

Question 28

What are the two forms of rotation?

Answer 28

Orthogonal - keep the x and y axis fixed relative to each other, but rotate them simultaneously
Oblique - like scissors, the axis are not fixed relative to eachother and one becomes closer and better able to explain the variables occurence

Question 29

When is principal axis factoring used?

Answer 29

When we have prior knowledge about the variables/ underlying factors for example if we know that there are 2 major underlying factors to look for.

Question 30

In SPSS, if we are carrying out principal axis factoring and we know that there are supposed to be two underlying factors that explain the variance then what do we do?

Answer 30

We tell SPSS that we want to look for two underlying factors which SPSS will then seek to extract - principal axis factoring (working forwards).

Question 31

What is the name of the table produced in SPSS for the rotated factors? What does it show?

Answer 31

Rotated Factor matrix - it shows the loading of the initial variables on to the extracted components from the PAF

Question 32

What is important to remember when deciding whether to use either PAF or PCA?

Answer 32

That the decision is context specific and there is no clear answer about which one to use specifically