Week 7

Question 1

What are the 2 types of FE effects?

Answer 1

• State fixed effects- unobserved, time-invariant characteristics
• Time fixed effects - capture common shocks that occur in a given period.

Question 2

Define factor analysis

Answer 2

This is a technique used to reduce a large amount of information (contained in a number of original variables) into fewer variables, with a minimum loss of information.

Question 3

Define latent variables

Answer 3

These are variables which can only be inferred indirectly from other directly observed or measured variables (i.e popularity)

Question 4

Main uses of factor analysis

Answer 4

1. Reduce clutter –> Reduce data complexity to a manageable size while retaining as much of the original information as possible.
2. Identify / verify patterns

Question 5

What are the 2 types of factor analysis?

Answer 5

Exploratory–> There is no pre-defined structure to verify.
- Searching for structures
- Understanding the groups of measured variables that relate to factors or theoretical constructs
- Looking for factors to identify.
- Data reducing, decluttering
Confirmatory- this is to verify the factor structure of a set of observed variables.
- The factor structure would be based off previous theories or research
- Confirms existing ideas, research, or measurement
- Assess the degree to which the data meet the expected structure
- Test hypothesis about the structure or the number of dimension underlying a set of variables.

Question 6

What are underlying dimensions in a factor analysis?

Answer 6

These are known as factors –> These are where variables may be in “clusters of meaningful correlations” which suggest that the variables associated to these clusters are referring to aspects of the same, common underlying assumption.

Question 7

What is factor loading?

Answer 7

These are the coordinates of a variable.
- Ideally, a variable should have large coordinates for one axis (one factor) and small coordinate for the other axis (if the second factor opposes the qualities of the first).
–> This would infer the variable is related to only one of the factors.

Question 8

How can you analyze a matrix of factor loadings?

Answer 8

It would look something similar to:

0.87. 0.01
0.96. 0.04
0.92. -0.03
0.00. 0.82

And there would be large brackets on each side. The columns would refer to the factors that are being studied, and the rows would refer to a variable.
i.e. The first variable has the ‘loading’ of 0.87 for the first factor and 0.01 for the second factor.

Question 9

What is a eigenvalue

Answer 9

A measure of how much the common variance (communality) of the observed variables a factor explains.
-> Any factor with an eigenvalue > 1 explain more variance than a single observed variable.
-> Indicates the importance of a factor, represents the amount of variation explained by a factor.
-> The factors which explain the least amount of variance often get discarded.
The higher the eigenvalue, the better.

Question 10

Kaiser’s criterion: Keep factors with eigenvalue > 1

Answer 10

Keep factors with eigenvalue > 1

Question 11

Scree plot

Answer 11

Graphical method to determine number of factors (exploratory factor analysis)

Question 12

When using a scree plot, how can you determine which (or how many) factors to keep

Answer 12

Find the “point of inflection” (elbow of the graph) and you keep the factors to the left of the elbow.

Question 13

What is a factor rotation?

Answer 13

Once the factors are extracted, the next step is to examine factor loadings.
Factor rotation is a tool to help interpret factor loadings:
- This is used to ensure that variables:
- Load maximally to only one factor
- Have minimal loading (close to 0) on the other factor.

Question 14

What are the 2 types of factor rotations

Answer 14

• Orthogonal (varimax)
  
  • Independent / Uncorrelated factors
  • May result in a loss of valuable information
• Oblique (oblimin)
  
  • Allows factors to be correlated
  • Produce more accurate and reproducible solution.
    The choice of which is dependent on whether there is a good theoretical reason to suppose that the factors are related or independent.

Question 15

Cronbach’s alpha

Answer 15

It is a measure of internal consistency and reliability, NOT VALIDITY. (Between 0 and 1)
High Cronbach’s alpha values –> Response values for each participant across a set of questions are consistent.
Low Conbach’s alpha values –> Response values do not reliably measure the same construct.