Lec 6

Question 1

What does factor analysis do?

Answer 1

• Identifies latent variables (underlying patterns) that may explain correlations among a set of data

Example: factor analysis (a process) may reveal these items (people who agree they enjoy parties, make friends easily, like being center of attention) could measure a latent trait of extraversion

Question 2

What are the objectives of factor analysis?

Answer 2

1. Data reduction (identify small number of underlying factors)
2. Structure (identify patterns in how variables relate to each other)
3. Theory development (related to understanding psych theories about latent constructs influencing behaviors)

Question 3

What does factor analysis give us?

Answer 3

• transforming e.g. 13 items into fewer factors
• factor loadings: how strongly each item relates to each factor
• communalities: variance, closer to 1.0 means well-explained by the factors we’ve chosen extracted
• variance explained
• a rotated solution
  Note:
  After rotation, the factor loadings change to give us a simpler and better interpretations. But the communalities (variances) do not change.

Question 4

How to write an analysis for factor analysis

Answer 4

1. This factor analysis examines responses on __ items to identify latent traits that explain response patterns
2. I used [principal factor extraction] with a correlation matrix, eigenvalue analysis and scree plot inspection to determine X-factor solution
3. A X-factor solution was identified, explaining XX% of variance
4. After Varimax rotation, a clearer pattern emerged with items … LOADING strongly on Factor 1, while items … LOADED strongly on Factor 2
5. Based on item content, Factor 1 appears to represent [construct] while Factor 2 suggests [construct]. Some items showed low communalities, suggesting a potential third factor

Question 5

How to use a factor loading table [slides]

Answer 5

1. Look for high loadings (above 0.3 usually)
2. Suppress low loadings (cross ‘em out)
3. Ideally, each variable should load strongly only on ONE factor
4. Check if any have high loadings on both factors
5. Group items based on the factor they load most strongly
6. Name the factors based on the content of the items => determine which psych. construct each factor may represent

Question 6

Criticisms of factor analysis

Answer 6

Subjectivity
- in decision making: which extraction method and rotation technique (bc produces different solutions)
- in interpretation / labelling factors: math is objective, but the choice of words / language is subjective
=> Issue of reification: we are defining the factor based on what it does, because it has no inherent quality.