Flashcards in Factor Analysis Lecture 4 Deck (12):

1

## What is Factor Rotation?

### A statistical adjustment to where the factors are on axis and rotated lines.

2

## Why do we rotate Factors?

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We rotate items as it's really hard to interpret items if they are placed arbitrarily in space. We rotate to fix this to try and get a better model.

By rotating, we get a clearer picture of what's happening between factors.

3

## What does Rotation change?

### Just puts the factor closer to variation. Variation remains the same. Communality remains the same. The Eigenvalues do not stay the same and all that is happening is that a solution and variance is easier to interpret.

4

## What is Simple Structure?

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Simple Structure: Each factor should have some large loadings and some small ones -each factor should only have substantial loadings on only a few items known as simple structure.

Avoid large numbers of mediocre loadings.

5

## What does Rotation depend upon?

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Depends upon theory and interpretation:

Use depends on theory –If expect to be uncorrelated orthogonal

–If expect to be correlated oblique

• Orthogonal rotation look at the Rotated Component Matrix

• Oblique rotation: Pattern Matrix

6

## What happens when you Rotate?

###
Communality of each variable remains the same

• Eigenvalues of factors do not. Factors positioned such that variance of the squared loadings is as large as possible.

Most stat packages use VARIMAX – MAXimisesVARIance of the (squared factor loadings) • Factors now explain more similar amount of variance.

7

## What is Varimax?

### MAXimisesVARIance of the (squared factor loadings) • Factors now explain more similar amount of variance.

8

## How do you know if the loading is significant for the sample size used?

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Loadings significant (alpha = .01, 2-tailed) when:

– n=50: loading > 0.722

– n=100: loading > 0.512

– n=300 loading > 0.298

– n=600 loading > 0.21

– n=1,000 loading > 0.162

9

## What is a Factor Score?

###
A single score from an individual entity representing their performance on some latent variable.

An individual's single score on a factor can be calculated from their responses to items that load onto that factor.

It Takes into account the factor loading –item with greater loading has a higher weighting.

10

## What are the benefits of Factor Scoring?

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Benefits –Use factor scores for subsequent tests

• T-tests etc.

–Multicollinearity issues should be resolved post-FA.

Correlated variables now in one factor

11

## How do you calculate Factor Score?

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Regression. Several methods to calculate –Regression(accounts for initial correlations btw variables) • But factor scores can correlate even if factors are orthogonal

–Bartlett& Anderson-Rubin: Fix some of the issues with regression.

Regression is simplest.

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