FA

Question 1

How many participants are needed for factor analysis?

Answer 1

A common rule of thumb is that a researcher needs at least needs 10-15 participants per item. At least 100 Subjects are always suggested, even if the number of variables is less than 10.
If a factor explains lots of variance in a dataset and variables correlate highly, it is reasonably reliable even with a small sample size.

Question 2

What is KMO?

Answer 2

• Kaiser-Meyer-Olkin measure of sampling adequacy
• Comares magnitudes of observed correlations to magnitudes of partial correlations
• Decides whether the correlations are worth factoring or not
• Should be at least 0.6- if lower then factor analysis is NOT a good choice
• Because small values mean that the correlations of pairs of variables cannot be explained by other variables i.e. there are not enough relationships between the data to identify an underlying factor
• 0.7 is ok
• 0.8 is good

Question 3

Steps in FA

Answer 3

1. Hypothesise about factors
2. Select FA or PCA
3. Measure variables
4. Compute correlations
5. Extract factors- how many?
6. Rotate factors to aid interpretation and find best fit between original factors and new variables
7. Interpret the results- decide what the new factors are to be called
8. Compute factor scores- decide how to compute them

Question 4

What to consider for extracting factors

Answer 4

	Eigenvalues
	Scree-plot
	Communalities
	Hypothesis testing
	Interpretability
	Parallel analysis

Question 5

What are eigen values?

Answer 5

Help us decide how many factors to extract
amount of variance accounted for by a factor
• Look at % of variance in data explained by 1st factor, then 2nd factor, etc
• 1 st factor extracted always has the largest variance
• By default, SPSS extracts only factors with Eigenvalues > 1

Question 6

What is the scree plot?

Answer 6

Shows the Eigenvalues in decreasing size for all the possible factors
• Factors following a change in slope (the ‘elbow’) are usually not meaningful

Question 7

What are the communalities?

Answer 7

 how much of the variance in each variable is explained by the factors: - the communalities
 Look at extraction column. Variable with communality less than 0.2 is not well represented by any of the factors. Eliminate factors with communalities less than 2. Should be .5 (50%)
You can also tell by looking at the communalities whether the analysis used was FA or PCA. If the initial communalities are all 1, this indicates that it was a PCA, as in PCA it is assumed that variance between all variables I shared and therefore all variance is analysed in PCA. FA only analyse actual shared variance

Question 8

How can you tell if FA or PCA was used?

Answer 8

You can also tell by looking at the communalities whether the analysis used was FA or PCA. If the initial communalities are all 1, this indicates that it was a PCA, as in PCA it is assumed that variance between all variables I shared and therefore all variance is analysed in PCA. FA only analyse actual shared variance.

Question 9

What are factor loadings?

Answer 9

SPSS tells us how strongly each variable is correlated with each factor- the factor loadings. You may have factors that have only weakly correlated items.
• 5 or more strongly loading items (.50 or better) are desirable and indicate a solid factor (Costello & Osborne, 2005)

Question 10

What is parallel analysis?

Answer 10

• Problem with using scree plot to decide how many factors to extract- some cases may present various drops and possible cutoff points, such that the graph may be ambiguous and difficult to interpret.
• PA compares the observed eigenvalues extracted from the correlation matrix to be analysed, with those obtained from uncorrelated normal variables.
• PA implies a Monte Carlo simulation process, since ‘expected’ eigenvalues are obtained by simulating normal random samples that parallel the observed data in terms of sample size and number of variables.
• When this technique was put forward, a factor was considered significant if the associated eigenvalue was bigger than the mean of those obtained from the random uncorrelated data. It is arguable that the PA criterion that a factor must simply outperform what would be expected by a random factor is too lenient for determining what constitutes a major common factor.
• For that reason, it is recommended to only extract factors that have eigenvalues greater than eigenvalues in the 95th percentile of the randomly generated data, i.e. only retain factors that eigen values with less than a 5% chance of occurring randomly.

Question 11

What is the recommended sample size for FA?

Answer 11

Recommendations vary.
Nunnally suggests participants:items 10:1
Comfrey and Lee suggest minimum 300 participants

Question 12

What is the recommended variables:factor ratio?

Answer 12

Tabachnik and Fidel 5:1