Factor Analysis Lecture 3. Flashcards
What are the two broad categories of Factor Analysis?
Exploratory Factor Analysis and Confirmatory Factor Analysis.
What are the two types of Exploratory Factor Analysis?
Principal component analysis and Factor analysis (principal axis factoring).
What are the two types of Confirmatory factor analysis?
Path analysis and Latent variable analysis.
What are the differences between EFA and CFA?
EFA: no prior assumptions about relationships among factors –Just describe relationships among items and group items as part of unified concepts.
CFA: tests a hypothesis that specific items are associated with specific factors –Structural equation modelling –Add-on packages to SPSS (& other programs)
How do you distinguish between Principal components analysis and principal axis factoring?
They are distinguished by their assumption regarding the possibility of unexplained variance. They differ in how they model data.
PCA does not discriminate between common and specific variance.
What are the assumptions principal component analysis makes?
PCA -all item variance explained by the factors –All items have a communality of 1 and the factors will, between them, account for 100% of the variation among the items.
Only common factors and measurement error influence responses observed.
Total variance = common factor variance + measurement error
What are the assumptions principal axis factoring makes?
It is possible that there is a specific factor influencing each variables. Items can have variances that are not influenced by factors.
Principal Axis Factoring: Total variance = common factor variance + specific item variance+ measurement error
Why is Principal axis factoring more complicated?
PAF is more complicated because it must determine how much of the variance relating to an item is “common-factor” variance and how much is “specific variance”.
What are the four purposes of FA?
1: Shows how many distinct common factors are measured by a set of test items –Are the supposed different constructs: neuroticism, anxiety, hysteria, ego strength, self-actualisation, and locus of control, 6 independent entities or would they be better described as only 2 factors?
2: Shows which items relate to which common factors –from previous example neuroticism belonged to the factor “Elements of Pathology”.
3: Determines whether tests that purportedly measure the same thing in fact do so –3 tests that claim to measure anxiety -FA may produce more than one factor indicating something in addition to anxiety is being measured
4: Checks the psychometric properties of questionnaire -with a different sample do the same factors materialise? –Would a different population made up of Native American Indians identify the constructs of extraversion-introversion & Neuroticism which have been found in European cultures? –Note this would need to be done through Confirmatory Factor Analysis
How do you know if Data is suitable?
1: Must be continuous, categorical = inappropriate
2: Variables are normally distributed and outliers have been appropriately dealt with
3: Relationship between all variables appear to be linear or at least not U-shaped or J shaped
4: All variables are independent -thus variables cannot be calculated from other variables – e.g., if item a was height and b was weight then it would be inappropriate for c to be a height to weight ratio since it would necessarily be correlated to both a and b.
5: There are at least some correlations in the matrix that are above .3 –If correlations are smaller than this then there would seem to be no real relationship between any of the items
6: Must be at least 100 participants.
What does the Kaiser Meyer Olkin measure?
KMO) measure of sampling adequacy and addresses if the sample is big enough.
Whay is the minimum sample size for KMO?
>.5 minimum .5-.7 is mediocre .7-.8 good . 8-.9 great . 9 superb
What does Bartlett’s test of Sphericity check?
Is the R-matrix an identity matrix(bunch of 1’s and 0’s)? –If it is all correlations are 0.
Small values (less than 0.05) of the significance level indicate that a factor analysis may be useful with your data.
How do you identify the number of factors? 3
Different criteria produce different results.
3 different criteria:
Kaiser[-Guttman]criterion -generated factors with eigenvalues above 1 are removed as real factors • Problem -is sensitive to the number of items. Increase in items = increase in eigenvalue
• Only valid if <30 variables & allcommunalities >.7
OR • Sample size > 250 & average communality >.6 –Otherwise may retain too many factors
2: Scree Plot: Graph test based on eigenvalues of an unrotated solution -depends on the relative values of eigenvalues and therefore should be independent of item number.
Finds the point in the plot where the shape of the curve changes direction and becomes horozontal.
No. of factors = the number of factors above the line
3: Parallel Analysis: Basically says what you have isn’t random. You check by looking at the Eigenvalues and seeing if the Eigenvalues are bigger than mean for random data. If the Eigenvalue is bigger, than that’s grounds for keeping your factor.
How do you estimate the communality for PAF?
Regression analysis to see how much of the variance in a variable shared with the others.
