Flashcards in 14-15 Factor Analysis: a simple introduction Deck (34)
How was factor analysis originally developed?
Factor analysis was originally developed by psychometrician Charles Spearman as a method to uncover the structure of mental abilities (Spearman's G)
Is factor analysis one particular method of analysis?
No, it's an umbrella term that refers to a number of advanced multivariate statistical techniques that are used to uncover the hidden (latent) structure/construct (dimensions) from a set of observed (manifest, measured) attributes
What is FA used for?
FA is used to condense a large number of observed attributes into a much smaller, yet meaningful, set of grouping constructs, called factors (or components)
What is the purpose of FA?
To explore the underlying variance structure of a set of correlation coefficients. Thus, factor analysis is useful for exploring and verifying patterns in a set of correlation coefficients.
What are the two major types of factor analysis?
1. Exploratory factor analysis – what are the factors?
2. Confirmatory factor analysis – do the hypothesised factors exist?
What is exploratory factor analysis (EFA)?
EFA is used when one is interested in identifying a (potentially) hidden structure/construct
What is the most commonly used type of EFA used in psychology?
Principal components analysis (PCA)
How does principal components analysis work?
Factor weights are computed in order to extract the maximum possible variance, with successive factoring continuing until there is no further meaningful variance left. The factor model must then be rotated for analysis.
What does principal components analysis assume?
That ALL the variance in the items can be explained by some hidden structure/construct
What is confirmatory factor analysis?
Confirmatory factor analysis is used when looking to confirm an already hypothesised, theorised or empirically identified structure/construct.
What is an item in FA?
An observed element of an attribute, e.g. a question in a questionnaire or a response in a single task
What is factorability in FA?
The suitability of an item (or data set) to be included in an FA model.
On what does factorability depend?
On the degree of numerical association between items. Items with very low .90 correlations need to be considered with caution.
What does Bartlett's Test of Sphericity test?
It assesses the factorability of a dataset. Specifically, whether the item correlation matrix is significantly different from a matrix with zero correlations. A significant result is desirable.
What is Simple Structure?
A pattern of loadings where items load most strongly on one factor, and much more weakly on the other factors. In other words, they form distinct groups based on the degree of their association.
A highly factorable dataset has ________ within-group correlations and ________ between-group correlations
A highly factorable dataset has high within-group correlations and low to none between-group correlations
In a simple structure items form highly ___________ dimensions.
In a simple structure items form highly independent dimensions.
What is a factor in FA?
A latent dimension that is made up of a group of related items.
For a factor to be meaningful, what two conditions must be fulfilled?
The items attached to the factor must be related both in a qualitative (conceptual) and quantitative (numerical) sense
What are orthogonal factors or components?
Dimensions that are considered to be independent of each other. E.g. Neuroticism and Extraversion are seen as orthogonal dimensions of personality
What are oblique factors or components?
Dimensions that are considered to be related to a degree to each other (e.g. Gf and Gc intelligence factors)
What is factor loading?
The correlation between an item and a factor.
Above what loading is an item considered to "belong" to or make up a factor?
When an item has a loading of >.40 (as a rule of thumb)
What does rotation do?
It geometrically transforms the factors (latent space) in order to generate a model that contains a simpler structure
What is Varimax (orthogonal) rotation?
When you rotate orthogonal factors in such a way that it maximises the variance each of them explains
What is Oblimin (oblique) rotation?
A rotation that is used for oblique (related) factors.
What are the pros and cons of Oblimin rotation?
Pro: It gives you a clearer picture of the underlying constructs
Con: It dangerously distorts the conceptual space
What is an eigenvalue?
An eigenvalue for a given factor measures the variance in all the variables which is accounted for by that factor. If a factor has a low eigenvalue, then it is contributing little to the explanation of variances in the variables and may be ignored as redundant with more important factors. Eigenvalues measure the amount of variation in the total sample accounted for by each factor.
In selecting number of factors, what is the Kaiser criterion?
Retain any factor that has an eigenvalue equal to or greater than one. I.e. retain factors that can explain the variance in at least a single item