Factor Analysis Flashcards
Define FA. What is its aim?
A family of statistical techniques used to examine the r/ships between a set of Vs & identify groups of highly correlated Vs. The aim is to simplify a set of inter-related measures without losing important info
What are factors?
Underlying, hypothesised constructs which are developed to account for correlations between Vs
Define & distinguish between CFA & EFA
EFA describes a set of correlations between Vs (i.e. a correlation matrix) using a smaller no. of common factors with minimal cross-loadings. CFA tests the goodness of fit of a dataset to a pre-specified model of factors (a nonsig fit is desired). Differences: descriptive (no p value given) vs. inferential (p value given)
Give 3 uses of FA with specific e.g.s
1) theory development: to identify the no. and nature of factors required to account for inter-correlations (EFA), 2) theory evaluation e.g. the cross-cultural applicability of a theory (CFA) & 3) data simplification
The final stage of FA is to give the factors ___
Names
Why is mathematical FA preferred to handwritten FA? 2 reasons
1) Because it is difficult to interpret factors from complex inter-correlation matrices
2) Because it allows us to specify what contribution each V makes to a factor I.e. the loading
Define a V’s loading
The extent to which it correlates with a factor
The product of V1 and V2’s loadings on to factor A equals the…
Correlation between V1 & V2 which can be attributed to factor A
Define the residual correlation between V1 and V2
The correlation between the two Vs which remains after removing the proportion of the V1-V2 correlation which can be explained by factor A
If residual correlations are low, this means that we don’t need to…
Add more factors to account for the remaining intercorrelation
So the residual correlation matrix contains correlations of ___ ___ size
Diminished absolute
What is one way of deciding which factor loadings are worth keeping?
Use correlation coefficient significance levels
Because FA is usually designed to extract factors which explain as much of the variance of ___ of the Vs, then cross-loadings are quite common. To remove these moderate loadings and ensure high or low loadings onto factors, ___ is necessary
All. Rotation
A h2 value is generated for each variable. This is a measure of that variable’s communality. What is communality? It can take any value from ___ to ___. If h2 was 0 this would mean that this V…
The amount of variance in the variable which is explained by all of the factors extracted or the sum of squares of factor loading for that V. From 0 to 1. Shared no variance in common with any of the extracted factors
The sum of squares of factor loadings for each factor tells us…. A value of 2.24 means that ___ of the variance of all Vs is explained by that factor. N.B. unlike in multiple regression, the % of variance explained is not the variance explained after…
How much of the total V each factor accounts for. 22.4%. Controlling for the variance explained by all other factors
Unrotated factor matrices are difficult to interpret because they displays lots of ___ factors with ___-loadings
Overlapping. Cross
Factors are represented graphically by lines at right angles because they are ___
Orthogonal
Varimax rotation attempts to ___ & ___ loadings on each factor so that they approach 0 and 1
Maximise, minimise
What changes after rotation: commonalities for each V &/or the sum of squares of factor loadings for each factor? Does the total variance explained by all factors change?
Commonalities stay the same. Total loadings for each factor change. No
Oblique rotation allows the factors to be non-orthogonal/ correlated & this is sometimes appropriate e.g….. The advantage is it may account….. The disadvantage is…..
Aggression towards family (F1) may be correlated with aggression towards authority (F2). For a larger % of the variance. A lack of clarity in the factor model (I.e. factors may need to be re-FA I.e. the point of FA is defeated) with loadings above 1
Name 3 methods of factor extraction. Which does psychology use by tradition?
PCA, canonical factoring, alpha factoring. PCA
Name 4 methods used to decide how many factors to keep
1) Kaiser criterion, 2) Scree method (where does the line on the “factor no. against % variance explained” graph change direction), 3) Factor interpretability, 4) Theoretical reasons
Give 2 problems with FA. All we can do is…
1) The factor solution reached is under the control of the experimenter
2) There is no definitely correct way to FA
….rule out factor structures which do not fit the data
What is cognitive failure? How many factors were expected by Broadbent? What were they? How many factors were actually found? These discrepancies & ultimate reliance on theory to determine how many factors are present causes some to see FA as an ___ rather a science
A person’s failure to complete a task which he/she is normally capable of completing. 3: memory slips, attention slips & psychomotor slips. Just 1 but modern research has found more (2, 4 & 5). Art
What is the advantage of CFA? What is it used for? What is CFA’s full name?
It’s more scientific because it depends less on judgement & experimenter decision. To cross-validate factor structures in different samples I.e. test their applicability. Confirmatory maximum likelihood factor analysis
How does CFA work? This contrasts with EFA which assumes that all Vs will…. So EFA is ___ & CFA is theoretical in as much in CFA the ___ between pre-specified factors & the data is tested
Loadings are pre-specified/ restricted to hypothesised values based on previous EFAs. Load onto all factors. Atheoretical. Linkage
In CFA we test whether unexpected, inappropriate links (e.g. between neuroticism traits & extraversion) have weights of ___. CFA finds that ___ factors fit cognitive failure questionnaire (CFQ) responses best
Zero. 4 (memory for names is the 4th)
