Wk 4 - EFA 2 Flashcards by Emma Richmond-Darvill

What are the 3 extraction methods used in EFA?

Principal Components Analysis (PCA)
Principal Axis Factoring (PAF)
Maximum Likelihood (ML)

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Explain Principal Components Analysis method of EFA (x4)

Communalities are set to 1 for each variable
o Assume all variance is shared (no error or unique )
o Therefore, it analyzes both communalities and unique variance together (other methods just do communal)
Extracts components that are assumed to be uncorrelated

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What are the pros of Principal Components Analysis? (x2)

o Finds the best mathematical solution

o Typically explains more variance than other methods

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What are the cons of Principal Components Analysis? (x2)

o Measurement assumption is inappropriate for psychology - factors routinely correlated
o Factor loadings may be artificially high

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Explain the Principal Axis Factoring (PAF) method of extraction in EFA?

Correlations estimated from empirical matrix - so will be <1
Only analyses shared variance between variables - no error or unique
Acknowledges effect of random factors - excludes it
Assumes factors may correlate

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What is the goal of Principal Axis Factoring method of extraction in EFA? (x1)

To maximise variance in observed variables explained by extracted factors

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What are the pros of Principal Axis Factoring method of extraction in EFA? (x2)

Appropriate measurement assumptions for psych -

Allows that variables may correlate at > 0

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How is the Maximum Likelihood (ML) method of extraction in EFA similar to PAF? (x3)

Communalities estimated from empirical correlation matrix,
Only examines shared variance,
And allows possibility of correlated factors

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How is the Maximum Likelihood (ML) method of extraction in EFA different to PAF? (x3)

Goal is to maximise likelihood of reproducing the observed variable correlations
(rather than explain the most variance in variables)
Which may result in different solution to just ‘fitting’ the variances

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Explain the Maximum Likelihood (ML) method of extraction in EFA? (x3)

Calculates a model,
Then tries to find values, factor loadings etc, that put the model in the best shape to predict the present data
o This tends to be preferable to PAF, but gives quite similar results

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What are pros of the Maximum Likelihood (ML) method of extraction in EFA? (x2)

Appropriate measurement assumptions for psychology

Gives Goodness of Fit test - Are diffs between our model and the data significant/problematic?

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How to choose an extraction method in EFA? (x4)

But you’ll find that… (x1)

PAF or ML for a priori ideas - more flexibility, more realistic assumptions
If no unique variance, PCA - but unlikely in psych
If independent test constructs, PCA
o If possibly correlated, PAF or ML

Results often consistent across methods

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What are the 2 classes of rotation methods in EFA?

OrthogonalOblique

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Explain orthogonal rotation in EFA? (x4)

o Assumes factors are independent (uncorrelated)
o Orthogonal – all axes move the same amount/degree
o So remain perpendicular to one another
• Maintains original eigenvectors

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Explain oblique rotation in EFA? (x2)

o Assumes factors can be correlated

o Factor axes may not be perpendicular to one another after rotation

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What are the 3 types of orthogonal rotation in EFA?

Varimax
Quartimax
Equamax

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Explain the Varimax method of orthogonal rotation in EFA (x3)

 Minimize complexity of FACTORS
 Identifies cluster of variables that defines any one factor
 The SPSS default

Explain the Quartimax method of orthogonal rotation in EFA (x2)

 Minimize complexity of VARIABLES

 Identifies variables defined by only one factor

Explain the Equamax method of orthogonal rotation in EFA (x2)

 Attempts to minimize complexity of both factors and variables, but results are unstable…
Don’t do this.

What 2 kinds of loadings are used in oblique rotation in EFA?

Pattern loadings

Structure loadings

Explain the Pattern Loadings used by oblique rotation methods in EFA? (x4)

Indexes unique relation between a factor and a variable,
Partialling out effects of other factors (like a partial correlation)
 How strongly does this variable relate to the factor, but controlling for others –
the unique effect of each factor, for each variable

Explain the Structure Loadings used by oblique rotation methods in EFA? (x4)

Indexes relation between a factor and a variable without accounting for other factors (like a bivariate correlation)
 More traditional – bivariate correlation, no accounting for other stuff

What are the 2 types of oblique rotation in EFA?

Oblimin

Promax

How does Oblimin method of oblique rotation work in EFA? (x2)

Minimizes sum of cross-products of pattern loadings

To get variables to load on only a single factor

How does Promax method of oblique rotation work in EFA? (x3)

Raises orthogonal loadings to a power to reduce small loadings (a number <1 gets smaller, and so can be ignored), Then rotates axes to accommodate this modified interim solution

How to choose a rotation method? (x2)

Varimax most common orthogonal is psych - we want simple factors more than simple variables If variables correlate, use oblique - Oblimin most common

What information is provided by SPSS when doing EFA? (x3, x1, x3, x1)

Initial Factor Solution o Communalities o Variance explained by each factor / component Factor loadings describing extracted factors / components Information about rotated factor solution o For orthogonal rotation: Factor loadings o For oblique : Pattern and Structure loadings Correlations between factors (only if oblique rotation used)

What do I need to do when interpreting SPSS output on EFA? (x3)

ID patterns in factor loadings - variables at >.70 on one factor but

What are the implications of findings mix of positive and negative factor loadings in EFA? (x3)

Don't worry about it in initial/unrotated factor solution More involved interpretion for rotated solution - ie, some variables are negatively related to outcome, some positively

What are the implications of a variable loading strongly on multiple factors in EFA? (x3)

Fails Data-reduction goal May reflect higher-order/more complex factor Could remove it, BUT - important variable? Theoretical relevance of higher factor?

What are the implications of a variable not loading strongly on any factor in EFA? (x2)

It has little to do with constructs of interest | Drop it and re-run analysis

What are the implications of a factor whose content renders it uninterpretable in EFA? (x2)

No use to anyone | Drop it and re-run analysis

What are Heywood Cases in EFA? (x2, plus why a problem x1 each)

When communality for a variable is estimated to be > 1 (can't explain more than all the variance) Or an eigenvalue for a factor is estimated to be negative (can't have negative squares)

Why do we get Heywood Cases in EFA? (x3)

Optimisation process has used logically impossible numbers to solve the math Perhaps you've not included appropriate constraints in analysis (ie, zero floor for eigenvalues, ceiling of 1 for communality)

What are the empirical causes of Heywood cases in EFA? (x2)

Too few data points for number of factors extracted | Highly correlated variables

How to deal with Heywood cases in EFA? (x3)

Drop highly correlated variables Collect more data to help clarify structure Maximum Likelihood methods more vulnerable - switch to PAF

What do you need to report from the findings of EFA? (x9)

List of variables (or items) used Choice of extraction and rotation methods (with justification, re correlations, error variance etc) Number of factors extracted, and stopping rule used to determine this Proportion of variance accounted for by each factor Factor labels and variables in each Factor loadings for each factor (rotated and unrotated) o List range, but provide a full matrix in a Table o Pattern loadings are most important for oblique rotations Correlations between factors (if relevant)

What are 2 important things to remember about the results of an EFA?

Just because you don't find a factor, doesn't mean it doesn't exist… And just because you do, doesn't mean you've found a fundamental construct

Example EFA question: If a researcher argues that * there is no random error in these test scores * it is hard to say how many factors might underlie the tests * these factors should be independent/orthogonal Which stopping rule, extraction and rotation method should be used, and why? (x3)

Kaiser's or Scree - explore number of factors PCA - independent factors, no error Orthogonal - fits PCA and a priori ideas of final structure

Example EFA question: research has argued his tests assess 3 distinct (but related constructs) Which stopping rule, extraction and rotation method should be used, and why? (x3)

A priori - constrain to existing ideas PAF/ML - safer to assume some measurement error Oblique - allows for correlated factors

Example EFA question: Research has no expectations re underlying constructs, measurement error assumed, factors should correlate Which stopping rule, extraction and rotation method should be used, and why? (x3)

Kaiser/Scree - no a priori constraints on number of factors PAF/ML - allows error Oblique - correlated factors