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Lecture 3: Exploratory Factor Analysis Aims & Objectives –To describe the basic factor model –Understand pre-analysis checks, extraction & rotation –To describe the basic process of conducting a EFA, and – To show when and where EFA is most appropriately use

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Basic principle of EFA EFA tries to explain a set of correlations among variables in terms of a set of smaller common factors and zero cross loadings

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Factor analysis of cognitive abilities Verbal Reasoning –Sentence completion –Comprehension –Cloze test Mathematical & Spatial –Spatial rotation –Computation –Find the figure

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Process Pre-analysis –Collect data of the 6 test Sample size, N of items, Social desirability –Create correlation matrix Extraction –How many factors? Rotation –How to best view the solution

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Pre-analysis checks: I Scaling –Likert-type –Dichotomous use Phi –% correct Item selection –Theory, a-priori structure (marker variables) Sampling –To the population where the results are to be generalised

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Pre-analysis checks: II Ratios & Stable structure –N (min = 100) –N:P (2:1, 10:1) –P:M (4:1) –N:M (6:1) Social desirability –Remove items correlating with social desirability

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SentenceCompreClozeRotationComputFigure Sentence 1 Compre..551 Cloze Rotation Comput Figure

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Pre-analysis checks:III V11 V201 V3001 V40001 V11 V2.231 V V Identity matrix Matrix to be analysed KMO greater than.5 Bartlett test of Sphericity

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Communalities The shared variance of a variable with a factor Initially need to estimate these. –Largest column r in the diagonal –SMC

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Number of factors to extract Eigenvalues Factors n Actual data (eigenvalues) Random eigenvalues

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Rotation & simple structure FIFIIFIFII Sentence Compreh Cloze Figure Rotation Coputat

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Rotation - orthogonal FI(a) FII(a) Verbal Math/spatial

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Rotate FI(a) FII(a) Verbal Math/spatial FI (b) FII (b)

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Rotation - oblique FI(a) FII(a) Delta

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The basic factor model Verbal Math/Spatial Common factors Loading Variables Unique factors

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Naming and next steps Factor naming –Re-captured Item Technique (RIT) –Markers –Raters Reliability & validity

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Use & abuses of EFA Uses –IQ –Personality & psychometrics –Education –Psychophysiology –Factorial validity –Data reduction? Problems –Garbage In Garbage Out (GIGO)

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