Index

Special Characters

%INCLUDE statement

A

absolute sample sizes

acquiescence

alpha

See Cronbach's coefficient alpha

alpha extraction

alpha factoring

ALPHA option

Estimation of Alpha in SAS
Estimation of Alpha in SAS [2]

American Psychological Association (APA)

analysis, retaining factors for

Armanino, C.

B

Baker, F.B.

Barrett, P.

Quantifying Replicability in EFA
Quantifying Replicability in EFA [2]

Berge J.M.F.

Bernstein, I.

Bianchini, J.

Blanchard, M.R.

Bond, T.G.

Detection of Random Responding
What Are Modern Alternatives?

bootstrap resampling

aligning procedure for factor loadings

application of

bootstrapped CI

EFA and

exercises

generalizability

Heywood cases

methods of

rise of

traditional CI with ML extraction

uses for

Briggs, S.R.

BY statement

C

camps, methods within

CFA (confirmatory factor analysis)

Cheek, J.M.

CI

bootstrapped

interpretation of

Comfrey, A.L.

communalities

about

factor loadings and

confidence intervals, for alpha

confirmatory factor analysis (CFA)

constant responding, compared with random responding

CONVERGE option

convergence

CORR procedure

Estimation of Alpha in SAS
Estimation of Alpha in SAS [2]
Confidence Intervals for Alpha

Costa, P.T.

Costello, A.B.

An Empirical Investigation in Sample Size
An Applied Example from Costello & Osborne
An Applied Example from Costello & Osborne [2]
Application: Impact of Sample Size on Interpretation
Best Practices for EFA

COVARIANCE option

criteria, for factor extraction

criticality

Cronbach, L.J.

Cronbach's coefficient alpha

about

What Comes Next?
What Is Cronbach’s Alpha (And What Is It Not)?

application of

confidence intervals for

error-free measurement

estimating

exercises

factors influencing

good enough

sample size and

D

data

incomplete

missing

response sets in

unexpected patterns in

data cleaning

about

application of

as a step in EFA

exercises

importance of

imputation

incomplete data

missing data

nonrandom missingness

outliers

random vs. constant responding

DATA option

Application: Replication of Marsh SDQ Data
Bootstrapped CI

Davison, A.C.

Bootstrap Resampling Methods
Bootstrap Resampling Methods [2]

direct oblimin rotation

dissimulation

E

Edelen, M.O.

Educational and Psychological Measurement, Journal of Educational Psychology, Personality and Individual Differences, and Psychological Assessment

EFA

See exploratory factor analysis (EFA)

eigenvalues

about

variance and

EM (expectation-maximization) algorithm

Embretson, S.E.

engineering data

Does Extraction Method Matter?
How Do the Criteria Compare?
Mechanics of Performing Second-Order Factor Analysis

equamax rotation

error-free measurement

examples

extraction

instruments for extraction used in

sample size

exercises

bootstrap resampling

Cronbach's coefficient alpha

data cleaning

extraction

extraction criteria

factor scores

higher-order factors

replication

rotation

sample size

expectation-maximization (EM) algorithm

exploratory factor analysis (EFA)

about

basic syntax for

best practices for

bootstrap resampling and

compared with principal components analysis (PCA)

post

quantifying replicability in

replication and

steps for

external replication

extraction

about

concepts of

example syntax and output for

exercises

instruments used in examples

methods of

Steps to Follow When Conducting EFA
Does Extraction Method Matter?

pedagogical examples

techniques for

extraction criteria

about

comparing

example syntax and output

exercises

F

Fabrigar, L.R.

factor extraction, criteria for

factor loading

aligning procedure for

communalities and

factor matrices, interpretation of

FACTOR procedure

Basic Syntax for EFA
Key Concepts
Key Concepts [2]
Key Concepts [3]
Summary
How Do the Criteria Compare?
Types of Rotation
Types of Rotation [2]
Types of Rotation [3]
Types of Rotation [4]
Interpretation of Factor Matrices
Interpretation of Factor Matrices [2]
Interpretation of Factor Matrices [3]
Bootstrapped CI
Bootstrapped CI [2]
Bootstrapped CI [3]
Bootstrapped CI [4]
Generalizability and Heywood Cases
Application: Nonrandom Missingness and Imputation
Mechanics of Performing Second-Order Factor Analysis

factor scores

about

application of

estimating

exercises

modern alternatives to

proper vs. improper

stability of

syntax and output

FACTOR statement

Basic Syntax for EFA
Example Syntax and Output
Example Syntax and Output [2]
Exploring Multiple Solutions
Traditional CI with ML
Generalizability and Heywood Cases
Example Syntax and Output

factor weighting, methods of

factors

See also higher-order factors

retaining for analysis

second-order

Fan, X.

Fitzpatrick, D.C.

Quantifying Replicability in EFA
Quantifying Replicability in EFA [2]
Quantifying Replicability in EFA [3]
Application: Replication of Marsh SDQ Data

Ford, J.K.

Forina, M.

four-factor replication analysis

Fox, C.M.

Detection of Random Responding
What Are Modern Alternatives?

FREQ procedure

Two Types of Outliers in EFA
What Is Missing or Incomplete Data?

FUZZ option

Exploring Multiple Solutions
Application: Impact of Sample Size on Interpretation

G

GDS data

generalizability

Generalizability and Heywood Cases
Best Practices for EFA

geriatric depression scale data

GLMMIX procedure

Detection of Random Responding
Detection of Random Responding [2]

Gorusch, R.L.

Grice, J.W.

Guadagnoli, E.

An Empirical Investigation in Sample Size
An Empirical Investigation in Sample Size [2]
An Empirical Investigation in Sample Size [3]
An Applied Example from Costello & Osborne
Application: Impact of Sample Size on Interpretation

H

Harris extraction

Harris factoring

Hatcher L.

Henson, R.K.

Heywood cases

HEYWOOD option

higher-order factors

about

application of

exercises

initial solution and

performing second-order factor analysis

replication of second-order factors

Hinkley, D.V.

Bootstrap Resampling Methods
Bootstrap Resampling Methods [2]

Hunka, S.

I

image extraction

image factoring

IML procedure

improper factor scores

imputation

incomplete data

inter-item correlation

internal consistency

internal replication

IRT procedure

Detection of Random Responding
Detection of Random Responding [2]

item response theory (IRT)

Detection of Random Responding
Detection of Random Responding [2]
What Are Modern Alternatives?

iterated principal axis factoring (iterated PAF) extraction

Steps to Follow When Conducting EFA
Extraction Techniques

iterations

J

Jöreskog, K.G.

Published Guidelines
Summary

K

Kaiser Criterion

Basic Syntax for EFA
Extraction Criteria
Example Syntax and Output
How Do the Criteria Compare?
How Do the Criteria Compare? [2]
What Does Bootstrapping Look Like?
Mechanics of Performing Second-Order Factor Analysis

Kaiser, H.

Kuder Richardson Formula 20 (KR-20)

L

Lanteri, S.

Leardi, R.

Lee, H.B.

legitimate missing data

Lord, F.M.

Luo, S.

M

MacCallum, R.C.

Steps to Follow When Conducting EFA
Sample Size in Practice

malingering

MAP (minimum average partial) analysis

Extraction Criteria
Example Syntax and Output

Markov chain Monte Carlo (MCMC) simulation

Marsh SDQ data, replication of

Marsh's Self-Description Questionnaire

matrix of associations

maximum likelihood (ML) extraction

Steps to Follow When Conducting EFA
Extraction Techniques
Traditional CI with ML

MAXIT ER option

McCrae, R.R.

MCMC (Markov chain Monte Carlo) simulation

Meier, R.R.

METHOD option

Basic Syntax for EFA
Extraction Techniques
Does Extraction Method Matter?
Application: Replication of Marsh SDQ Data
Bootstrapped CI

methods

of bootstrap resampling

of factor weighting

rotation

within camps

MI procedure

Application: Nonrandom Missingness and Imputation
Application: Nonrandom Missingness and Imputation [2]

MIANALYZE procedure

minimum average partial (MAP) analysis

Extraction Criteria
Example Syntax and Output

minimum eigenvalue, as an extraction criteria

Extraction Criteria
Example Syntax and Output
How Do the Criteria Compare?

Minnesota Multiphasic Personality Inventory (MMPI-2)

missing data

What Is Missing or Incomplete Data?
Dealing with Missing Data
Best Practices for EFA

ML (maximum likelihood) extraction

Steps to Follow When Conducting EFA
Extraction Techniques

MMPI-2 (Minnesota Multiphasic Personality Inventory)

Monte Carlo methods

multidimensionality, influence on alpha of

N

negative item-total correlations

Neuhaus, J.O.

NFACTORS option

NHST (null statistical hypothesis testing)

NLMIXED procedure

Detection of Random Responding
Detection of Random Responding [2]

NODUPKEY option

nonrandom missingness

Novick, M.R.

null statistical hypothesis testing (NHST)

Nunnally, J.C.

O

O'Connor, B.P.

Example Syntax and Output
Example Syntax and Output [2]
Best Practices for EFA

oblique rotation, compared with orthogonal rotation

Orthogonal vs Oblique Rotation
Orthogonal vs Oblique

ODS (Output Delivery System)

orthogonal rotations

Types of Rotation
Orthogonal vs Oblique Rotation
Orthogonal vs Oblique

Osborne, J.W.

Sample Size in Practice
An Empirical Investigation in Sample Size
An Applied Example from Costello & Osborne
An Applied Example from Costello & Osborne [2]
An Applied Example from Costello & Osborne [3]
Application: Impact of Sample Size on Interpretation
Quantifying Replicability in EFA
Quantifying Replicability in EFA [2]
Quantifying Replicability in EFA [3]
Application: Replication of Marsh SDQ Data
What Can Bootstrap Resampling Do, and What Should It Not Be Used For?
What Can Bootstrap Resampling Do, and What Should It Not Be Used For? [2]
How Common Is Random Responding?
Best Practices for EFA

OUT option

Application: Replication of Marsh SDQ Data
Bootstrapped CI
Application: Factor Score Estimation
Application: Factor Score Estimation [2]

OUTHITS option

outliers

influence on alpha of

types of

output

examples for extraction criteria

extraction examples

factor scores

rotation examples

Output Delivery System (ODS)

OUTPUT statement

OUTSTAT option

Example Syntax and Output
Application: Factor Score Estimation

P

PAF (principal axis factoring) extraction

Steps to Follow When Conducting EFA
Extraction Techniques

parallel analysis, as an extraction criteria

Extraction Criteria
Example Syntax and Output
How Do the Criteria Compare?

pattern matrix

Interpretation of Factor Matrices
Interpretation of Factor Matrices [2]

patterns in data

PCA

See principal components analysis (PCA)

PCTLPTS option

PLOTS option

POWER option

Preacher, K.J.

PREROTATE option

principal axis factoring (PAF) extraction

Steps to Follow When Conducting EFA
Extraction Techniques

principal components analysis (PCA)

about

A Tool for Exploration
Best Practices for EFA

compared with exploratory factor analysis (EFA)

Prior Communality Estimates

PRIOR S = SMC option

PRIORS option

promax rotation

Types of Rotation
Methods within a Camp

proper factor scores

proportion of variance, as an extraction criteria

Extraction Criteria
Example Syntax and Output
How Do the Criteria Compare?
How Do the Criteria Compare? [2]

PROPORTION= option

Q

quartimax rotation

R

random responding

about

commonality of

compared with constant responding

detection of

influence on alpha of

Rao-Guttman method

Rasch measurement

Detection of Random Responding
What Are Modern Alternatives?

ratios, case for

Reeve, B.B.

reference structure matrix coefficients

Reise, S.P.

REORDER option

Exploring Multiple Solutions
Application: Impact of Sample Size on Interpretation
Application: Impact of Sample Size on Interpretation [2]

REP option

replicability analysis, procedural aspects of

replication

about

EFA and

exercises

importance of

of Marsh SDQ data

of second-order factors

procedural aspects of replicability analysis

quantifying replicability in EFA

resampling, rise of

response sets

in data

influence on alpha of

response styles, peculiar to educational testing

results

interpreting

replicating

reverse coded items

Roberts, J.K.

ROTATE option

Basic Syntax for EFA
Types of Rotation

rotation

about

example syntax and output

exercises

interpretation of factor matrices

methods of

multiple solutions

oblique

Orthogonal vs Oblique Rotation
Orthogonal vs Oblique

orthogonal

Types of Rotation
Orthogonal vs Oblique Rotation
Orthogonal vs Oblique

types of

rotation method

RUN statement

S

sample size

about

alpha and

applied example

empirical investigation in

exercises

impact on interpretation of

importance of

in practice

published guidelines for

SAMPRATE option

SCORE option

Example Syntax and Output
Application: Factor Score Estimation

SCREE option

Example Syntax and Output
Example Syntax and Output [2]
Example Syntax and Output [3]

scree plot, as an extraction criteria

Extraction Criteria
Example Syntax and Output
How Do the Criteria Compare?

second-order factors

analyzing

Mechanics of Performing Second-Order Factor Analysis
Mechanics of Performing Second-Order Factor Analysis [2]

replicating

SEED option

Application: Replication of Marsh SDQ Data
Bootstrapped CI

self-description questionnaire data

Does Extraction Method Matter?
How Do the Criteria Compare?

SEM (structural equation modeling)

What Are Modern Alternatives?
An Example with the Coefficient of Determination
Summary

SGPLOT procedure

simple correlation matrix

Smith, E.V.

Smith, R.M.

social desirability

Sörbom, D.

Published Guidelines
Summary

SORT procedure

Spearman, C.

A Tool for Exploration
EFA vs PCA

Stevens, J.P.

Strahan, E.J.

structural equation modeling (SEM)

What Are Modern Alternatives?
An Example with the Coefficient of Determination
Summary

structure matrix coefficients

SURVEYSELECT procedure

Application: Impact of Sample Size on Interpretation
Application: Replication of Marsh SDQ Data
Bootstrapped CI
Bootstrapped CI [2]
Bootstrapped CI [3]
Sample Size and the Precision of Alpha
Confidence Intervals for Alpha

syntax

examples for extraction criteria

extraction examples

factor scores

for EFA

rotation examples

T

TABLE statement

Tait, M.

Task Force on Statistical Inference

techniques, for extraction

theory, as an extraction criteria

Extraction Criteria
How Do the Criteria Compare?
How Do the Criteria Compare? [2]

Thompson, B.

The Magic of Rotation
Types of Rotation
Interpretation of Factor Matrices
Importance of Replication
Summary
Confidence Intervals for Alpha

three-factor replication analysis

traditional CI, with ML extraction

Tucker, L.R.

two-factor replication analysis

U

ULS (unweighted least squares) extraction

Steps to Follow When Conducting EFA
Extraction Techniques

ULTRAHEYWOOD option

Generalizability and Heywood Cases
Generalizability and Heywood Cases [2]

UNIVARIATE procedure

Bootstrapped CI
Bootstrapped CI [2]
An Aligning Procedure for Factor Loadings
What Does Bootstrapping Look Like?
Confidence Intervals for Alpha

unrotated factor matrix coefficients

unweighted least squares (ULS) extraction

Steps to Follow When Conducting EFA
Extraction Techniques

V

VAR statement

Basic Syntax for EFA
Basic Syntax for EFA [2]
Bootstrapped CI
Application: Nonrandom Missingness and Imputation
Estimation of Alpha in SAS

variable

variance, eigenvalues and

varimax rotation

Types of Rotation
Methods within a Camp

Velicer, W.F.

Extraction Criteria
An Empirical Investigation in Sample Size
An Empirical Investigation in Sample Size [2]
An Empirical Investigation in Sample Size [3]
An Applied Example from Costello & Osborne
Application: Impact of Sample Size on Interpretation

W

Wegener, D.T.

weighted linear combination

Widaman, K.F.

Wrigley, C.

Z

Zhang, G.