Lecture 5 (ALT 2): Confirmatory Factor Analysis & Structural Equation Modelling

Question 1

What is Confirmatory Factor Analysis (CFA) situated within?

Answer 1

CFA is situated within the broader framework of Structural Equation Modelling (SEM).

Question 2

What does SEM model in psychological research?

Answer 2

SEM models networks of constructs to data by explicitly modelling both latent (unobserved) and observed (measured) variables.

Question 3

Which standard statistical techniques are subsumed by SEM?

Answer 3

Regression, moderation, mediation, ANOVA, multilevel modelling, and CFA.

Question 4

What do circles/ovals and boxes represent in SEM diagrams?

Answer 4

• Circles/ovals represent latent variables;
• boxes represent observed variables.

Question 5

In SEM diagrams, what do single-headed and double-headed arrows represent?

Answer 5

Single-headed arrows suggest causal paths; double-headed arrows represent correlations.

Question 6

What are the two main components of SEM?

Answer 6

The measurement model and the structural model.

Question 7

What does the measurement model describe in SEM?

Answer 7

It describes how latent constructs are indicated by observed variables (i.e. CFA).

Question 8

What does the structural model specify in SEM?

Answer 8

It specifies the hypothesised causal relations among latent variables (i.e. path analysis).

Question 9

How does CFA differ from EFA in terms of theoretical orientation?

Answer 9

CFA is theory-driven, whereas EFA is data-driven.

Question 10

What does EFA do with all factor loadings regardless of size?

Answer 10

EFA computes and represents all loadings in the model, even if they are low or theoretically uninteresting.

Question 11

How does CFA test specific hypotheses about factor structure?

Answer 11

By constraining certain loadings to zero based on theory.

Question 12

What is the goal of CFA’s model constraints?

Answer 12

To create a parsimonious model that better reflects theoretically meaningful relationships while accounting for observed covariances.

Question 13

What allows researchers to test whether a hypothesised factor structure holds in the data in CFA?

Answer 13

Imposing constraints (e.g., fixed to zero) on parameters such as cross-loadings or factor correlations.

Question 14

How can EFA and CFA be used together?

Answer 14

By conducting exploratory analysis with EFA and then confirmatory analysis with CFA on split samples or separate datasets.

Question 15

What are the steps in specifying a CFA model?

Answer 15

Checking assumptions, defining the number of factors, specifying which indicators load on which factors, determining whether factors are correlated, and identifying the most important aspects of the data.

Question 16

In CFA, what are free parameters?

Answer 16

Parameters estimated from the data (e.g., primary factor loadings).

Question 17

In CFA, what are fixed parameters?

Answer 17

Parameters constrained based on theory (e.g., cross-loadings set to zero).

Question 18

What does the chi-square test evaluate in CFA?

Answer 18

How well the predicted variance-covariance matrix matches the observed matrix.

Question 19

Why is the chi-square test commonly adjusted in CFA?

Answer 19

It is sensitive to large sample sizes and commonly adjusted using the χ²/df ratio.

Question 20

What is considered an acceptable value for χ²/df ratio?

Answer 20

Less than 2.

Question 21

What do absolute and relative fit indices assess in CFA?

Answer 21

How well the model explains the data, typically compared against a baseline zero-correlation model.

Question 22

What values are considered good for fit indices like CFI or GFI?

Answer 22

Values greater than .95.

Question 23

What do residual fit indices like RMSEA and SRMR measure?

Answer 23

How much variance is left unexplained.

Question 24

What values are considered good for RMSEA and SRMR?

Answer 24

RMSEA < .06 and SRMR < .08.

Question 25

Why must model fit be evaluated with respect to parsimony?

Answer 25

To determine what aspects of the data can be ignored without loss of explanatory power.

Question 26

Does good model fit imply model correctness in CFA?

Answer 26

No, multiple models may fit the data equally well.

Question 27

What are nested models in CFA?

Answer 27

Models that can be converted into one another by constraining or freeing specific parameters.

Question 28

How are nested models compared in CFA?

Answer 28

Using chi-square difference testing to evaluate whether added complexity significantly improves model fit.

Question 29

What criterion is used to compare non-nested models in CFA?

Answer 29

Akaike’s Information Criterion (AIC).

Question 30

What does the AIC balance when comparing models?

Answer 30

Quality of fit against relative parsimony.

Question 31

When comparing nested models, what does a non-significant chi-square difference indicate?

Answer 31

The simpler model is not significantly worse and should be chosen for parsimony.

Question 32

What does model misspecification suggest in CFA?

Answer 32

That certain constraints are inappropriate.

Question 33

Why must post hoc model modifications be transparently reported in CFA?

Answer 33

To avoid data dredging or HARKing (hypothesising after results are known).

Question 34

What is the minimum recommended sample size in CFA?

Answer 34

5–10 participants per estimated parameter, ideally more than 10.

Question 35

What does CFA output allow researchers to test?

Answer 35

Direct hypothesis testing regarding the structure of psychological constructs.

Question 36

What does SEM allow researchers to examine beyond CFA?

Answer 36

Direct and indirect effects among latent variables through path analysis.

Question 37

What kinds of designs can SEM support?

Answer 37

Cross-sectional, longitudinal, and experimental designs.

Question 38

What are SEM’s major strengths?

Answer 38

Ability to model complex, theory-driven hypotheses, decomposition of measurement error, enhanced statistical power, and support for multiple data types and designs.

Question 39

What are the challenges of using SEM?

Answer 39

It is computationally intensive and methodologically complex, requiring substantial expertise.

Question 40

What is the trade-off of using CFA over EFA?

Answer 40

Increased complexity in exchange for greater interpretive clarity, stronger inferences, and more powerful insights.

Question 41

What is an example of SEM application in behavioural genetics?

Answer 41

Biometrical modelling using twin data to separate genetic from environmental contributions.

Question 42

What type of SEM model can test causal directionality in longitudinal data?

Answer 42

Longitudinal cross-lagged models.

Question 43

What psychological example illustrates causal testing with SEM?

Answer 43

Examining whether procrastination leads to guilt more than vice versa.

Question 44

What is the convention regarding the reporting of model fit indices in CFA?

Answer 44

At least two types of fit statistics should be reported.

Question 45

What do free parameters represent in CFA?

Answer 45

Parameters estimated from the data, such as primary factor loadings.

Question 46

What do fixed parameters represent in CFA?

Answer 46

Parameters constrained based on theory, such as cross-loadings set to zero.

Question 47

What does model misspecification in CFA often indicate?

Answer 47

That certain constraints, such as disallowing factor correlations or cross-loadings, are inappropriate.

Question 48

What are examples of inappropriate constraints that may cause poor model fit in CFA?

Answer 48

Disallowing factor correlations or cross-loadings that are supported by the data.

Question 49

Why must post hoc model modifications be transparently reported in CFA?

Answer 49

To avoid data dredging or HARKing (hypothesising after results are known).

Question 50

What is meant by ‘data dredging’ in the context of CFA?

Answer 50

Exploring data post hoc to find patterns without theoretical justification.

Question 51

What does HARKing stand for in psychological research?

Answer 51

Hypothesising After Results are Known.

Question 52

What are the full terms for the residual fit indices RMSEA and SRMR?

Answer 52

Root Mean Square Error of Approximation (RMSEA) and Standardised Root Mean Square Residual (SRMR).

Question 53

What is the central philosophical justification for using CFA over EFA?

Answer 53

CFA provides a principled, hypothesis-testing framework for understanding latent psychological constructs.

Question 54

According to the summary, what is the main benefit of CFA despite its complexity?

Answer 54

It allows for greater interpretive clarity, stronger inferences, and more powerful insights compared to data-driven approaches like EFA.

Question 55

What is the trade-off involved in using CFA within SEM?

Answer 55

Increased complexity in exchange for theoretical precision and methodological transparency.