Questions: Confirmatory Factor Analysis and Measurement Validation
3 questions to test your understanding
Score: 0 / 3
Question 1 Multiple Choice
A researcher specifies a CFA model in which all six items on a depression scale load onto a single latent factor. The model returns CFI = 0.96 and RMSEA = 0.05. What does this primarily indicate?
AThe depression items are uncorrelated with each other
BThe hypothesized one-factor structure fits the data well
CThe scale measures depression better than any alternative scale
DThe factor loadings are all statistically significant
CFI close to 1.0 and RMSEA below 0.06 are conventional thresholds indicating the pre-specified model fits the observed covariance structure well. Good fit means the proposed factor structure is plausible — it does not speak to item correlations, comparative validity, or individual loading significance.
Question 2 True / False
A CFA model with CFI = 0.97 and RMSEA = 0.04 is sufficient evidence to conclude that a scale validly measures the intended construct.
TTrue
FFalse
Answer: False
Good model fit is necessary but not sufficient for construct validity. Fit indices only evaluate whether the factor structure matches the data's covariance pattern — they say nothing about whether the latent factor actually corresponds to the intended real-world construct. External validity evidence (convergent, discriminant, criterion-related) is still required.
Question 3 Short Answer
What is the fundamental difference between exploratory factor analysis (EFA) and confirmatory factor analysis (CFA)?
Think about your answer, then reveal below.
Model answer: EFA discovers factor structure from data without prior specification; CFA tests whether data fit a theoretically pre-specified factor structure.
In EFA, the researcher lets the analysis determine how many factors exist and which items load on which factors. In CFA, the researcher specifies the number of factors, which items load on each factor, and (often) which cross-loadings are constrained to zero — then tests whether this theory-driven model fits the observed covariance matrix. CFA is hypothesis-testing; EFA is hypothesis-generating.