How to Write the CFA Section | Applied Linguistics

What is CFA?

Confirmatory Factor Analysis (CFA) tests whether your data fit a pre-specified measurement model (the factor structure suggested by theory or EFA). In practice, you estimate the model (e.g., in AMOS) and evaluate fit indices.

The report should be concise, but for learning, we need to understand the meaning behind every number.

Model Example (Publication Style)

Confirmatory Factor Analysis (CFA). CFA was conducted in AMOS to validate the three-factor measurement model derived from the EFA. The results indicated a good fit: χ²(132) = 227.61, p < .001; CMIN/DF = 1.724; RMSEA = .052 (90% CI [.040–.063], PCLOSE = .385); CFI = .969; TLI = .964; NFI = .930; GFI = .916. Parsimony indices (PNFI = .802; PCFI = .836) and information criteria (AIC = 305.61; BIC = 446.10) further supported model adequacy. Overall, the three-factor model demonstrated acceptable construct validity and an adequate fit to the data.

Fit Indices Explained

Fit Index	Value	Threshold	Explanation
χ²/df (CMIN/DF)	1.724	< 3 good < 5 acceptable	Chi-square Minimum Discrepancy. Adjusts for complexity. Lower is better.
RMSEA (90% CI)	.052 (.040–.063)	≤ .06 good ≤ .08 acceptable	Root Mean Square Error. Measures misfit. PCLOSE > .05 is desirable.
CFI	.969	≥ .95 good	Comparative Fit Index. Values close to 1 are excellent.
TLI	.964	≥ .95 good ≥ .90 acceptable	Tucker-Lewis Index. Adjusts for complexity. Near 1 is ideal.
NFI	.930	≥ .90 acceptable	Normed Fit Index. An older metric, but still commonly reported.
GFI	.916	≥ .90 acceptable	Goodness-of-Fit Index. Variance explained by the model.
AIC / BIC	305.61 / 446.10	Lower = Better	Information criteria used to compare models (Model A vs Model B).

Use this table for learning. In a journal, report only key indices (e.g., χ²/df, RMSEA, CFI, TLI).

Good Fit Template

Confirmatory Factor Analysis (CFA). CFA was conducted in AMOS to validate the [k]-factor measurement model derived from the EFA. The results indicated a good fit: χ²([df]) = [value], p < .001; CMIN/DF = [x.xx]; RMSEA = [.xx] (90% CI [.xx–.xx], PCLOSE = [value]); CFI = [.xxx]; TLI = [.xxx]; NFI = [.xxx]; GFI = [.xxx]. Parsimony indices (PNFI = [.xxx]; PCFI = [.xxx]) and information criteria (AIC = [value]; BIC = [value]) further supported model adequacy. Overall, the model demonstrated excellent construct validity and a strong fit to the data.

Acceptable Fit Template

Confirmatory Factor Analysis (CFA). CFA was conducted in AMOS to validate the [k]-factor measurement model derived from the EFA. The results indicated an acceptable fit: χ²([df]) = [value], p < .001; CMIN/DF = [x.xx]; RMSEA = [.xx] (90% CI [.xx–.xx], PCLOSE = [value]); CFI = [.xxx]; TLI = [.xxx]; NFI = [.xxx]; GFI = [.xxx]. Although some indices were slightly below recommended thresholds, parsimony indices (PNFI = [.xxx]; PCFI = [.xxx]) and relative criteria (AIC = [value]; BIC = [value]) supported overall adequacy. The model demonstrated reasonable construct validity but may benefit from refinement in future studies.

Poor Fit Template

Confirmatory Factor Analysis (CFA). CFA was conducted in AMOS to validate the [k]-factor measurement model derived from the EFA. The results indicated a poor fit: χ²([df]) = [value], p < .001; CMIN/DF = [x.xx]; RMSEA = [.xx] (90% CI [.xx–.xx], PCLOSE = [value]); CFI = [.xxx]; TLI = [.xxx]; NFI = [.xxx]; GFI = [.xxx]. Most indices fell below recommended thresholds, suggesting that the measurement model did not adequately capture the data structure. Model refinement is strongly recommended (e.g., reviewing item loadings, modification indices, and theoretical alignment) before proceeding with structural analyses.