Read the paragraph below and answer the questions that follow. A researcher carried out SEM-based confirmatory factor analysis (CFA) of six indicators on a sample of 500 respondents. Three indicators measure altruism and three measure trust. The ML estimates are obtained. The baseline model has chi-square of 1312 (p < .001). She tested three models: The chi-square for M1, M2 and M3 are 230 (p < .01), 120 (p < .01) and 65 (p < .01) respectively. The GFI for M1, M2 and M3 are 0.81, 0.90 and 0.95 and the AGFI are 0.71, 0.85 and 0.91 respectively. The Root Mean Square Residual is 0.21, 0.09 and 0.04 respectively for M1, M2 and M3, with phi = 0.54 for M3.
Question: Which model is the best fit in the above example?
Only M3
Model fit in CFA improves as chi-square decreases, GFI and AGFI approach 1, and the Root Mean Square Residual approaches 0. Comparing the three models, M3 has the smallest chi-square (65), the highest GFI (0.95), the highest AGFI (0.91) and the lowest RMR (0.04).
M1 (unifactor) shows the poorest fit on every index, and M2 (two orthogonal factors) improves fit but is still clearly inferior to M3. The oblique specification of M3, with phi = 0.54, better represents the substantive correlation between trust and altruism.
Hence, the best-fitting model is Only M3.
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