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: What is the df of the baseline model in the above example?
12
In this CFA there are six observed indicators, so the sample covariance matrix contains 6(6+1)/2 = 21 unique elements. The baseline (null) model specified in this SEM analysis fixes the between-indicator covariances and estimates the observed variances together with the marker constraints used for scaling.
Under the parameterisation adopted here, the baseline model estimates nine parameters, leaving degrees of freedom equal to 21 - 9 = 12. This matches the very large baseline chi-square of 1312 against which the nested M1, M2 and M3 models are compared for incremental fit.
Hence, the df of the baseline model in the given example is 12.
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