Abstract
In this simulation study we designed 6 sample-size conditions, 6 factor-loading conditions, 4 rating-category conditions, and 2 distribution conditions. To each data-set in the conditions a correct model and a mis-specified model are fitted. In the correct model there are 15 items and 3 factors, each factor is measured by 5 items. While in the mis-specified model the factors are measured by 6, 4, and 5 items, we call the mis-specified model wrong-parameterized model, which is different from those studied by former researchers.
The results are: 1) Sample size, loading size, rating category and distribution form all have influence on the values of fit indices. And the influence of distribution form is the largest. The values of NNFI, IFI are most stable across all conditions, values of CFI, RMSEA and SRMR are less stable, but their variations are rather small, these 5 indices should be recommended. 2) In normal distribution conditions, when sample size ≥ 1000, model right-wrong judgment based on NNFI, IFI, CFI, RMSEA, SRMR all have low two type error (α + β) rate. But distribution forms are non-normal and when sample size <1000, α + β error rate cannot be reduced to satisfactory level. 3) 2-indices strategy recommended by Hu & Bentler (1999) cannot reduce α + β error rate significantly in many conditions. 4) Since model judgment is difficult when samples are small and distributions are non-normal, we present 2-cutoff-value strategy. 2-cutoff-value strategy means, when the value of a model is lower than the low bound cut-off of the recommended indices, the model can be judged as wrong, when the value of a model is higher than the upper bound cut-off of the recommended indices, the model can be judged as right, when the value of a model fall between lower and upper bound of the recommended indices, the model cannot be judged as right or wrong. When a model cannot be judged as right or wrong, larger sample size and cross-validation of the model are needed before a clear conclusion can be drawn.
| Keywords: | Structural Equation Modeling; model-data fit; 2-indice strategy; 2-cutoff-value strategy |
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