不同条件下拟合指数的表现及临界值的选择

在本模拟研究中设计了6种样本容量，6种因子载荷，和4种评分等级，并考察了正态和非正态分布两种情况。采用的错误模型为参数误置（真模型中每个因子各由5个题目来测量，错误模型中则是第一个因子由6个题测量，另两个因子各由4个和5个题来测量，即有一个因子载荷被误置）模型。结果发现（1）样本量、载荷量、评分等级数和分布形态都对GOF的取值确有影响。其中分布形态的影响最大。NNFI、IFI在不同条件下的平均值是最稳定的，其次是CFI、RMSEA和SRMR。它们都算是值得推荐的GOF，尤其是NNFI和IFI。（2）在正态分布中，当样本量≥1000时，根据NNFI、IFI、CFI、RMSEA、SRMR对模型是否拟合做出判断时有很低的两类错误率，在样本量<1000时则不理想。在偏态条件下无论选择哪个GOF两类错误率都很高。（3）采用2指数策略在很多情况下也不能显著降低两类错误率。（4）由于在数据分布非正态，或正态但样本量<1000时是难判断模型是否拟合的。因此我们提出了2界值策略。即为每个GOF确定上下两个界值。低于下界值时可判断模型是不正确的，而高于上界值时则可判断模型是正确的。GOF取值处于上下界值之间时难以判断模型是否拟合，只能说越高拟合的可能性越大。这时就要通过跨样本验证和增加样本量来确定模型是否正确

Performance of Fit Indices in Different Conditions and the Selection of Cut - off Values

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&;#65380;IFI are most stable across all conditions, values of CFI&;#65380;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&;#65380;IFI&;#65380;CFI&;#65380;RMSEA&;#65380;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.