Evaluation of model fit in nonlinear multilevel structural equation modeling
Evaluation of model fit in nonlinear multilevel structural equation modeling
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DOI：
10.3389/fpsyg.2014.00181
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发表时间：
2014-03-04
影响因子：
3.8
通讯作者：
Klein, Andreas G.
中科院分区：
文献类型：
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作者：
Schermelleh-Engel, Karin;Kerwer, Martin;Klein, Andreas G.
由于没有足够的检验统计量，评估非线性多级结构方程模型 (MSEM) 中的模型拟合提出了挑战。尽管如此，使用乘积指标方法提供了线性模型的似然比检验，这对于非线性 MSEM 也可能有用。非线性模型的主要问题是产品变量是非正态分布的。尽管已经为线性 SEM 开发了稳健的检验统计数据以确保非正态条件下的有效结果，但尚未对非线性 MSEM 进行研究。在蒙特卡罗研究中，使用无约束乘积指标方法研究了具有单水平潜在交互效应的模型的鲁棒似然比检验的性能。由于整体模型拟合评估在检测单个级别的不拟合（即使对于线性模型）时也存在潜在限制，因此还使用部分饱和模型研究了特定级别的模型拟合评估。考虑了四种群体模型：在两个水平上都有交互作用的模型、在组内水平上有交互作用的模型、在组间水平上有交互作用的模型以及在两个水平上都没有交互作用的模型。对于这些模型，组数、预测相关性和模型错误指定各不相同。结果表明稳健检验统计量表现得足够好。证明了用于检测模型失配的特定级别模型拟合评估的优点。
Evaluating model fit in nonlinear multilevel structural equation models (MSEM) presents a challenge as no adequate test statistic is available. Nevertheless, using a product indicator approach a likelihood ratio test for linear models is provided which may also be useful for nonlinear MSEM. The main problem with nonlinear models is that product variables are non-normally distributed. Although robust test statistics have been developed for linear SEM to ensure valid results under the condition of non-normality, they have not yet been investigated for nonlinear MSEM. In a Monte Carlo study, the performance of the robust likelihood ratio test was investigated for models with single-level latent interaction effects using the unconstrained product indicator approach. As overall model fit evaluation has a potential limitation in detecting the lack of fit at a single level even for linear models, level-specific model fit evaluation was also investigated using partially saturated models. Four population models were considered: a model with interaction effects at both levels, an interaction effect at the within-group level, an interaction effect at the between-group level, and a model with no interaction effects at both levels. For these models the number of groups, predictor correlation, and model misspecification was varied. The results indicate that the robust test statistic performed sufficiently well. Advantages of level-specific model fit evaluation for the detection of model misfit are demonstrated.