On the likelihood ratio test in structural equation modeling when parameters are subject to boundary constraints
On the likelihood ratio test in structural equation modeling when parameters are subject to boundary constraints
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DOI：
10.1037/1082-989x.11.4.439
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发表时间：
2006-12-01
影响因子：
7
通讯作者：
van den Wittenboer, Godfried
中科院分区：
文献类型：
--
作者：
Stoel, Reinoud D.;Garre, Francisca Galindo;van den Wittenboer, Godfried
作者展示了如何使用不等式约束的结构方程模型中的参数可能会影响分布的似然比检验。不平等约束隐含地用于检验常用的结构方程模型，如共同因素模型、自回归模型和潜在增长曲线模型，尽管这一点并不被普遍承认。这样的约束是零假设的结果，其中参数值被放置在参数空间的边界上。例如，这发生在测试生长参数的方差是否显著不同于0时。它表明，在这些情况下，卡方差的渐近分布不能被视为一个中心卡方分布的随机变量的自由度等于约束的数量。对于上述3个结构方程模型，推断出一次测试1个或几个参数的正确分布。随后，作者描述并说明了获得该分布应采取的步骤。一个重要的信息是，使用正确的分布可能会带来明显更大的统计功效。
The authors show how the use of inequality constraints on parameters in structural equation models may affect the distribution of the likelihood ratio test. Inequality constraints are implicitly used in the testing of commonly applied structural equation models, such as the common factor model, the autoregressive model, and the latent growth curve model, although this is not commonly acknowledged. Such constraints are the result of the null hypothesis in which the parameter value or values are placed on the boundary of the parameter space. For instance, this occurs in testing whether the variance of a growth parameter is significantly different from 0. It is shown that in these cases, the asymptotic distribution of the chi-square difference cannot be treated as that of a central chi-square-distributed random variable with degrees of freedom equal to the number of constraints. The correct distribution for testing 1 or a few parameters at a time is inferred for the 3 structural equation models mentioned above. Subsequently, the authors describe and illustrate the steps that one should take to obtain this distribution. An important message is that using the correct distribution may lead to appreciably greater statistical power.