Wu Wei, West Stephen G
a University of Kansas.
b Arizona State University.
Multivariate Behav Res. 2010 May 28;45(3):420-52. doi: 10.1080/00273171.2010.483378.
This study investigated the sensitivity of fit indices to model misspecification in within-individual covariance structure, between-individual covariance structure, and marginal mean structure in growth curve models. Five commonly used fit indices were examined, including the likelihood ratio test statistic, root mean square error of approximation, standardized root mean square residual, comparative fit index, and Tucker-Lewis Index. The fit indices were found to have differential sensitivity to different types of misspecification in either the mean or covariance structures with severity of misspecification controlled. No fit index was always more (or less) sensitive to misspecification in the marginal mean structure relative to those in the covariance structure. Specifying the covariance structure to be saturated can substantially improve the sensitivity of fit indices to misspecification in the marginal mean structure; this result might help identify the sources of specification error in a growth curve model. An empirical example of children's growth in math achievement ( Wu, West, & Hughes, 2008 ) was used to illustrate the results.
本研究调查了拟合指数对增长曲线模型中个体内协方差结构、个体间协方差结构和边际均值结构模型误设的敏感性。研究考察了五个常用的拟合指数，包括似然比检验统计量、近似均方根误差、标准化均方根残差、比较拟合指数和塔克-刘易斯指数。在控制误设严重程度的情况下，发现拟合指数对均值或协方差结构中不同类型的误设具有不同的敏感性。相对于协方差结构中的误设，没有一个拟合指数对边际均值结构中的误设总是更敏感（或更不敏感）。将协方差结构指定为饱和结构可以显著提高拟合指数对边际均值结构中误设的敏感性；这一结果可能有助于识别增长曲线模型中设定误差的来源。使用一个儿童数学成绩增长的实证例子（Wu、West和Hughes，2008）来说明结果。
