潜变量交互效应模型标准化估计中的检验问题

讨论了潜变量交互效应模型是否能直接用统计软件输出的原始估计的t值对模型的标准化估计进行检验的问题,详细介绍了标准化估计的t值计算及其难点,用Bootstrap方法算出标准化估计的标准误和相应的t值（记为t_bs）,并将其与原始估计的t值比较.结果发现,当原始估计t值超过3时,无论用t值还是用t_ bs检验,结果都是显著,即可以使用t值进行检验.而当t值不超过3时,与t_bs很接近,也可以用t值检验,但t值在临界值附近（例如1.5 ～2.5）时,最好还是使用Bootstrap法计算t_bs进行检验.

Testing the Standardized Solutions in Structural Equation Models with Interaction Effects

It is well known that common statistical software does not provide standard errors and t - values of usual standardized estimates. For structural equation models （SEM） without interaction effects, when a parameter estimate and its standard error estimate are both rescaled by the same rescaling, the corresponding t - statistic for evaluating the significance of the parameter will not change because of the simultaneous canceling in the rescaling process （HCudeek, 1989H ）. Thus, the significance of the standardized parameter estimates can be determined by examining the t - values of the original parameter estimates instead. For SEM with interaction models, however, the scale - free property of the t - values of original solutions has not been proved. Could the appropriate standardized parameter estimates （Wen, Marsh, ＆ Hau ,2010 ）be tested by using the t - values of original solutions given by SEM software？ In this paper, we applied Bootstrap method to calculate the standard errors of the appropriate standardized parameter estimates and related t - values, which was compared with the t - values of original solutions. Results show that the testing of the significance of the appropriate standardized parameter estimates in models with interaction effects is analogous to that in models without interaction effects—— determined by examining the t - values of the original solutions. However, if the t - values of original solutions lie in the border area of cutoff point of t - value （ 1.5 - 2.5 ）, the bootstrap method was recommended to be used to calculate t - values of the appropriate standardized estimates for testing.