Is a model accepted in a small sample really better than a model rejected in a large sample?

1.本项目采用探索性因子分析模型。在因子分析中，一个合适的模型往往会在大样本中被拒之门外，然后通常会增加因素的数量。结果，得到了一个不适当的解。这个项目的最终目的是讨论当出现这样的问题时，是否应该采用被拒绝的模式。为此，我们需要研究解决不当的原因。这个项目在这方面的一个成果是提出如何确定不适当解决方案的原因，并在许多真实的例子中发现它是有用的。这一成果是在1998年在罗密欧举行的IFCS1998会议上作为特邀讲座提出的。在因子分析中拒绝一个合适的模型的一个可能的原因是包括了一个与所考虑的模型不一致的变量。我们建议了一种新的方法来识别关于拟合优度的不一致变量。这项研究结果将发表在国际心理测量学杂志《心理学》上。变量选择的新方法是使用Java编程的，并以网页的形式向公众开放。我们将该计划称为SEFA.4。我们在1999年日本心理学会年会上举办了一次关于SEFA的研讨会，通过将该计划应用于面向统计的研究的各个领域来讨论该计划的有用性。描述了变量增量法和变量消去法。结果表明，变量消去法对于探索性研究是有用的，而变量增量法对于研究中有一些重要变量无法消除的情况是重要的。

1. In this project, exploratory factor analysis model is considered. A suitable model is often rejected in a large sample in factor analysis, and then one usually increases in the number of factors. As a result, an improper solution is obtained. The ultimate aim of this project is to discuss whether the model rejected should be adopted in case when such a problem arises. For this we need to study causes of the improper solution. One fruit of this project on this respect is to suggest how to identify the cause of an improper solution and to find it useful in many real examples. This result was presented as an invited lecture at the IFCS1998 conference at Rome.2. One possible cause of rejecting a suitable model in factor analysis is to include an variable inconsistent with the model considered. We suggest a new way of identifying an inconsistent variable with respect to a measure of goodness-of-fit. The result will be published in Psychometrika, an international journal on psychometrics.3. The new way of the variable selection was programmed using JAVA and was open to public as a Web Page. We refer to the program as SEFA.4. We held a workshop on SEFA in the annual meeting of the Japanese Psychological Society in 1999 to discuss usefulness of the program through applications to various fields of statistical oriented studies. Both a variable augmentation method and variable elimination method are described. It was shown that the variable elimination method is useful for exploratory purpose while the variable augmentation method is important for the case where there are some important variables that can not be eliminated in the research.