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

1.本研究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在大样本中被拒绝，然后通常会增加因子的数量。结果，得到不适当的解。本项目的最终目的是讨论在出现此类问题时，是否应采用被拒绝的模型。为此，我们需要研究解决方案不当的原因。这个项目在这方面的一个成果是建议如何识别不正确的解决方案的原因，并发现它在许多真实的例子中是有用的。这一结果已作为特邀演讲在2002年2月举行的IFCS 1998会议上发表。在因子分析中拒绝合适的模型的一个可能原因是包括与所考虑的模型不一致的变量。我们提出了一种新的方法来确定一个不一致的变量的拟合优度的措施。研究结果将发表在国际心理测量学期刊《心理测量学》上。用JAVA语言编写了变量选择的新方法，并以网页形式向公众开放。我们称该方案为SEFA。我们在1999年日本心理学会年会上举办了SEFA研讨会，讨论该计划在统计研究的各个领域的应用。本文介绍了一种变量增广法和一种变量消去法。结果表明，变量剔除法适用于探索性研究，而变量增广法适用于研究中存在重要变量无法剔除的情况。

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.