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

1. 本课题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，然后一个模型通常会增加因子的数量。结果，得到了一个不正确的解。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型。为此我们需要研究解决方法不当的原因。在这方面，本项目的一个成果是建议如何确定不适当解决方案的原因，并在许多实际示例中发现它很有用。这一结果在罗马举行的IFCS1998会议上作为特邀演讲提出。在因子分析中拒绝合适模型的一个可能原因是包含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识别一个不一致的变量相对于拟合优度的措施。该研究结果将发表在国际心理测量学期刊Psychometrika上。这种新的变量选择方法是用JAVA编写的，并作为Web页面向公众开放。我们把这个项目称为SEFA.4。1999年，我们在日本心理学会年会上举办了一个关于SEFA的研讨会，讨论了该计划在统计导向研究的各个领域中的应用。描述了一种变量增广法和变量消去法。结果表明，变量消去法在探索性研究中是有用的，而变量增值法在研究中有一些重要变量无法消除的情况下是重要的。

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.