基于主成分因素分析法的展开型数据单维性检验研究

The Study on Test of Unfolding Data′s Unidimensionality Based on the Principal Factor Analysis

以拓广的等级展开模型(GGUM)模拟6种情形下的展开型数据,使用主成分因素分析法检验展开型数据的单维性.研究发现:在项目位置参数服从均匀分布且被试特质同质性较强的情形下,前2个因子的特征值比(E_(1)/E_(2))小于3,其余情形的比值均大于3;当被试样本特质同质性较弱时,特征值大于1的因子有3个,其余情形的因子有2个;当测验项目位置参数服从两端分布时,项目2因素负荷图呈“括号”形;当测验项目位置参数服从均匀分布时,项目2因素负荷图呈“马蹄”形.研究结果表明:能力反应数据单维性的检验标准并不适用于展开型数据,当从因子特征值比、项目负荷图判定展开型数据的单维性时,应考虑项目位置参数分布特点和被试样本特质的同质性程度.

The six different types of unfolding data are simulated based on the generalized graded unfolding model(GGUM)and the results of factor analysis(FA)based on using component analysis are investigated.The results show that ratio of the first eigenvalue to the second eigenvalue is less than 3 when items′locative parameters distribute uniformly and the hemogeneity of sample is strong,the ratio is more than 3 in other cases.When the heterogeneity of sample is strong,the number of factors whose eigenvalues are more than 1 is 3,the number is 2 in other cases.When items′locative parameters distribute in both ends,the shape of items′loading in two factors is a parenthese.In another case,the shape is a horseshoe.The result shows that the current testing standards about unidimensionality of unfolding data by the factor analysis(FA)are not comprehensive,the results of FA,including eigenvalue ratio of the first two factors and item loding′s figure,shall be related with item′s locative parameter and the hemogeneity of subjects.