New developments in penalized optimal scoring

惩罚性最优评分的新进展

• 批准号: 16500180
• 负责人: ADACHI Kohei
• 金额: $ 1.73万
• 依托单位: Osaka University (2005)Ritsumeikan University (2004)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2004
• 资助国家: 日本
• 起止时间: 2004 至 2005
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-16500180/
• 关键词: Multivariate analysis; Optimal scaling; Penalty functions; Principal component analysis; Spline functions; Nonlinear correlation; Transition trends; Cross-validation; 数量化法; 多重対応分析; カテゴリカルデータ; トレンド・ベクトル

In optimal scoring, also known as multiple correspondence analysis and homogeneity analysis, multivariate categorical data is analyzed and optimal scores are assigned to categories and individuals. In this study, we extend the optimal scoring and developed (A) a method for graphically representing inter-variable nonlinear relationships and (B) a method for representing transition trends of individuals by vectors. In both (A) and (B), an objective function to be minimized is defined as combing the loss function of the existing optimal scoring and a penalty function. Next, we detailed the studies on (A) and (B).(A)We developed a method for representing variables by nonlinear trajectories in a low-dimensional configuration. In this method, the values on quantitative variables are regarded as nominal categories to be given optimal coordinates, and the trajectories connecting the coordinates are defined as natural cubic spline functions. The penalty function expresses the loss of the smoothness of trajectories, and the penalty weight is chosen by a cross-validation procedure. Simulation study and real data analysis shows that the above method represents inter-variable nonlinear relations better than the existing optimal scoring and principal component analysis.(B)We proposed a method for analyzing transition frequency tables and representing transition trends by vectors in a low-dimensional configuration. This method finds scores of individuals, those of categories, and vectors for trends, in such a way that individuals' scores become homogeneous to the scores of chosen categories and trend vectors become homogeneous to the inter-occasion changes in individuals' scores. The applications to real data show that the resulting configurations of trend vectors allow us easily to grasp trends. Further, this method is extended to treat movers and stayers differently.

在最佳评分中，也称为多重对应分析和同质性分析，分析多变量分类数据，并将最佳得分分配给类别和个体。在这项研究中，我们扩展了最佳评分，并开发了（A）一种方法，以图形方式表示变量间的非线性关系和（B）的方法表示的过渡趋势的个人的向量。在（A）和（B）中，将待最小化的目标函数定义为组合现有最优评分的损失函数和惩罚函数。接下来，我们详细介绍了（A）和（B）的研究。(A)We开发了一种方法来表示变量的非线性轨迹在低维配置。该方法将定量变量上的值作为名义范畴，给出最优坐标，将连接坐标的轨迹定义为自然三次样条函数。惩罚函数表示轨迹的平滑性损失，并且通过交叉验证过程来选择惩罚权重。仿真研究和真实的数据分析表明，该方法比现有的最优评分法和主成分分析法更能反映变量间的非线性关系。(B)We提出了一种在低维结构下分析变迁频率表和用向量表示变迁趋势的方法。该方法找到个人的分数、类别的分数和趋势向量，以这样的方式，个人的分数变得与所选择的类别的分数同质，并且趋势向量变得与个人分数的跨场合变化同质。对真实的数据的应用表明，所得到的趋势向量的配置使我们能够很容易地把握趋势。此外，这种方法被扩展到区别对待搬家者和住宿者。

项目成果

対応分析と多重対応分析と同時対応分析

对应分析、多重对应分析、同时对应分析

• 发表时间: 2004
• 期刊: 心理学評論 46・4
• 作者: M.Iida;I.Hofuku;中村 剛;Hiroshi Sakai;足立浩平
• 通讯作者: 足立浩平

Correct classification rates in multiple correspondence analysis

多重对应分析中的正确分类率

• 发表时间: 2005
• 期刊: Journal of the Japanese Society of Computational Statistics 17
• 作者: Wang;J. (2005);Kohei Adachi
• 通讯作者: Kohei Adachi

SPSS辞典(小野寺孝義, 山本嘉一郎編) 165-176,215-220頁

SPSS Dictionary（由 Takayoshi Onodera 和 Kaichiro Yamamoto 编辑）第 165-176、215-220 页

• 发表时间: 2004
• 作者: Hiroshi Sakai;Michinori Nakata;安立浩平
• 通讯作者: 安立浩平

Multiple correspondence spline analysis for graphically representing nonlinear relationships between variables

多重对应样条分析用于以图形方式表示变量之间的非线性关系

• 发表时间: 2004
• 期刊: COMPSTAT 2004: Proceedings in computational statistics(A.Jaromir (Ed.))(Physica-Verlag/Springer)
• 作者: Aki;S.;Hirano;K.;Kohei Adachi;Kohei Adachi;Kohei Adachi;Kohei Adachi;Kohei Adachi
• 通讯作者: Kohei Adachi

SPSS事典(小野寺孝義, 山本嘉一郎編)

SPSS百科全书（由小野寺隆良、山本嘉一郎主编）

• 发表时间: 2004
• 作者: Wang;J.;足立浩平
• 通讯作者: 足立浩平