# Structural Space Scaling

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Structural Space Scaling. SHOJIMA Kojiro The National Center for University Entrance Examinations shojima@rd.dnc.ac.jp. Purpose. MDS では項目群は 1 つの 空間 S にプロットされる S がいくつかの部分空間から成るとしたら？ 部分 空間間に構造（因果、 影響） が あったら？ S の構造 を仮説検証的（確認的）に 同定したい 構造空間尺度法 (structural space scaling) を提案 - PowerPoint PPT Presentation

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Structural Space ScalingSHOJIMA KojiroThe National Center for University Entrance Examinationsshojima@rd.dnc.ac.jpPurposeMDS1SSS

(structural space scaling)MDSPath DiagramGraphical ModelsStructural Equation ModelsBeyesian Networks

Entire Space and Subspaces8SS1S2S1S2SS2S1

MapPath DiagramO1(m11, m12)S1f11f12S2f21f22

Exogenous and Endogenous SpacesPath DiagramStructural Coordinates

Structural CoordinatesMeasurement CoordinatesG: (selection matrix taking x out of t): (inner product structure): (distance structure, model distance)D: 1-mode 2-wayG: (selection matrix taking x out of t): (inner product structure): (distance structure, model distance)D: 1-mode 2-wayMeasurement CoordinatesDistance Structure: Inter-Subspace Inner Product Structure r1: f11f12

Measurement EquationsDistance StructureG: (selection matrix taking x out of t): (inner product structure): (distance structure, model distance)D: 1-mode 2-wayMeasurement EquationsDistance StructureG: (selection matrix taking x out of t): (inner product structure): (distance structure, model distance)D: 1-mode 2-wayGoodness of Fit IndicesSummary (1) SEM Approach in MDSStructural Space Scaling (SSS)MDS(inter-subspace structure)MDSSummary (2) DimensionalityMDS23442D (3D)44

A1A2A3B1B2B3A112556A211565A312565B143321B233411B334321

5.53.5Expansion to Asymmetric Structure

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