This practical guide teaches nonstatisticians how to analyze and interpret loglinear models using the multigraph
The Association Graph and the Multigraph for Loglinear Models will help students, particularly those studying the analysis of categorical data, to develop the ability to evaluate and unravel even the most complex loglinear models without heavy calculations or statistical software. This supplemental text reviews loglinear models, explains the association graph, and introduces the multigraph to students who may have little prior experience of graphical techniques, but have some familiarity with categorical variable modeling. The author presents logical step-by-step techniques from the point of view of the practitioner, focusing on how the technique is applied to contingency table data and how the results are interpreted.
| About the Author |
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vii | |
| Series Editor's Introduction |
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ix | |
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1 | (5) |
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2 Structures of Association |
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6 | (8) |
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2.1 Statistical Independence for Discrete Variables |
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6 | (1) |
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2.2 The Odds Ratio: Two-Way Tables |
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7 | (2) |
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2.3 The Odds Ratio: Three-Way Tables |
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9 | (3) |
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2.4 Model Fitting: Three-Way Tables |
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12 | (1) |
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13 | (1) |
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14 | (14) |
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3.1 Two-Way Contingency Table |
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14 | (3) |
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3.2 Three-Way Contingency Table |
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17 | (3) |
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3.3 Relationships Among the LLMs for a Three-Way Table |
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20 | (3) |
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3.4 LLM and Contingency Table Properties |
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23 | (3) |
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26 | (2) |
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4 Association Graphs for Loglinear Models |
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28 | (17) |
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4.1 Basic Graph Theory Principles |
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28 | (6) |
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4.2 Association Graphs for Three-Way Tables |
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34 | (3) |
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4.3 Association Graphs for Multi-Way Tables |
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37 | (4) |
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41 | (2) |
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43 | (2) |
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5 Collapsibility Conditions and the Association Graph |
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45 | (11) |
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5.1 Collapsing in a Three-Way Contingency Table |
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45 | (3) |
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5.2 The Collapsibility Theorem and the Association Graph |
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48 | (4) |
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52 | (4) |
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6 The Generator Multigraph |
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56 | (23) |
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6.1 Construction of the Multigraph |
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56 | (1) |
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6.2 Multigraphs for Three-Way Tables |
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56 | (2) |
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6.3 Multigraphs for Multi-Way Tables |
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58 | (3) |
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6.4 Maximum Spanning Trees |
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61 | (5) |
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66 | (4) |
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6.6 Factorization of Joint Probabilities for Decomposable LLMs |
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70 | (3) |
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6.7 Fundamental Conditional Independencies in Decomposable LLMs |
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73 | (6) |
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7 Fundamental Conditional Independencies for Nondecomposable Loglinear Models |
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79 | (11) |
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79 | (4) |
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7.2 FCIs for Nondecomposable LLMs |
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83 | (5) |
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7.3 Collapsibility Conditions Using the Multigraph |
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88 | (1) |
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88 | (2) |
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8 Conclusions and Additional Examples |
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90 | (23) |
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8.1 Comparison of the Association Graph and the Multigraph |
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90 | (4) |
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8.2 Additional Real-Data Examples |
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94 | (16) |
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110 | (3) |
| Data Sets |
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113 | (2) |
| References |
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115 | (4) |
| Author Index |
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119 | (2) |
| Subject Index |
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121 | |
Harry J. Khamis is a Professor in the Department of Mathematics & Statistics with a joint appointment in the Boonshoft School of Medicine at Wright State University, Dayton, Ohio. He received his B.S. degree in mathematics at Santa Clara University, and he received his M.S. degree in mathematics (1976) and his Ph.D. degree in statistics (1980) at Virginia Tech. He has been at Wright State University since 1980 except for teaching, research, and consulting visiting positions at Uppsala, Umeå, and Dalarna Universities in Sweden. Dr. Khamis has been Director of the Statistical Consulting Center at Wright State University since 1993. Specializing in statistical methodology, especially categorical response models, goodness of fit tests, and the Cox regression model, Dr. Khamis has 80 authored or coauthored publications. In addition to teaching and research, Dr. Khamis also consults extensively with researchers at the university as well as clients external to the university. Major external clients include Astra-Arcus Pharmaceuticals, B.F. Goodrich, Cancer Prevention Institute, Carnation Co., Center for Election Integrity, Clinical Research Consultants, Community Blood Center, Genentech Inc., Isolab Inc., Kunesh Eye Surgery Center, Mandal Diabetes Research Institute, Nestles, Pharmacia-Upjohn Pharmaceuticals, and Sifo Marketing Research.
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