Amos 7.0 User's Guide

602 Pages·2006·5 MB·English

Amos™ 7.0 User’s Guide
James L. Arbuckle
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Amos 7.0 User’s Guide
Copyright © 1995–2006 by Amos Development Corporation
All rights reserved.
Printed in the United States of America.
No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by
any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written
permission of the publisher.
1 2 3 4 5 6 7 8 9 0 09 08 07 06
ISBN-13: 978-1-56827-386-0
ISBN-10: 1-56827-386-X
C o n t e n t s
Part I: Getting Started
1 Introduction 1
Featured Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
About the Tutorial. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
About the Examples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
About the Documentation . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Other Sources of Information . . . . . . . . . . . . . . . . . . . . . . . . . 4
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 New Features 7
Estimation for Ordered-Categorical and Censored Data. . . . . . . . . . 7
Data Imputation for Ordered-Categorical and Censored Data . . . . . . 8
No Bayesian Prerequisites. . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3 Tutorial: Getting Started with
Amos Graphics 11
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11
About the Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12
Launching Amos Graphics. . . . . . . . . . . . . . . . . . . . . . . . . . .13
Creating a New Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14
iii
Specifying the Data File . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Specifying the Model and Drawing Variables . . . . . . . . . . . . . . . 15
Naming the Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Drawing Arrows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Constraining a Parameter. . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Altering the Appearance of a Path Diagram . . . . . . . . . . . . . . . . 19
Setting Up Optional Output . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Performing the Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Viewing Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Printing the Path Diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Copying the Path Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Copying Text Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Part II: Examples
1 Estimating Variances and Covariances 27
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
About the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Bringing In the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Analyzing the Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Viewing Graphics Output . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Viewing Text Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Optional Output. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Distribution Assumptions for Amos Models . . . . . . . . . . . . . . . . 39
Modeling in VB.NET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Modeling in C# . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Other Program Development Tools . . . . . . . . . . . . . . . . . . . . . 44
iv
2 Testing Hypotheses 45
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .45
About the Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .45
Parameters Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . .45
Moving and Formatting Objects. . . . . . . . . . . . . . . . . . . . . . . .49
Data Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .50
Optional Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .52
Labeling Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .55
Hypothesis Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .56
Displaying Chi-Square Statistics on the Path Diagram. . . . . . . . . . .57
Modeling in VB.NET. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .59
3 More Hypothesis Testing 63
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .63
About the Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .63
Bringing In the Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .63
Testing a Hypothesis That Two Variables Are Uncorrelated . . . . . . .64
Specifying the Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .64
Viewing Text Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .66
Viewing Graphics Output. . . . . . . . . . . . . . . . . . . . . . . . . . . .67
Modeling in VB.NET. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .69
4 Conventional Linear Regression 71
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .71
About the Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .71
Analysis of the Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .72
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Specifying the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
Fixing Regression Weights . . . . . . . . . . . . . . . . . . . . . . . . . . 74
Viewing the Text Output. . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
Viewing Graphics Output . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
Viewing Additional Text Output. . . . . . . . . . . . . . . . . . . . . . . . 79
Modeling in VB.NET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5 Unobserved Variables 85
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
About the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Model A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
Measurement Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
Structural Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
Specifying the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
Results for Model A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
Model B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Results for Model B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
Testing Model B against Model A . . . . . . . . . . . . . . . . . . . . . 100
Modeling in VB.NET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
6 Exploratory Analysis 105
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
About the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
Model A for the Wheaton Data. . . . . . . . . . . . . . . . . . . . . . . 106
Model B for the Wheaton Data. . . . . . . . . . . . . . . . . . . . . . . 111
Model C for the Wheaton Data. . . . . . . . . . . . . . . . . . . . . . . 118
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Multiple Models in a Single Analysis. . . . . . . . . . . . . . . . . . . . 120
Output from Multiple Models . . . . . . . . . . . . . . . . . . . . . . . . 123
Modeling in VB.NET. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
7 A Nonrecursive Model 133
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
About the Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
Felson and Bohrnstedt’s Model . . . . . . . . . . . . . . . . . . . . . . . 134
Model Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
Results of the Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
Modeling in VB.NET. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
8 Factor Analysis 141
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
About the Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
A Common Factor Model. . . . . . . . . . . . . . . . . . . . . . . . . . . 142
Identification. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
Specifying the Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
Results of the Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Modeling in VB.NET. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
9 An Alternative to Analysis of Covariance 149
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
Analysis of Covariance and Its Alternative . . . . . . . . . . . . . . . . 149
About the Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
Analysis of Covariance. . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
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Model A for the Olsson Data . . . . . . . . . . . . . . . . . . . . . . . . 151
Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
Specifying Model A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
Results for Model A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
Searching for a Better Model. . . . . . . . . . . . . . . . . . . . . . . . 153
Model B for the Olsson Data . . . . . . . . . . . . . . . . . . . . . . . . 155
Results for Model B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
Model C for the Olsson Data . . . . . . . . . . . . . . . . . . . . . . . . 157
Results for Model C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
Fitting All Models At Once . . . . . . . . . . . . . . . . . . . . . . . . . 158
Modeling in VB.NET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
10 Simultaneous Analysis of Several Groups 163
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
Analysis of Several Groups . . . . . . . . . . . . . . . . . . . . . . . . . 163
About the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
Model A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
Model B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
Modeling in VB.NET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
11 Felson and Bohrnstedt’s Girls and Boys 179
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
Felson and Bohrnstedt’s Model . . . . . . . . . . . . . . . . . . . . . . 179
About the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
Specifying Model A for Girls and Boys . . . . . . . . . . . . . . . . . . 180
Text Output for Model A. . . . . . . . . . . . . . . . . . . . . . . . . . . 183
Graphics Output for Model A . . . . . . . . . . . . . . . . . . . . . . . . 185
Model B for Girls and Boys . . . . . . . . . . . . . . . . . . . . . . . . . 186
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Results for Model B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
Fitting Models A and B in a Single Analysis . . . . . . . . . . . . . . . . 192
Model C for Girls and Boys. . . . . . . . . . . . . . . . . . . . . . . . . . 192
Results for Model C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
Modeling in VB.NET. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
12 Simultaneous Factor Analysis for
Several Groups 199
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
About the Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
Model A for the Holzinger and Swineford Boys and Girls . . . . . . . . 200
Results for Model A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
Model B for the Holzinger and Swineford Boys and Girls . . . . . . . . 204
Results for Model B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
Modeling in VB.NET. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
13 Estimating and Testing Hypotheses
about Means 213
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
Means and Intercept Modeling . . . . . . . . . . . . . . . . . . . . . . . 213
About the Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
Model A for Young and Old Subjects . . . . . . . . . . . . . . . . . . . . 214
Mean Structure Modeling in Amos Graphics . . . . . . . . . . . . . . . 214
Results for Model A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
Model B for Young and Old Subjects . . . . . . . . . . . . . . . . . . . . 218
Results for Model B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
Comparison of Model B with Model A . . . . . . . . . . . . . . . . . . . 220
Multiple Model Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
Mean Structure Modeling in VB.NET. . . . . . . . . . . . . . . . . . . . 221
ix
14 Regression with an Explicit Intercept 225
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
Assumptions Made by Amos . . . . . . . . . . . . . . . . . . . . . . . . 225
About the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
Specifying the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
Results of the Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
Modeling in VB.NET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
15 Factor Analysis with Structured Means 233
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
Factor Means. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
About the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
Model A for Boys and Girls . . . . . . . . . . . . . . . . . . . . . . . . . 234
Understanding the Cross-Group Constraints . . . . . . . . . . . . . . . 236
Results for Model A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
Model B for Boys and Girls . . . . . . . . . . . . . . . . . . . . . . . . . 239
Results for Model B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
Comparing Models A and B. . . . . . . . . . . . . . . . . . . . . . . . . 241
Modeling in VB.NET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
16 Sörbom’s Alternative to
Analysis of Covariance 245
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
About the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
Changing the Default Behavior. . . . . . . . . . . . . . . . . . . . . . . 247
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