Amos™ 6.0 User's Guide

562 Pages·2005·5.18 MB·English

by  James L. Arbuckle

Amos 6.0 User’s Guide
™
James L. Arbuckle
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Amos 6.0 User’s Guide
Copyright © 1995–2005 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 08 07 06 05
ISBN 1-56827-366-5
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
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5
2 New Features 7
Bayesian Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7
Data Imputation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7
Print Preview for Path Diagrams . . . . . . . . . . . . . . . . . . . . . . .8
Improved Zooming and Scrolling. . . . . . . . . . . . . . . . . . . . . . . .9
Drawing Path Diagrams. . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Copying Path Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Multiple Path Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Incompatibilities with Amos 5.0 . . . . . . . . . . . . . . . . . . . . . . . 11
Other Changes between Amos 5.0 and Amos 6.0 . . . . . . . . . . . . . 11
iii
3 Tutorial: Getting Started with
Amos Graphics 13
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
About the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Launching Amos Graphics . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Creating a New Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Specifying the Data File . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Specifying the Model and Drawing Variables . . . . . . . . . . . . . . . 17
Naming the Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Drawing Arrows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Constraining a Parameter. . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Altering the Appearance of a Path Diagram . . . . . . . . . . . . . . . . 21
Setting Up Optional Output . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Performing the Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Viewing Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Printing the Path Diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Copying the Path Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Copying Text Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Part II: Examples
1 Estimating Variances and Covariances 29
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
About the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Bringing In the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Analyzing the Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Viewing Graphics Output . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Viewing Text Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
iv
Optional Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .39
Distribution Assumptions for Amos Models . . . . . . . . . . . . . . . . .41
Modeling in VB.NET. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .42
Modeling in C#. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .45
Other Program Development Tools . . . . . . . . . . . . . . . . . . . . . .46
2 Testing Hypotheses 47
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .47
About the Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .47
Parameters Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . .47
Moving and Formatting Objects. . . . . . . . . . . . . . . . . . . . . . . .51
Data Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .52
Optional Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54
Labeling Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .57
Hypothesis Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .58
Displaying Chi-Square Statistics on the Path Diagram. . . . . . . . . . .59
Modeling in VB.NET. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .61
3 More Hypothesis Testing 65
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .65
About the Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .65
Bringing In the Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .65
Testing a Hypothesis That Two Variables Are Uncorrelated . . . . . . .66
Specifying the Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .66
Viewing Text Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .68
Viewing Graphics Output. . . . . . . . . . . . . . . . . . . . . . . . . . . .69
Modeling in VB.NET. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .71
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4 Conventional Linear Regression 73
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
About the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
Analysis of the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
Specifying the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
Fixing Regression Weights . . . . . . . . . . . . . . . . . . . . . . . . . . 77
Viewing the Text Output. . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
Viewing Graphics Output . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Viewing Additional Text Output. . . . . . . . . . . . . . . . . . . . . . . . 82
Modeling in VB.NET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5 Unobserved Variables 87
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
About the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
Model A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
Measurement Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
Structural Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
Specifying the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
Results for Model A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
Model B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
Results for Model B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
Testing Model B against Model A . . . . . . . . . . . . . . . . . . . . . 102
Modeling in VB.NET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
vi
6 Exploratory Analysis 107
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
About the Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
Model A for the Wheaton Data . . . . . . . . . . . . . . . . . . . . . . . 108
Model B for the Wheaton Data . . . . . . . . . . . . . . . . . . . . . . . 113
Model C for the Wheaton Data . . . . . . . . . . . . . . . . . . . . . . . 120
Multiple Models in a Single Analysis. . . . . . . . . . . . . . . . . . . . 122
Output from Multiple Models . . . . . . . . . . . . . . . . . . . . . . . . 125
Modeling in VB.NET. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
7 A Nonrecursive Model 135
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
About the Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
Felson and Bohrnstedt’s Model . . . . . . . . . . . . . . . . . . . . . . . 136
Model Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
Results of the Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
Modeling in VB.NET. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
8 Factor Analysis 143
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
About the Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
A Common Factor Model. . . . . . . . . . . . . . . . . . . . . . . . . . . 144
Identification. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Specifying the Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
Results of the Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
Modeling in VB.NET. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
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9 An Alternative to Analysis of Covariance 151
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
Analysis of Covariance and Its Alternative . . . . . . . . . . . . . . . . 151
About the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
Analysis of Covariance . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
Model A for the Olsson Data . . . . . . . . . . . . . . . . . . . . . . . . 153
Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
Specifying Model A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
Results for Model A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
Searching for a Better Model. . . . . . . . . . . . . . . . . . . . . . . . 155
Model B for the Olsson Data . . . . . . . . . . . . . . . . . . . . . . . . 156
Results for Model B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
Model C for the Olsson Data . . . . . . . . . . . . . . . . . . . . . . . . 159
Results for Model C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
Fitting All Models At Once . . . . . . . . . . . . . . . . . . . . . . . . . 160
Modeling in VB.NET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
10 Simultaneous Analysis of Several Groups 165
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
Analysis of Several Groups . . . . . . . . . . . . . . . . . . . . . . . . . 165
About the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
Model A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
Model B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
Modeling in VB.NET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
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11 Felson and Bohrnstedt’s Girls and Boys 181
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
Felson and Bohrnstedt’s Model . . . . . . . . . . . . . . . . . . . . . . . 181
About the Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
Specifying Model A for Girls and Boys. . . . . . . . . . . . . . . . . . . 182
Text Output for Model A . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
Graphics Output for Model A . . . . . . . . . . . . . . . . . . . . . . . . 187
Model B for Girls and Boys . . . . . . . . . . . . . . . . . . . . . . . . . 188
Results for Model B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
Fitting Models A and B in a Single Analysis . . . . . . . . . . . . . . . . 194
Model C for Girls and Boys. . . . . . . . . . . . . . . . . . . . . . . . . . 194
Results for Model C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
Modeling in VB.NET. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
12 Simultaneous Factor Analysis for
Several Groups 201
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
About the Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
Model A for the Holzinger and Swineford Boys and Girls . . . . . . . . 202
Results for Model A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
Model B for the Holzinger and Swineford Boys and Girls . . . . . . . . 206
Results for Model B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
Modeling in VB.NET. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
ix
13 Estimating and Testing Hypotheses
about Means 215
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
Means and Intercept Modeling . . . . . . . . . . . . . . . . . . . . . . 215
About the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
Model A for Young and Old Subjects . . . . . . . . . . . . . . . . . . . 216
Mean Structure Modeling in Amos Graphics. . . . . . . . . . . . . . . 216
Results for Model A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
Model B for Young and Old Subjects . . . . . . . . . . . . . . . . . . . 220
Results for Model B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
Comparison of Model B with Model A. . . . . . . . . . . . . . . . . . . 222
Multiple Model Input. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
Mean Structure Modeling in VB.NET . . . . . . . . . . . . . . . . . . . 223
14 Regression with an Explicit Intercept 227
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
Assumptions Made by Amos . . . . . . . . . . . . . . . . . . . . . . . . 227
About the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
Specifying the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
Results of the Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
Modeling in VB.NET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
15 Factor Analysis with Structured Means 235
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
Factor Means. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
About the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236
x