Amos 6.0 User’s Guide ™ James L. Arbuckle For more information, please contact: Marketing Department Amos Development Corporation SPSS, Inc. 1121 N. Bethlehem Pike, Suite 60 - #142 233 S. Wacker Dr., 11th Floor Spring House, PA 19477, U.S.A. Chicago, IL 60606-6307, U.S.A. URL: http://amosdevelopment.com Tel: (312) 651-3000 Fax: (312) 651-3668 URL: http://www.spss.com SPSS® is a registered trademark and the other product names are the trademarks of SPSS Inc. for its proprietary computer software. Amos™ is a trademark of Amos Development Corporation. No material describing such software may be produced or distributed without the written permission of the owners of the trademark and license rights in the software and the copyrights in the published materials. The SOFTWARE and documentation are provided with RESTRICTED RIGHTS. Use, duplication, or disclosure by the Government is subject to restrictions as set forth in subdivision (c)(1)(ii) of the Rights in Technical Data and Computer Software clause at 52.227-7013. Contractor/manufacturer is SPSS Inc., 233 S. Wacker Dr., 11th Floor, Chicago, IL 60606-6307. Access®, Excel®, Explorer®, FoxPro®, Microsoft®, Visual Basic®, and Windows® are registered trademarks of Microsoft Corporation. General notice: Other product names mentioned herein are used for identification purposes only and may be trademarks of their respective companies. Microsoft® Visual Basic® and Windows® screen shots reproduced by permission of Microsoft Corporation. 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 v 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 vii 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 viii 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