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Amos ™ 6.0 User’s Guide James L. Arbuckle For more information, please contact: 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 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 iii Contents 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 iv 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 v 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 vi 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 vii 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 viii 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 ix 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 x 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 [...]... that must be communicated to Amos Launching Amos Graphics You can launch Amos Graphics in any of the following ways: Click Start on the Windows task bar, and choose Programs → Amos 6 → Amos Graphics Double-click any path diagram (*.amw) Drag a path diagram (*.amw) file from Windows Explorer to the Amos Graphics window Click Start on the Windows task bar, and choose Programs → Amos 6 → View Path Diagrams... TotalEffects Other Changes between Amos 5.0 and Amos 6.0 On the Amos Graphics menus, View/Set has been renamed View, and Model-Fit has been renamed Analyze The key combination Ctrl+B is now a shortcut for Analyze → Bayesian In Amos 5.0, Ctrl+B was a shortcut for Tools → Outline In Amos 5.0, you could open the Object Properties dialog box by double-clicking an object in a path diagram In Amos 6.0, double-clicking... Diagrams In previous versions of Amos Graphics, you could view only one path diagram at a time Now you can open multiple Amos Graphics windows, each one displaying a different path diagram 11 New Features Incompatibilities with Amos 5.0 By default, path diagram files (*.amw files) that are saved by Amos 6.0 cannot be read by Amos 5.0 To save a *.amw file that can be read by Amos 5.0, from the menus choose... File → Save As In the Save As dialog box, select Amos 5 Input file from the Save as type dropdown list Amos Basic programs and Visual Basic 6 programs require upgrading to VB.NET or C# Two members of the AmosEngine class were renamed in order to avoid conflicts with VB.NET keywords The Structure method was renamed AStructure The Dir property was renamed AmosDir Members of the TMatrixID enum and the TMatrixContents... errors Amos makes these techniques especially easy to use, and we hope that they will become more commonplace Tip: If you have questions about a particular Amos feature, you can always refer to the extensive online Help provided by the program About the Documentation Amos 6.0 comes with extensive documentation, including an online Help system, this user’s guide, and advanced reference material for Amos. .. the object and choose Object Properties from the pop-up menu In Amos 6.0, Object Properties is the first item on the pop-up menu (In Amos 5.0, it was the last item.) For most Amos 6.0 windows, context-sensitive online Help can be displayed with the F1 key or with Shift+F1 For some windows, context-sensitive online Help is obtained, as in Amos 5.0, by right-clicking a window element such as a label or... shortcuts to drawing and labeling path diagrams in Amos Graphics that you will discover as you work through the examples in this user’s guide or as you refer to the online Help The intent of this tutorial is to simply get you started using Amos Graphics It will cover some of the basic functions and features of Amos and guide you through your first Amos analysis Once you have worked through the tutorial,... demonstrating all of the basic features of Amos There are sometimes good reasons for using Amos to do something simple, like estimating a mean or correlation or testing the hypothesis that two means are equal For one thing, you might want to take advantage of the ability of Amos to handle missing data Or maybe you want to use the bootstrapping capability of Amos, particularly to obtain confidence intervals... Kercher, Morton Kleban, Sik-Yum Lee, Michelle Little, Sheela Pandey, Rachel Pruchno, and Shu Zou A last word of warning: While Amos Development Corporation and SPSS have engaged in extensive program testing to ensure that Amos operates correctly, all complicated software, Amos included, is bound to contain some undetected bugs We are committed to correcting any program errors If you believe you have... and fellow researchers The numeric methods implemented in Amos are among the most effective and reliable available Featured Methods Amos provides the following methods for estimating structural equation models: Maximum Unweighted least squares Generalized least squares Browne’s asymptotically distribution-free criterion Scale-free least squares Amos goes well beyond the usual capabilities found in other . 10 Incompatibilities with Amos 5.0 . . . . . . . . . . . . . . . . . . . . . . . 11 Other Changes between Amos 5.0 and Amos 6.0 . . . . . . . . . . . . . 11 iv 3 Tutorial: Getting Started with Amos Graphics. 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. 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: