Modeling intraindividual variability with repeated measures data

Modeling Intraindividual Variability with Repeated Measures Data: Methods and Applications MULTIVARIATE APPLICATIONSBOOK SERIES The multivariate Applications book series was developed to encourage the use of rigorous methodology in the study of meaningful scientific issues, and to describe the applications in easy to understand language The series is sponsored by the Society of Multivariate Experimental Psychology and welcomes methodological applications from a variety of disciplines, such as psychology, public health, sociology, education, and business The main goal is to provide descriptions of applications of complex statistical methods to the understanding of significant social or behavior issues The descriptions are to be accessible to an intelligent, non-technical oriented readership (e.g., non-methodological researchers, teachers, students, government personnel, practitioners, and other professionals) Books can be single authored, multiple authored, or edited volumes The ideal 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Juffcutt (2001) Modeling Intraindividual Variability with Repeated Measures Data: Methods and Applications, co-edited by D S Moskowitz and S L Hershberger (2002) Anyone wishing to propose a book should address the following: (1) title; (2) author(s); (3) timeline including planned completion date; (4) Brief overview of focus for the book including a table of contents and a sample chapter (or more); ( ) mention any competing publications in this area; (6) mention possible audiences for the proposed book More information can be obtained from the editor, Lisa Harlow, at: Department of Psychology, University of Rhode Island, 10 Chafee Rod., Suite , Kingston, RI 02881-0808; Phone: 401-874-4242; Fax: 401-874-5562; or e-mail: Lharlow@uri.edu Information can also be obtained from one of the advisory board members: Leona Aiken (Arizona State University), Gwyneth Boodoo (Educational Testing Service), Susan Embretson (University of Kansas), Michael Neale (Virginia Commonwealth University), Bill Revelle (Northwestern University), and Steve West (Arizona State University) Modeling Intraindividual Variability with Repeated Measures Data: Methods and Applications Edited by D S Moskowitz M cGill University Scott L Hershberger California State University, Long Beach 2002 LAWRENCE ERLBAUM ASSOCIATES, PUBLISHERS Mahwah, New Jersey London The final camera copy for this work was prepared by the editors and therefore the publisher takes no responsibility for consistency or correctness of typographical style However, this arrangement helps to make publication of this kind of scholarship possible Copyright @ 2002 by Lawrence Erlbaum Associates, Inc All rights reserved No part of the book may be reproduced in any form, by photostat, microform, retrieval system, or any other means, without the prior written permission of the publisher Lawrence Erlbaum Associates, Inc., Publishers 10 Industrial Avenue Mahwah, New Jersey 07430 I Cover design by Kathryn Houghtaling Lacey I ISBN 0-8058-3125-8 Books published by Lawrence Erlbaum Associates are printed on acid-free paper, and their bindings are chosen for strength and durability Printed in the United States of America 10 List of Contributors David A Kenny, Department of Psychology, University of Connecticut, Babbidge Road Unit 1020, Storrs, C T 06269-1020 Nial Bolger, Department of Psychology, New York University, Washington Place, room 752, New York, N.Y 10003 Deborah A Kashy, Department of Psychology, Texas A&M University, College Station, T X 77843-4235 Stephan E Raudenbush, School of Education, Michigan State University, 610 E University, Ann Arbor, MI 48109-1159 Patrick J Curran, Department of Psychology, University of North Carolina, Chapel Hill, NC 27599-3270 Andrea M Hussong, Department of Psychology, University of North Carolina, Chapel Hill, NC 27599-3270 J.O Ramsay, Department of Psychology, McGill University, 1205 Dr Penfield Avenue, Montreal, Quebec, Canada, H3A 1B1 Dennis Wallace, Department of Preventive Medicine, University of Kansas Medical Centre, 4004 Robinson Hall, 3901 Rainbow Blvd., Kansas City, KS 66160 Samuel B Green, Department of Psychology in Education, Arizona State University, 308G Payne Hall, Tempe, AZ 85287-0611 Judith D Singer, Graduate School of Education, Harvard University, Roy E Larsen Hall, Appian Way, Cambridge, MA 02138 Terry E Duncan, Oregon Research Institute, 1715 Franklin, Blvd., Eugene, OR 97403-1983 Susan C Duncan, Oregon Research Institute, 1715 Franklin, Blvd., Eugene, OR 97403-1983 Fuzhong Li, Oregon Research Institute, 1715 Franklin, Blvd., Eugene, OR 97403-1983 Lisa A Strycker, Oregon Research Institute, 1715 Franklin, Blvd., Eugene, OR 97403-1983 Steven Hillmer, School of Business, University of Kansas, 203 Summerfield Hall, Lawrence, KS 66044-2003 John R Nesselroade, Department of Psychology, The University of Virginia, 102 Gilmer Hall, P.O Box 400400, Charlottesville, VA 22904-4400 John J McArdle, Department of Psychology, The University of Virignia, 102 Gilmer Hall, P.O Box 400400, Charlottesville, VA 22904-4400 Steven H Aggen, Department of Psychiatry, Virginia Commonwealth University, P.O Box 980710, Richmond, VA 23286-0440 Jonathan M Meyers, Department of Psychology, The University of Virginia, 102 Gilmer Hall, P.O Box 400400, Charlottesville, VA 22904-4400 Contents ix Preface Traditional Methods for Estimating Multilevel Models David A Kenny, Nial Bolger, and Deborah A Kashy Alternative Covariance Structures for Polynomial Models of Individual Growth and Change Stephen W Raudenbush 25 Structural Equation Modeling of Repeated Measures Data: Latent Curve Analysis Patrick J Curran and Andrea M Hussong 59 Multilevel Modeling of Longitudinal and Functional Data J Ramsay 87 Analysis of Repeated Measures Designs with Linear Mixed Models Dennis Wallace and Samuel B Green 103 Fitting Individual Growth Models Using SAS PROC MIXED Judith D Singer 135 Multilevel Modeling of Longitudinal and Functional Data Terry E Duncan, Susan C Duncan, Fuzhong Li, and Lisa A Strycker Times Series Regressions Steven Hillmer 171 203 vii viii Dynamic Factor Analysis Models for Representing Process in Multivariate Time-Series John R Nesselroade, John J McArdle, Steven H Aggen, and Jonathan M Meyers 233 Author Index 267 Subject Index 273 Preface This volume began as a nightmare Once upon a time, life for social and behavioral scientists was (relatively) simple When a research design called for repeated measures data, the data were analyzed with repeated measures analysis of variance The BMDP 2V module was frequently the package of choice for the calculations Life today is more complicated There are many more choices Does the researcher need to model behavior at the level of the individual as well as at the level of the group? Should the researcher use the familiar and well-understood least-squares criterion? Should the researcher turn to the maximum likelihood criterion for assessing the overall fit of a model? Is it possible and is it desirable to represent the repeated measures data within structural equation modeling? So the nightmare began as (shall we be dishonest and say) one night of deliberations among these choices The thought then arose that it would be useful to have the statistical experts writing in the same volume about the possibilities and some of the dimensions that are pertinent to making these choices Hence the origin of the present volume The issue of the analysis of repeated measures data has commonly been examined within the context of the study of change, particularly with respect to longitudinal data (cf., Collins & Horn, 1991; Gottman, 1995) This volume contains three chapters whose primary focus is on the study of growth over several years time (Raudenbush, chapter 2; Curran & Hussong, chapter 3; Duncan, Duncan, Li, & Strycker, chapter 7) Studies of change typically imply the expectation that variation, movement in scores, is genup or generally down Not all repeated erally unidirectional-generally measures data are concerned with change, and change is only one aspect of the variability that occurs within individuals To illustrate, consider an example from the study of social behavior Personality, social, and organizational psychologists are often interested in the effects of situations on behavior: to what extent are individuals’ behaviors consistent across sets of situations and to what extent does the behavior of individuals change as a function of the situation For example, the focus might be on how people’s dominant and submissive behaviors change as a function of being in a subordinate, co-equal, or supervisory work role There might also be interest in whether people’s responses t o these ix 262 Nesselroade et al Cattell (Ed.) , Handbook of multivariate experimental psychology (p 355-402) Chicago, IL: Rand McNally Cattell, R B., Cattell, A K S., & Rhymer, R M (1947) P-technique demonstrated in determining psychophysical source traits in a normal individual Psychometrika, 12, 267-288 Eizenman, D R., Nesselroade, J R., Featherman, D L., & Rowe, J W (1997) Intra-individual variability in perceved control in an elderly sample: The MacArthur successful aging studies Psychology and Aging, 12, 489-502 Engle, R., & Watson, M (1981) A one-factor multivariate time series model of metropolitan wage rates Journal of American Statistical Association, 76, 774-781 Fiske, D W., & Maddi, S R (Eds.) 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165, 172, 173, 174, 183, 185, 188 Burstein, L 172 Byram, W 174 Ageton, S S 61 Aiken, L S 20, 148, 167 Aitkin, M 172 Akaike, H 210 Akers, R L 174 Albert, P 29, 45, 53 Alpert, A 178, 179, 180 Anderson, T W 66, 204, 236 Andrade, D F 112 Andrews, K 175 Arbuckle, J L 180 Baker, P C 63 Baltes, P B 236 Bandura, A 174 Barnes, G M 175, 189 Bauman, K E 174 Bell, W R 214, 219, 221, 222 Bern, D J 60 Bentler, P M 65 Bereiter, C 236 Bock, R 36 Boker, S M 236 Bolger, N 16 Bollen, K A 59, 67, 79 Bosker, R J 158 Box, G E P 205,206, 207, 208, 209, 211, 212, 214, 219 Bozdogan, H 125 Brand, D 27 Brook, J S 175, 189 Brown, D 235, 243, 246 Brown, K W 93 Browne, M W 70 Browne, W 16 Bryk, A S 16, 18, 20, 25, 26, 27, 29, 34, 45, 47, 53, 71, 73, 76, 105, Capaldi, D M 174 Casella, G 93, 172 Caspi, A 60 Cattell, A K S 235, 236, 238 Cattell, R B 235,236,237, 238,239 Chan, W 27, 29, 30, 44 Chassin, L 67, 80 Cholette, P 221 Christensen, R 124 Cicchetti, D 60 Cochran, J E 174 Cohen, P 175, 189 Coie, J D 60 Congdon, R T 16,18,53,135,185, 188 Cooper, D M 210 Corneal, S E 235, 243 Cox, D R 214 Cudeck, R 70 Curran, P J 59, 67, 70, 73, 79, 80 Dalzell, C 89, 91 Davidson, K 27 Davis, J 26 de Leeuw, J 20, 121, 148, 158, 167, 172 Diggle, P J 53, 89, 92, 93, 97, 99, 101, 105, 131 Dishion, T J 60, 61 Dodge, K A 60 Draper, D 16 Duncan, S C 67,172,173,175,176, 267 268 178, 179, 180, 189 Duncan, T E 67,172,173,175,176, 178, 179, 180, 189 Dwyer, J H 65 Eizenman, D R 236 Elder, G H 60 Elliott, D 30, 175 Elliott, D S 61 Elliott, P R 193 Engle, R 237, 239 Entwistle, B 172 Epstein, D 67, 68 Farrington, D P 174 Featherman, D L 236, 254 Ferring, D 236, 239 Fiske, D W 236 Fletcher, J 27 Flewelling, R L 174 Flugel, J C 236 Fly, J W 174 Ford, D H 236 Francis, D 27 Fuller, W A 209, 220 Author Index Hedeker, D 16, 26 Heise, D R 66 Helms, R W 104, 112, 124 Herrnstein, R J 61 Hershberger, S L 122, 235, 243 Hillmer, S C 210, 214,219, 221,222 Hirschi, T 30 Hocking, R R 111 Hofer, S M 191 Holtzman, W H 236, 237, 239 Hops, H 67, 172, 175, 176, 178,189 Horn, J L 236, 242 Horney, J 27 Hudak,' G 216 Huizinga, D 30, 61 Humphreys, L G 66 Hundleby, J D 236 Huttenlocher, J E 27 Jacobs, D R Jacobs, M R 60 Jenkins, G M 205, 206, 207, 208, 209, 211, 212 Jennrich, R 28, 36, 38, 47, 90, 111 Johnson, D E 105 Johnson, W 124 Geweke, J F 237, 239, 243 Jones, C J 236, 237 Gibbons, R 26 Jones, K 236 Goldsmith, H H 253 Goldstein, H 16, 26, 28, 29, 36, 53, Joreskog, K 27 Joreskog, K G 65, 66, 238, 246 105, 135, 141, 164, 165 Goldstein, H I 172 Kalaian, H 29, 36 Gordon, A S 175, 189 Kandel, D B 175 Gottfredson, M 30 Kang, S 29 Grady, J J 124 Kaplan, D 193 Graham, J W 191 Kashy, D A 5, 6, 7, 16, 21 Gray, H L 210 Kazdin, A E 60, 61 Green, S B 122 Keck, C K 63 Guttman, L A 66 Kelley, G D 210 Haight, W 27 Kenny, D A 16, 236 Hannan, P J 121 Kielcolt-Glaser, J 74 Marford, T C 73 Kim, C 74 Harville, D A 111, 112 Kim, E 236 Kealy, M 16 Kirk, R E 105 Healy, M J R 164 Kreft, I 121, 158, 172 Beckman, N 93 Kreft, I G 172 Author Index 269 Milliken, G A 105, 111, 112, 123, 131, 136, 150, 164 Mintz, J 236, 237 Laird, N 193 Moffitt, T E 61 Laird, N M 25, 111, 131 Molenaaar, P C 235, 243 Larsen, R J 236 Molenaar, P C M 235, 236,237,239, Lebo, M A 246 241, 243, 246 Leeper, J D 112 Morry, M 221 Lewis, C E 121 Moskowitz, D S 93 Li, F 179, 180 Mott, F L 63 Li, X 91 Liang, K.-Y 29, 45, 53, 89, 92, 93, Mullally, P R 191 Muthkn, B 67, 172, 173, 178, 180, 97, 99, 101, 105, 131 182, 183, 192 Lindquist, E G 105 M u t h h , B 28,63,65,67,73,80, Lindsey, J K 105 Littell, R C 105,111,112,123,131, 172, 173, 176, 180, 182, 183, 185 M u t h h , L K 63, 65, 80, 172, 173, 136, 150, 164 180, 182, 183, 185 Little, R 26 Little, R J A 36, 38, 63, 65, 90 Neale, M C 180 Liu, K 121 Nelder, J A 53 Liu, L 216 Nesselroade, J R 236,237,246,254 Ljung, G 211 Newbold, P 219 Loeber, R 60 Longford, N 172 Osgood, D 27 Longford, N T 26, 53, 105, 172 Luborsky, L 236, 237 Patterson, G R 60, 61, 174, 191 Kreft, I G G 20, 148, 167 MacCallum, R C 74 Magnusson, D 236 Malarkey, W 74 Marquis, J G 122 Marshall, I 27 Mason, W M 172 McArdle, J J 27,67,68,76,80, 172, 235, 237, 239, 242, 246 253 McCarroll, K '112 McCollam, K M 122 McCulloch, C E 93, 172 McCullogh, P 53 McDermott, D 175, 189 McIntire, D D 210 McLean, R A 136 McNamara, C k 125 Menard, S 30 Meredith, W 27, 28, 67, 178 Michael, M 125 Milby, J B 125 ' Patterson, H D 111 Pawlik, K 236 Pearson, L M 124 Piccinin, A M 191 Pierce, D A 211 Plewis, I 16 Popkin, S 125 Prosser, R 135 Quenneville, B 221 Quinlan, S V 63 Raftery, A E 160 Ramsay, J 89, 91, 93, 98 Rao, C R 67 Rasbash, J 16, 29, 135, 164 Raudenbush, S 'Mi 16, 18, 20, 26, 27, 29, 30, 34, 36, 44, 45, 47, 53, 54, 71, 73, 76, 105, 135, 141, 165, 172, 173, 174, 183, 185, 188 Reese, H W 236 270 Author Index Reid, J B 60, 61 Tellegen, A 236 Reinsel, G C 205,206,207,209,211 Thompson, K 175 Reis, H T Thompson, M S 122 Rhymer, R M 235, 236, 238 Thompson, N 27 Rice, L 236 Thompson, R 111 Thum, Y 29, 47, 52 Ricks, D F 236 Tiao, G C 210, 214 Rogosa, D R 27, 59, 66, 67 Rowan, B 29 Tisak, J 27, 28, 67, 178 Rowe, J W 236 Tsay, R S 210 Rubin, D B 36, 38, 63, 65, 90 Tucker, L R 67 Usdan, S 125 Salineas, T 219, 221 Valsiner, J 236 Sanders, W L 136 VanLeeuwen, D M 164 SAS Institute 100, 136 Satorra, A 172 Wallace, D 121, 125 Sayer, A 79 Walters, R H 174 Sayer, A G 27, 28, 30, 75, 179 Ware, J H 25,26,27, 103, 111,131, Schafer, J 26, 53 Schluchter, M 28,36,38,47,90,111 193 Waternaux, C 26 Schmidt McCollam, K M 254 Watson, M 237, 239 Schmitt, M 236, 239 Weisberg, H 25 Schumacher, J E 125 Welte, J W 175, 189 Schwartz, C 210 Wessman, A E 236 Searle, S R 93, 172 Wheeler, L Seltzer, M 27 Whiteman, M 175, 189 Seltzer, M H 26, 29, 52 Willett, J B 27, 28, 30,67, 75, 137, Shenker, N 26 179 Silverman, B 93 D 121 Williams, Silverman, B W 89, 98 Willms, J D 29 Singer, D G 236 Wilsnack, R 175 Singer, J D 123, 136, 140, 167, 168 Wilson, J Q 61 Singer, J L 236 M 65 Windle, Singleton, K J 237, 239, 243 B J 105, 172 Winer, Snijders, T A B 158 Wolfinger, R D 105, 111, 112, 120, Sorbom, D 27, 65, 238, 246 123, 125, 131, 136, 150, 159, 164 Steyer, R 236, 239 Wong, G 172 Stice, E 67, 80 Wood, E F 210 Stiratelli, R 193 P 235, 243, 246 Wood, Stoolmiller, M 67, 172, 178 G 16 Woodhouse, Strenio, J 25 H 236 Woodrow, Stroup, W W 105, 111, 112, 123, F 112 Woolson, R 131, 136, 150, 164 Strycker, L A 179, 180 Yang, M 16 Stubing, K 27 Sweetsir, D A 174 Zajonc, R B 191 Author Index Zautra, A 236 Zeger, S 29, 45, 53 Zeger, S L 53, 89, 92, 93, 97, 99, 101, 105, 131 Zevon, M 236 Zimowski, M 27 271 Subject Index Between structure, 181 Ad hoc estimator, 173 Alcohol use, 171, 174, 175, 178, 183, 184, 186, 188-190, 193 Analysis of variance, 1-5, 9, 11, 14, 15, 23, 26, 34, 59,97, 105, 112, 114, 115, 119, 141, 142, 146, 172, 174 Antisocial behavior, 30,60-63,6674, 76, 77, 79 Assumption, 25-27,29, 30,32,36, 39,43-45, 50, 52, 53, 89, 95,96, 106, 111,113,114, 117, 122, 147, 154, 158160, 164, 165, 192, 203, 204, 212, 218 homoscedasticity, 117 Linearity, 110, 165 normality, 29,45, 50,111,164, 165, 194, 204 Autocorrelation, 28,39,100,203207, 209-211, 213, 214, 216, 219, 220, 222, 225227, 251 Autocorrelation function, 205-207, 209, 210, 213, 214, 216, 219, 220, 222, 226 Autoregressive, 22, 39, 59, 65,66, 119, 159, 162, 164, 205209, 220, 226, 235, 238, 239, 241, 243, 250 Autoregressive model, 119, 205, 206, 209, 243 Centering, 6, 20, 136, 148, 150, 179 Cluster, 29, 53, 173, 180, 193, 194 Coding, 18, 20, 150 Compound symmetry, 34, 36, 39, 42, 159, 160 Conditional growth model, 155, 156, 165 Covariance parameter, 33, 42, 43, 45, 111, 112, 117, 129, 151 DAFS Model, 239, 241, 243, 245, 246, 248, 250, 251, 253257 Degrees of freedom, 3, 17,97,100, 101, 112, 113, 150, 154, 216, 243, 246, 248, 253 Developmental psychopathology, 79 Developmental trajectories, 61,68, 70, 74, 77, 79 Differencing, 209, 213, 219, 222, 226, 227 Easter effect, 222, 227 Efficiency, 18, 22 Ergodicity, 237 Error variance, 4, 11, 17, 27, 107, 164 Error variance-covariance, 136,159, 168 Extraneous factor, 231 Balanced data, 1, 2, 5, 11, 14, 90, 144,167, 173, 183, 193 Between level, 188, 193 Factor analysis model, 238 273 74 Factor score, 173, 235, 237-239, 241, 243, 244, 251, 253 Factor-of-curves, 171,173,174,177, 180, 182, 184, 186, 188, 190, 192 Family, 27, 61, 98, 104, 171, 175, 177-186, 188-190, 192, 193 Fixed effect, 21, 30,32,34, 36, 39, 42,45, 49,50, 52, 53, 67, 69, 75, 76, 97, 101, 106109, 111-117, 119, 121125, 127, 129, 131, 135, 136, 142, 144, 146, 149151, 154, 156, 160, 172 Subject Index 108-110, 115-117, 123, 127, 129, 142-144, 147151, 153, 155, 156, 158, 159, 162, 164, 165, 173, 180, 186, 188, 189 Interindividual differences, 149,236 Intraclass correlation, 146 Intraindividual change, 236, 237 Intraindividual variability, 236-238, 254 Known intervention, 203, 227 Heterogeneous, 28,43-45,50,172, 175 Heteroscedasticity, 158 Hierarchical data, 172 Hierarchical linear modeling, 2630,38,39,42-45,47-50, 52,87,105,136,141,~43, 148, 171-174, 176, 184, 185, 188, 189, 193 Homogeneous, 25, 42, 44, 45, 50, 106, 168, 175 Lag, 159, 204-207, 209, 211, 213, 214, 216, 225, 226, 239, 241, 243-246, 248-250, 253-257 Lagged covariance matrix, 248 Latent curve analysis, 59-61, 67, 80, 87 Level-1 model, 32, 36, 38, 43, 44, 49, 50, 53, 141, 148, 149, 156 Level-2 model, 27, 31, 32, 34, 37, 38, 45, 49, 53, 141, 147149, 156, 165 Level-3 model, 53 Linear stationary model, 205 Linear structural equation model, 238 Longitudinal data, 30, 59, 87-89, 92, 94, 95, 97-99, 101, 113, 114, 117, 121, 136, 137, 140, 167, 171-173, 190, 194 Longitudinal data analysis, 87 Lower level, 5-7, 9, 11, 16, 17, 22, 71,73, 79,88,89,94,96, 97 Individual growth model, 29, 135137, 140, 141, 144, 146151, 153, 155, 164, 167, 168, 178, 184, 188 Intercept, 7, 9, 11, 14, 17, 18, 20, 21, 23, 28, 32, 34, 49, 65,66,69-73,75-77,79, Maximum likelihood, 15, 16, 18, 20-23, 26, 28, 54, 111, 112, 122, 154, 173, 180, 186, 192, 210 full information ML, 154,171174, 177, 180, 182-184, 186, 188, 190, 192, 193 Goodness of fit statistic log-likelihood statistic, 154 Schwarz’s Bayesian Criterion, 154, 155, 160, 162, 164 Goodness of fit statistics Akaike’s Information Criterion, 154, 155, 160, 162, 164, 210 Growth curve modeling, 28 Growth function, 75, 190, 193 275 Subject Index restricted information ML, 26, 111, 112, 122, 127, 129, 154 Maximum likelihood estimation, 2, 16, 18, 23, 28,63, 173, 183, 193, 220, 227 Measurement, 4, 27, 30, 62, 63, 65,80,89,90,92,93,97, 98, 103, 104, 110, 113, 119, 137, 141-144, 146, 148, 153, 167, 172, 178, 182, 184, 190, 192, 236, 238, 239, 243, 246 MLwiN, 16, 135, 136, 141, 144, 146, 164 Model building, 208, 216, 219 Model diagnostic checking, 211 Model estimation, 182, 192, 210 Model identification, 178,209, 210, 219 Moving average model, 206, 207, 226 Multilevel, 2-7, 9, 11, 14-16, 2023, 29, 80, 87-91,93, 94, 96-101, 135, 136, 142144, 146, 149, 164, 165, 168, 171-173, 180, 188190, 192, 194 Multilevel Model, 2, 5, 9, 11, 14, 15, 20, 23,88, 89,93, 96, 97, 100, 135, 136, 142, 143, 164, 165, 168 Multilevel modeling, 2-7, 9, 15, 16, 22, 96, 164 MUML, 171, 172, 183 Normal probability plot, 165 Ordinary least squares, 2, 6, 11, 14, 15, 18-23, 165, 204 Person-level covariate, 136, 151, 155, 158 Person-level data set, 137, 140 Person-level predictor, 11, 147, 148, 150 Person-period data set, 137, 140, 144, 147, 151, 168 PROC MIXED, 23,100,122,123, 129, 135-137, 141, 143, 144, 148, 149, 154, 156, 159, 164, 165, 168 class statement, 143, 151, 167 model statement, 17, 123,143, 144, 149, 150, 156, 165, 167 random statement, 123, 129, 143, 144, 149-151, 159, 162, 168 Process, 60, 61, 73, 74, 76, 8892, 95, 99, 112, 124, 125, 131, 204, 208, 211, 213, 216, 219, 227, 235, 237, 239, 245, 251, 253, 254, 257 Proportionality constraint, 253 Qualitative difference, 192 Random effect, 4, 11, 14, 29, 31, 33,45, 52, 53, 69, 71, 75, 76, 106, 107, 110, 111, 113-117, 121, 124, 125, 136, 142, 144, 146, 147, 149-151, 153-156, 160, 162, 173, 174, 184, 185, 194 Reading recognition, 62, 63, 6668, 72-74, 76, 77, 79 Regression model, 16, 23, 36, 38, 53, 105, 144, 203, 204, 218, 221, 222, 226 Repeated measures, 1, 2, 5, 14, 22, 26, 29, 45, 50, 59, 66-69, 71, 74, 76, 80, 87, 89,97,103-105,113-116, 119, 131, 135, 172, 177179, 181, 182, 192 Repeated measures data, 5, 14, 22, 50, 59, 68, 80, 89, 105, 113, 131, 135, 178 276 Residual, 4, 27-29, 31, 33, 3739, 45, 49, 52, 65, 70, 77,92,94,106,108-111, 116, 117, 127, 129, 142, 144, 150, 158, 159, 164, 165, 178, 179, 182, 193, 204, 211, 216, 220, 226, 227, 250, 255-257 Rochester Interaction Record, 2, SAS, 14-16, 18, 90, 100, 112, 113, 122, 123, 127, 129, 135, 136, 140, 143, 144, 146, 149, 150, 156, 159, 160, 162, 168 Scale invariance, 18, 20 Secondary intervention, 231 Structural equation modeling, 2730,36,44, 59, 65,68,80, 97, 172, 173, 180, 182, 183, 192, 193, 238, 239 Test score, 237 Three-level model, 29,47, 167, 174, 184, 185, 188 Time series, 26-28, 30, 38, 52, 89, 203-214, 218-222, 225227, 231, 235, 236, 238, 239, 241, 243, 244, 251, 253, 257 Time varying covariate, 72 Trading day variation, 221 Two level model, 27-29, 36, 44, 47, 53 Unbalanced data, 5, 15, 173, 180, 183, 186, 190 Unconditional growth model, 149, 153 Unconditional means model, 141144, 147, 149, 153 Uniqueness, 241, 243, 244, 248, 253 Upper level, 5-7, 9, 14-18,88, 89, 94-97 Subject Index Variance component, 23, 87, 9597,99-101,111-114,116, 117, 119, 121, 123, 129, 141, 142, 146, 149, 153, 158, 172 Weighted least squares, 2, 15-23 Within level, 181 Within slope, 18, 19, 23, 182 Within structure, 181 Within-person variability, 153 WNFS Model, 243-246,248,250, 251, 253-257 ... Modeling of Repeated Measures Data: Latent Curve Analysis Patrick J Curran and Andrea M Hussong 59 Multilevel Modeling of Longitudinal and Functional Data J Ramsay 87 Analysis of Repeated Measures. .. Equation Modeling with AMOS, by B Byrne (2001) Conducting Meta-Analysis Using SAS, co-authored by W Arthur, Jr., W Bennett, Jr., and A I Juffcutt (2001) Modeling Intraindividual Variability with Repeated. .. (Northwestern University), and Steve West (Arizona State University) Modeling Intraindividual Variability with Repeated Measures Data: Methods and Applications Edited by D S Moskowitz M cGill University