Longitudinal Data Analyses Using Linear Mixed Models in SPSS: Concepts, Procedures and Illustrations

Although different methods are available for the analyses of longitudinal data, analyses based on generalized linear models (GLM) are criticized as violating the assumption of independence of observations. Alternatively, linear mixed models (LMM) are commonly used to understand changes in human behavior over time. In this paper, the basic concepts surrounding LMM (or hierarchical linear models) are outlined. Although SPSS is a statistical analyses package commonly used by researchers, documentation on LMM procedures in SPSS is not thorough or user friendly. With reference to this limitation, the related procedures for performing analyses based on LMM in SPSS are described. To demonstrate the application of LMM analyses in SPSS, findings based on six waves of data collected in the Project P.A.T.H.S. (Positive Adolescent Training through Holistic Social Programmes) in Hong Kong are presented.

[1]  P. Greenbaum,et al.  Five methods for computing significant individual client change and improvement rates: support for an individual growth curve approach. , 1995, Journal of consulting and clinical psychology.

[2]  N. Way,et al.  Self-Esteem Trajectories among Ethnic Minority Adolescents: A Growth Curve Analysis of the Patterns and Predictors of Change. , 2005 .

[3]  J. Singer,et al.  The design and analysis of longitudinal studies of development and psychopathology in context: Statistical models and methodological recommendations , 1998, Development and Psychopathology.

[4]  Timothy G. Gregoire,et al.  Linear modelling of irregularly spaced, unbalanced, longitudinal data from permanent-plot measurements , 1995 .

[5]  Craig K. Enders,et al.  Using the SPSS Mixed Procedure to Fit Cross-Sectional and Longitudinal Multilevel Models , 2005 .

[6]  Gudela Grote,et al.  A longitudinal study of determinants of perceived employability. , 2010 .

[7]  Patrick Onghena,et al.  An Analysis of WellBeing in Secondary School with Multilevel Growth Curve models and Multilevel Multivariate Models , 2005 .

[8]  William Meredith,et al.  Latent curve analysis , 1990 .

[9]  Chhun-Huor Ung,et al.  A variance-covariance structure to take into account repeated measurements and heteroscedasticity in growth modeling , 2007, European Journal of Forest Research.

[10]  Anthony S. Bryk,et al.  Hierarchical Linear Models: Applications and Data Analysis Methods , 1992 .

[11]  Robert S. Barcikowski,et al.  Statistical Power with Group Mean as the Unit of Analysis , 1981 .

[12]  The Chinese Positive Youth Development Scale , 2007 .

[13]  K. Clarke-Stewart,et al.  Trajectories of externalizing behavior from age 2 to age 9: relations with gender, temperament, ethnicity, parenting, and rater. , 2008, Developmental psychology.

[14]  J. Gill.  Hierarchical Linear Models , 2005 .

[15]  D. Bailey,et al.  Using Growth Curve Analysis to Evaluate Child Change in Longitudinal Investigations , 1994 .

[16]  J. Singer,et al.  Applied Longitudinal Data Analysis , 2003 .

[17]  J. Brooks-Gunn,et al.  Developmental transitions: linking human development with tobacco prevention research. , 1999, Nicotine & tobacco research : official journal of the Society for Research on Nicotine and Tobacco.

[18]  G. A. Marcoulides.  Multilevel Analysis Techniques and Applications , 2002 .

[19]  John B. Willett,et al.  Questions and Answers in the Measurement of Change , 1988 .

[20]  Scott L. Graves,et al.  Multilevel modeling and school psychology: A review and practical example. , 2009 .

[21]  Laurence E. Lynn,et al.  Means and Ends: A Comparative Study of Empirical Methods For Investigating Governance and Performance , 2001 .

[22]  Russell D. Wolfinger,et al.  The Analysis of Repeated Measurements with Mixed-Model Adjusted F Tests , 2004 .

[23]  R. Wolfinger.  Heterogeneous Variance-Covariance Structures for Repeated Measures , 1996 .

[24]  Second Edition,et al.  Statistical Package for the Social Sciences , 1970 .

[25]  S. Raudenbush,et al.  Tests for linkage of multiple cohorts in an accelerated longitudinal design. , 2000, Psychological methods.

[26]  Larry E. Toothaker,et al.  Multiple Regression: Testing and Interpreting Interactions , 1991 .

[27]  Brady T. West,et al.  Linear Mixed Models: A Practical Guide Using Statistical Software , 2006 .

[28]  D. Bates,et al.  Mixed-Effects Models in S and S-PLUS , 2001 .

[29]  R. Bosker.  Boekbespreking van "A.S. Bryk & S.W. Raudenbusch - Hierarchical linear models: Applications and data analysis methods" : Sage Publications, Newbury Parki, London/New Delhi 1992 , 1995 .

[30]  John B. Willett,et al.  Some Results on Reliability for the Longitudinal Measurement of Change: Implications for the Design of Studies of Individual Growth , 1989 .

[31]  Lorne Campbell,et al.  Estimating Actor, Partner, and Interaction Effects for Dyadic Data Using PROC MIXED and HLM: A User–Friendly Guide , 2002 .

[32]  P. Cohen,et al.  Using individual growth model to analyze the change in quality of life from adolescence to adulthood , 2006, Health and quality of life outcomes.

[33]  R. Wolfinger.  Covariance structure selection in general mixed models , 1993 .

[34]  S. Maxwell.  Longitudinal designs in randomized group comparisons : When will intermediate observations increase statistical power ? , 1998 .

[35]  Yuk Fai Cheong,et al.  HLM 6: Hierarchical Linear and Nonlinear Modeling , 2000 .

[36]  Timothy J. Robinson,et al.  Multilevel Analysis: Techniques and Applications , 2002 .

[37]  D. Shek.  Effectiveness of the Tier 1 Program of the Project P.A.T.H.S.: Preliminary Objective and Subjective Outcome Evaluation Findings , 2006, TheScientificWorldJournal.

[38]  D. Shek.  Objective Outcome Evaluation of the Project P.A.T.H.S. in Hong Kong: Findings Based on Individual Growth Curve Models , 2010, TheScientificWorldJournal.

[39]  Cecilia M. S. Ma,et al.  Dimensionality of the Chinese Positive Youth Development Scale: Confirmatory Factor Analyses , 2010 .

[40]  S. Raudenbush,et al.  Application of Hierarchical Linear Models to Assessing Change , 1987 .

[41]  A. Cillessen,et al.  Developmental trajectories of adolescent popularity: a growth curve modelling analysis. , 2006, Journal of adolescence.

[42]  U. Trautwein,et al.  Athletic classmates, physical self-concept, and free-time physical activity: A longitudinal study of frame of reference effects , 2008 .

[43]  D. VanLeeuwen,et al.  A note on the covariance structure in a linear model , 1997 .

[44]  I. Kreft.  Are multilevel techniques necessary?: An overview, including simulation studies , 2005 .

[45]  Robin Mermelstein,et al.  Individual and Contextual Influences on Adolescent Smoking , 2004, Annals of the New York Academy of Sciences.

[46]  Rachel C. F. Sun,et al.  Interim Evaluation of the Secondary 2 Program of Project P.A.T.H.S.: Insights Based on the Experimental Implementation Phase , 2008, TheScientificWorldJournal.

[47]  Stephen W. Raudenbush,et al.  A multivariate hierarchical model for studying psychological change within married couples. , 1995 .

[48]  N M Thompson,et al.  Analysis of change: modeling individual growth. , 1991, Journal of consulting and clinical psychology.

[49]  Jan de Leeuw,et al.  Questioning Multilevel Models , 1995 .

[50]  Valerie LeMay,et al.  MSLS: a linear least squares technique for fitting a simultaneous system of equations with a generalized error structure , 1990 .

[51]  H Goldstein,et al.  Multilevel time series models with applications to repeated measures data. , 1994, Statistics in medicine.

[52]  J. Eccles,et al.  The influence of family relations on trajectories of cigarette and alcohol use from early to late adolescence. , 2011, Journal of adolescence.

[53]  Robert E. Ployhart,et al.  Growth Modeling Using Random Coefficient Models: Model Building, Testing, and Illustrations , 2002 .

[54]  Terry E. Duncan,et al.  An Introduction to Latent Variable Growth Curve Modeling: Concepts, Issues, and Application, Second Edition , 1999 .

[55]  A Villers Ruiz,et al.  Statistical package for the social sciences (spss) , 1981 .

[56]  Judith D. Singer,et al.  Using SAS PROC MIXED to Fit Multilevel Models, Hierarchical Models, and Individual Growth Models , 1998 .

[57]  Theodore A. Walls,et al.  An Introduction to Latent Variable Growth Curve Modeling: Concepts, Issues, and Applications (2nd ed.) , 2007 .

[58]  G. J. Mitchell,et al.  Principles and procedures of statistics: A biometrical approach , 1981 .

[59]  Jaume Arnau,et al.  Using linear mixed models in longitudinal studies: Application of SAS PROC MIXED , 2007 .