Student Mobility in Multilevel Growth Modeling: A Multiple Membership Piecewise Growth Model

ABSTRACT This study proposes a new model, termed the multiple membership piecewise growth model (MM-PGM), to handle individual mobility across clusters frequently encountered in longitudinal studies, especially in educational research wherein some students could attend multiple schools during the course of the study. A real data set containing some students who switched elementary schools was used to demonstrate and explain the MM-PGM. Parameter and model fit differences were compared between the MM-PGM and two other techniques for handling student mobility: the first school-PGM, which only used school membership at the first measurement occasion, and the delete-PGM, which removed mobile students from the analysis. Results indicated that the three approaches of handling mobile students led to different conclusions about the impact of school-level predictors of growth parameters and the school-level variability in the growth rates. Furthermore, deleting mobile students altered the impact of student-level predictors compared to the other two approaches.

[1]  William J. Browne,et al.  Bayesian and likelihood-based methods in multilevel modeling 1 A comparison of Bayesian and likelihood-based methods for fitting multilevel models , 2006 .

[2]  A. O'connell,et al.  Growing readers : A hierarchical linear model of children's reading growth during the first 2 years of school , 2006 .

[3]  Harvey Goldstein,et al.  Modelling the effect of pupil mobility on school differences in educational achievement , 2007 .

[4]  David G Steel,et al.  Ignoring a Level in a Multilevel Model: Evidence from UK Census Data , 2001 .

[5]  Gregory J. Palardy.  The Multilevel Crossed Random Effects Growth Model for Estimating Teacher and School Effects: Issues and Extensions , 2010 .

[6]  Yih-Ing Hser,et al.  Piecewise growth curve modeling approach for longitudinal prevention study , 2004, Comput. Stat. Data Anal..

[7]  Oi-Man Kwok,et al.  Please Scroll down for Article Multivariate Behavioral Research the Impacts of Ignoring a Crossed Factor in Analyzing Cross-classified Data , 2022 .

[8]  K. Mengersen,et al.  Latent class piecewise linear trajectory modelling for short-term cognition responses after chemotherapy for breast cancer patients , 2010 .

[9]  Risto Lethonen.  Multilevel Statistical Models (3rd ed.) , 2005 .

[10]  Stephen W. Raudenbush,et al.  A Crossed Random Effects Model for Unbalanced Data With Applications in Cross-Sectional and Longitudinal Research , 1993 .

[11]  Jacob E. Cheadle.  Educational Investment, Family Context, and Children's Math and Reading Growth from Kindergarten Through the Third Grade , 2008 .

[12]  Cornelia M. Ashby.  K-12 Education: Many Challenges Arise in Educating Students Who Change Schools Frequently. Report to Congressional Requesters. GAO-11-40. , 2010 .

[13]  Nikki L. Aikens,et al.  Socioeconomic Differences in Reading Trajectories: The Contribution of Family, Neighborhood, and School Contexts. , 2008 .

[14]  Mylien T. Duong,et al.  Twelve-Month Outcomes of a Randomized Trial of the Positive Thoughts and Action Program for Depression Among Early Adolescents , 2016, Prevention Science.

[15]  D. Betsy McCoach,et al.  Using Time-Varying Covariates in Multilevel Growth Models , 2010, Front. Psychology.

[16]  Barbara J Lehman,et al.  Effectively Analyzing Change over Time in Laboratory Research on Stress and Health: A Multilevel Modeling Approach , 2015 .

[17]  Patrick Onghena,et al.  The Effects of Ignoring a Level in Multilevel Analysis , 2005 .

[18]  Michael J. Kieffer.  Converging Trajectories , 2011 .

[19]  Hgoldstein A.H.leyland.  Multilevel modeling of health statistics , 2013 .

[20]  George Leckie,et al.  The complexity of school and neighbourhood effects and movements of pupils on school differences in models of educational achievement , 2009 .

[21]  Audrey J. Leroux,et al.  Estimation of a Latent Variable Regression Growth Curve Model for Individuals Cross-Classified by Clusters , 2018, Multivariate behavioral research.

[22]  S Natasha Beretvas,et al.  Incorporating Student Mobility in Achievement Growth Modeling: A Cross-Classified Multiple Membership Growth Curve Model , 2010, Multivariate behavioral research.

[23]  Mirjam Moerbeek,et al.  The Consequence of Ignoring a Level of Nesting in Multilevel Analysis , 2004, Multivariate behavioral research.

[24]  S. N. Beretvas,et al.  A Comparison of Techniques for Handling and Assessing the Influence of Mobility on Student Achievement , 2017 .

[25]  Mark Wilson,et al.  Incorporating Mobility in Growth Modeling for Multilevel and Longitudinal Item Response Data , 2016, Multivariate behavioral research.

[26]  Craig K. Enders,et al.  Centering predictor variables in cross-sectional multilevel models: a new look at an old issue. , 2007, Psychological methods.

[27]  Andrew Thomas,et al.  The BUGS project: Evolution, critique and future directions , 2009, Statistics in medicine.

[28]  Cengiz Zopluoglu,et al.  Longitudinal mathematics development of students with learning disabilities and students without disabilities: a comparison of linear, quadratic, and piecewise linear mixed effects models. , 2015, Journal of school psychology.

[29]  Jacob E. Cheadle.  Parent educational investment and children’s general knowledge development , 2009 .

[30]  M. Plummer.  Penalized loss functions for Bayesian model comparison. , 2008, Biostatistics.

[31]  S Natasha Beretvas,et al.  The Impact of Inappropriate Modeling of Cross-Classified Data Structures , 2006, Multivariate behavioral research.

[32]  D. Rubin,et al.  Inference from Iterative Simulation Using Multiple Sequences , 1992 .

[33]  S. Natasha Beretvas,et al.  The Impact of Using Incorrect Weights With the Multiple Membership Random Effects Model , 2014 .

[34]  Andrew Thomas,et al.  WinBUGS - A Bayesian modelling framework: Concepts, structure, and extensibility , 2000, Stat. Comput..

[35]  Michelle Najarian,et al.  Early Childhood Longitudinal Study, Kindergarten Class of 2010-11 (ECLS-K:2011). User's Manual for the ECLS-K:2011 Kindergarten Data File and Electronic Codebook, Public Version. NCES 2015-074. , 2015 .

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

[37]  Sarah Depaoli,et al.  Just Another Gibbs Sampler (JAGS) , 2016 .

[38]  S. Natasha Beretvas,et al.  A comparison of procedures for handling mobility and missing level-2 identifiers in two-level data , 2014 .

[39]  Oi-Man Kwok,et al.  The Consequences of Ignoring Individuals' Mobility in Multilevel Growth Models , 2012 .

[40]  Debbie L. Hahs-Vaughn,et al.  Head Start Program Quality: Examination of Classroom Quality and Parent Involvement in Predicting Children's Vocabulary, Literacy, and Mathematics Achievement Trajectories. , 2012 .

[41]  Karen E. Rambo-Hernandez,et al.  High-Achieving and Average Students’ Reading Growth: Contrasting School and Summer Trajectories , 2015 .

[42]  William J. Browne,et al.  Modelling non-hierarchical structures , 2001 .

[43]  Li Cai,et al.  Consequences of Unmodeled Nonlinear Effects in Multilevel Models , 2009 .

[44]  Bradley P. Carlin,et al.  Bayesian measures of model complexity and fit , 2002 .

[45]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[46]  Hyewon Chung,et al.  The impact of ignoring multiple membership data structures in multilevel models. , 2009, The British journal of mathematical and statistical psychology.

[47]  Jon Rasbash,et al.  Cross-Classified and Multiple Membership Models† , 2014 .

[48]  Audrey J. Leroux,et al.  Estimating a Three-Level Latent Variable Regression Model With Cross-Classified Multiple Membership Data , 2018 .

[49]  Fuzhong Li,et al.  Piecewise Growth Mixture Modeling of Adolescent Alcohol Use Data , 2001 .