Multilevel linear modeling (MLM) is a powerful and well-defined tool often used to evaluate time-varying associations between two or more variables measured in longitudinal studies. Such variables carry information about stable, between-person differences as well as information about within-person variability. For emerging adults, this variability figures prominently across a variety of developmental domains. A single variable measured on repeated occasions can be easily summarized into two new variables that represent the unique within- and between-person sources of information contained in the original variable. Well-known procedures for statistically disaggregating time-varying predictors in an MLM are straightforward but often not accessible to a nontechnical readership. Using SAS syntax, this tutorial provides step-by-step instructions to recode a single repeated-measures variable into separate between- and within-person predictor variables. Strategies are suggested for testing and interpreting main effects and interactions in the MLM, drawing on a daily diary example of first-year, first-time college-attending emerging adults.
BauerD. J. (2011). Evaluating individual differences in psychological processes. Current Directions in Psychological Science, 20, 115–118.
4.
BollenK. A.CurranP. J. (2004). Autoregressive latent trajectory models (ALT): A synthesis of two traditions. Sociological Methods and Research, 32, 336–383.
5.
BuboltzW.JrBrownF.SoperB. (2001). Sleep habits and patterns of college students: a preliminary study. Journal of American College Health, 50, 131–135.
6.
CohenJ.CohenP.WestS. G.AikenL. S. (2003). Applied multiple regression/correlation analysis for the behavioral sciences (3rd ed.). Mahwah, NJ: Lawrence Erlbaum.
7.
CurranP. J.BauerD. J. (2011). The disaggregation of within-person and between-person effects in longitudinal models of change. Annual Review of Psychology, 62, 583–619.
8.
CurranP. J.LeeT. H.HowardA. L.LaneS. T.MacCallumR. C. (2012). Disaggregating within-person and between-person effects in multilevel and structural equation growth models. In HarringJ. R.HancockG. R. (Eds.), Advances in longitudinal methods in the social and behavioral sciences (pp. 217–253). Charlotte, NC: Information Age Publishing.
9.
CurranP. J.HowardA. L.BainterS.LaneS. T.McGinleyJ. S. (2014). The separation of between-person and within-person components of individual change over time: A latent curve model with structured residuals. Journal of Consulting and Clinical Psychology, 82, 879–894.
10.
CurranP. J.WilloughbyM. T. (2003). Implications of latent trajectory models for the study of developmental psychopathology. Development and Psychopathology, 15, 581–612.
11.
DavilaJ.KarneyB. R.HallT. W.BradburyT. N. (2003). Depressive symptoms and marital satisfaction: Within-subject associations and the moderating effects of gender and neuroticism. Journal of Family Psychology, 17(4):557–570.
12.
DelwicheL. D.SlaughterS. J. (2012). The little SAS® book: A primer (4th ed.). Cary, NC: SAS Institute, Inc.
13.
DuncanC.JonesK.MoonG. (1998). Context, composition and heterogeneity: Using multilevel models in health research. Social Science & Medicine, 46, 97–117.
14.
DuncanO. D. (1969). Some linear models for two-wave, two-variable panel analysis. Psychological Bulletin, 72, 177–182.
15.
EndersC. K.TofighiD. (2007). Centering predictor variables in cross-sectional multilevel models: A new look at an old issue. Psychological Methods, 12, 121–138. doi:10.1037/1082-989X.12.2.121
16.
FerrerE.McArdleJ. J. (2010). Longitudinal modeling of developmental changes in psychological research. Current Directions in Psychological Science, 19, 149–154.
17.
FlookL.FuligniA. J. (2008). Family and school spillover in adolescents’ daily lives. Child Development, 79(3), 776–787.
18.
GalambosN. L.DaltonA. L.MaggsJ. L. (2009). Losing sleep over it: Daily variation in sleep quantity and quality in Canadian students’ first semester of university. Journal of Research on Adolescence, 19, 741–761.
19.
GrimmK. J. (2007). Multivariate longitudinal methods for studying developmental relationships between depression and academic achievement. International Journal of Behavioral Development, 31, 328–339.
20.
HoffmanL.StawskiR. S. (2009). Persons as contexts: Evaluating between-person and within-person effects in longitudinal analysis. Research in Human Development, 6, 97–120. doi:10.1080/15427600902911189
21.
HofmannD. A.GavinM. B. (1998). Centering decisions in hierarchical linear models: Implications for research in organizations. Journal of Management, 24, 623–641.
KreftI.de LeeuwJ.AikenL. (1995). The effect of different forms of centering in hierarchical linear models. Multivariate Behavioral Research, 30, 1–21.
24.
LaurentH.PowersS. (2007). Emotion regulation in emerging adult couples: Temperament, attachment, and HPA response to conflict. Biological Psychology, 76, 61–71. doi:10.1016/j.biopsycho.2007.06.002
25.
MacCallumR.KimC.MalarkeyW.Kiecolt-GlaserJ. (1997). Studying multivariate change using multilevel models and latent curve models. Multivariate Behavioral Research, 32, 215–254.
26.
MaherJ. P.DoerksenS. E.ElavskyS.HydeA. L.PincusA. L.RamN.ConroyD. E. (2013). A daily analysis of physical activity and satisfaction with life in emerging adults. Health Psychology, 32, 647–656. doi:10.1037/a0030129
27.
MolenaarP. (2004). A manifesto on psychology as idiographic science: Bringing the person back into scientific psychology, this time forever. Measurement: Interdisciplinary Research & Perspective, 2, 201–218.
28.
PaccagnellaO. (2006). Centering or not centering in multilevel models? The role of the group mean and the assessment of group effects. Evaluation Review, 30, 66–85.
29.
PeughJ. L.EndersC. K. (2005). Using the SPSS Mixed procedure to fit cross-sectional and longitudinal multilevel models. Educational and Psychological Measurement, 65, 717–741.
30.
PreacherK. J.CurranP. J.BauerD. J. (2006). Computational tools for probing interactions in multiple linear regression, multilevel modeling, and latent curve analysis. Journal of Educational and Behavioral Statistics, 31, 437–448. doi:10.3102/10769986031004437
31.
RaudenbushS. (1989a). A response to Longford and Plewis. Multilevel Modelling Newsletter, 1, 8–11.
32.
RaudenbushS. (1989b). “Centering” predictors in multilevel analysis: Choices and consequences. Multilevel Modelling Newsletter, 1, 10–12.
33.
RaudenbushS. W.BrykA. S. (2002). Hierarchical linear models: Applications and data analysis methods (2nd ed.). Thousand Oaks, CA: Sage.
SeligJ. P.PreacherK. J. (2009). Mediation models for longitudinal data in developmental research. Research in Human Development, 6, 144–164.
38.
ShiehG. (2011). Clarifying the role of mean centring in multicollinearity of interaction effects. British Journal of Mathematical and Statistical Psychology, 64, 462–477.
39.
SingerJ. D. (1998). Using SAS PROC MIXED to fit multilevel models, hierarchical models, and individual growth models. Journal of Educational and Behavioral Statistics, 24, 323–355.
40.
SingerJ. D.WillettJ. B. (2003). Applied longitudinal data analysis. New York, NY: Oxford University Press.
41.
SnijdersT. A. B.BoskerR. J. (2012). Multilevel analysis: An introduction to basic and advanced multilevel modeling (2nd ed.). Thousand Oaks, CA: Sage.
42.
SterbaS. K.BauerD. J. (2010). Matching method with theory in person-oriented developmental psychopathology research. Development and Psychopathology, 22, 239. doi:10.1017/S0954579410000015
43.
TaylorZ. E.DoaneL. D.EisenbergN. (2014). Transitioning from high school to college: Relations of social support, ego-resiliency, and maladjustment during emerging adulthood. Emerging Adulthood, 2, 105–115.
44.
WangM.-T.DishionT. J.StormshakE. A.WILLETTJ. B. (2011). Trajectories of family management practices and early adolescent behavioral outcomes. Developmental Psychology, 47(5), 1324–1341.
45.
WillettJ. B.SayerA. G. (1995). Cross-domain analyses of change over time: Combining growth modeling and covariance structure analysis. In MarcoulidesG. A.SchumackerR. E. (Eds.), Advanced structural equation modeling: Issues and techniques (pp. 22–51). Hillsdale, NJ: Lawrence Erlbaum.
