Suggested Readings in

Longitudinal Data Analysis

Below I’ve listed a number of rather broad topics that are often encountered in longitudinal data analysis, and with each section I’ve provided a few citations that might be of interest for further reading. This list is by no means exhaustive, and the inclusion or exclusion of any given paper is to be taken as a reflection of absolutely nothing. This is simply a partial listing of some of the papers that we have found helpful in my own research group, and they may or may not be helpful to you as well. This is very much a work in progress, and I update it when the mood strikes me.

 

Overviews of traditional analysis of longitudinal data:

Rogosa, D.R. (1995). Myths and methods: "Myths about longitudinal research" plus supplemental questions. In J. Gottman (Ed.), The Analysis of Change, (pp. 2-65). New Jersey: Lawrence Erlbaum Associates.

Willett, J.B. (1988).  Measuring change: The difference score and beyond.  In H.J. Walberg and G. D. Haertel (Eds.), The International Encyclopedia of Educational Evaluation. Oxford, England: Pergamon Press.

Willett, J.B., Singer, J.D., & Martin, N.C. (1998). The design and analysis of longitudinal studies of development and psychopathology in context: Statistical models and methodological recommendations. Development and Psychopathology, 10, 395-426.

 

Early developments in growth curve modeling:

Gompertz, B.  (1825).  On the nature of the function expressive of the law of human mortality.  Philosophical Transactions of the Royal Society, 115, 513-583.

Rao, C. R. (1958). Some statistical models for comparison of growth curves. Biometrics, 14, 1-17.

Rogosa, D., & Willett, J.B. (1985). Satisfying simplex structure is simpler than it should be. Journal of Educational Statistics, 10, 99-107.

Rogosa, D. & Willett, J.B. (1985).  Understanding correlates of change by modeling individual differences in growth.  Psychometrika, 50, 203-228.

Tucker, L. R (1958). Determination of parameters of a functional relation by factor analysis. Psychometrika, 23, 19-23.

Wishart, J. (1938).  Growth rate determination in nutrition studies with bacon pig and their analysis.  Biometrika, 30, 16-28.

 

Core developments in latent curve modeling (LCM):

McArdle, J. J. (1986). Latent growth within behavior genetic models. Behavioral Genetics, 16, 163-(200.

McArdle, J. J. (1988). Dynamic but structural equation modeling of repeated measures data. In R. B. Cattell & J. Nesselroade (Eds.), Handbook of multivariate experimental psychology (2nd ed., pp. 561-614). New York: Plenum Press.

McArdle, J. J. (1989). Structural modeling experiments using multiple growth functions. In P. Ackerman, R. Kanfer & R. Cudeck (Eds.), Learning and Individual Differences: Abilities, Motivation, and Methodology (pp. 71-117). Hillsdale, NJ: Lawrence Erlbaum Associates Inc

McArdle, J. J. & Epstein, D. (1987). Latent growth curves within developmental structural equation models. Child Development, 58, 110-133.

Meredith, W., & Tisak, J. (1984). "Tuckerizing" curves. Paper presented at the annual meeting of the Psychometric Society, Santa Barbara, CA.

Meredith, W., & Tisak, J. (1990). Latent curve analysis. Psychometrika, 55, 107-122.

Muthén, B. (1991). Analysis of longitudinal data using latent variable models with varying parameters. In L. M. Collins & J. L. Horn (Eds.), Best Methods for the Analysis of Change: Recent Advances, Unanswered Questions, Future Directions. Washington, D.C: APA.

 

Text books and general overviews of latent curve modeling:

Bollen, K.A., & Curran, P.J. (2006). Latent Curve Models: A Structural Equation Approach. Wiley Series on Probability and Mathematical Statistics.

Curran, P. J., & Hussong, A. M. (2002). Structural equation modeling of repeated measures data. In D. Moskowitz & S. Hershberger (Eds.), Modeling Intraindividual Variability with Repeated Measures Data: Methods and Applications (pp. 59-86). New York: Erlbaum Associates.

Curran, P. J., & and Hussong, A. M. (2003). The use of latent trajectory models in psychopathology research. Journal of Abnormal Psychology, 112, 526-544.

Duncan, T. E., Duncan, S. C., Strycker, L. A., Li, F., & Alpert, A. (1999). An Introduction to Latent Variable  Growth Curve Modeling: Concepts, Issues, and Applications. Mahwah NJ: Lawrence Erlbaum Associates.

Muthén, B. O., & Curran, P. J. (1997). General longitudinal modeling of individual differences in experimental designs: A latent variable framework for analysis and power estimation. Psychological Methods, 2, 371–402.

 

Core developments and overviews of multilevel growth models:

Bryk, A. S., & Raudenbush, S. W. (1987). Application of Hierarchical Linear Models to Assessing Change. Psychological Bulletin, 101, 147-158.

Laird, N. M. and Ware, J. H.(1982). Random-effects models for longitudinal data. Biometrics, 38, 963-974.

Raudenbush, S. W. (2001). Toward a coherent framework for comparing trajectories of individual change. In L. Collins and A. Sayer (Eds.), Best Methods for Studying Change (pp. 33-64). Washington, DC: The American Psychological Association.

Singer, J. D. and Willett, J. B. (2003). Applied Longitudinal Data Analysis: Modeling Change and Event Occurrence. Oxford: Oxford University Press.

Willett., J. B., Singer, J. and Martin, N. C. (1998). The Design and Analysis of Longitudinal Studies of Development and Psychopathology in Context: Statistical Models and Methodological Recommendations. Development and Psychopathology, 10, 395-426.

 

Relationship between latent curve models and multilevel growth models:

Bauer, D.J. (2003). Estimating multilevel linear models as structural equation models. Journal of Educational and Behavioral Statistics, 28, 134-167.

Curran, P.J. (2003). Have multilevel models been structural equation models all along? Multivariate Behavioral Research, 38, 529-569.

MacCallum, R. C., Kim, C., Malarkey, W., & Kiecolt-Glaser, J. (1997). Studying Multivariate Change Using Multilevel Models and Latent Curve Models. Multivariate Behavioral Research, 32, 215-253.

Raudenbush, S. W. (2001). Toward a coherent framework for comparing trajectories of individual change. In L. M. Collins & A. G. Sayer (Eds.) New methods for the analysis of change. Washington, DC: American Psychological Association.

Rovine, M. J., & Molenaar, P. C. M. (2000). A structural modeling approach to a multilevel random coefficients model. Multivariate Behavioral Research, 35(1), 51-88.

Rovine, M. J., & Molenaar, P. C. M. (2001). A structural equations modeling approach to the general linear mixed model. In L. M. Collins & A. G. Sayer (Eds.) New methods for the analysis of change. Washington, DC: American Psychological Association.

Willett, J. B., & Sayer, A. G. (1994). Using covariance structure analysis to detect correlates and predictors of individual change over time. Psychological Bulletin, 116(2), 363-381.

 

Interactions in growth models:

Bauer, D.J., & Curran, P.J. (2005). Probing interactions in fixed and multilevel regression: Inferential and graphical techniques. Multivariate Behavioral Research, 40, 373-400.

Curran, P.J., Bauer, D.J., & Willoughby, M.T. (2004). Testing and probing main effects and interactions in latent curve analysis. Psychological Methods, 9, 220-237.

Curran, P.J., Bauer, D.J, & Willoughby, M.T. (2006). Testing and probing interactions in hierarchical linear growth models. In C.S. Bergeman & S.M. Boker (Eds.), The Notre Dame Series on Quantitative Methodology,  Volume 1: Methodological Issues in Aging Research (pp.99-129). Mahwah, NJ: Lawrence Erlbaum Associates.

Tate, R. (2004). Interpreting hierarchical linear and hierarchical generalized slopes as outcomes. The Journal of Experimental Education, 73, 71-95.

 

Multivariate growth models:

Bollen, K.A., & Curran, P.J. (2004). Autoregressive latent trajectory (ALT) models: A synthesis of two traditions. Sociological Methods and Research, 32, 336-383.

Curran, P. J., & Bollen, K. A. (2001). The best of both worlds: Combining autoregressive and latent curve models. In L. M. Collins, & A. G. Sayer (Eds.), New methods for the analysis of change. Washington, DC: American Psychological Association.

MacCallum, R. C., Kim, C., Malarkey, W. B., & Kiecolt-Glaser, J. K. (1997). Studying multivariate change using multilevel models and latent curve models. Multivariate Behavioral Research, 32(3), 215-253.

McArdle, J. J. (2001). A latent difference score approach to longitudinal dynamic structural analysis. In Cudeck, R., du Toit, S. H. C., & Joreskog, K. G. (Eds), Structural equation modeling: Present and future (pp. 341-380). Lincolnwood, IL: Scientific Software.

Raudenbush, S. W., Johnson, C., & Sampson, R. J. (2003). A multivariate multilevel Rasch model with application to self-reported criminal behavior. Sociological Methodology, 33, 169-212.

Raudenbush, S.W.., Rowan, B., & Kang, S-J. (1991). A Multilevel, Multivariate Model for Studying School Climate with Estimation Via the EM Algorithm and Application to U.S. High-School Data. Journal of Educational Statistics. 16(4): 295-330.

 

Alternative measures of time and the effects of re-coding time:

Biesanz, J.C., Deeb-Sossa, N., Aubrecht, A.M., Bollen, K.A., & Curran, P.J. (2004). The role of coding time in estimating and interpreting growth curve models. Psychological Methods, 9(1), 30-52.

Mehta, P. D., & West, S. G. (2000). Putting the individual back into individual growth curves. Psychological Methods, 5(1), 23-43.

 

Multiple indicator latent factors and measurement invariance:

Chan, D. (1998). The conceptualization and analysis of change over time: An integrative approach incorporating longitudinal mean and covariance structures analysis (LMACS) and multiple indicator latent growth modeling (MLGM). Organizational Research Methods, 1, 421 -- 483.

Cheung, G. W., & Rensvold, R. B. (1999). Testing factorial invariance across groups: A reconceptualization and proposed new method. Journal of Management, 25, 1-27.

Cheung, G. W., & Rensvold, R. B. (2002). Evaluating goodness-of-fit indexes for testing measurement invariance. Structural Equation Modeling, 9, 233-255.

Hancock, G. R., Kuo, W., & Lawrence, F. R. (2001). An illustration of second-order latent growth models. Structural Equation Modeling, 8, 470 -- 489.

McArdle, J. J., & Catell, R. B. (1994). Structural equation models of factorial invariance in parallel proportional profiles and oblique confactor problems. Multivariate Behavioral Research, 29, 63-113.

Meredith, W. (1964). Notes on factorial invariance. Psychometrika, 29, 177 – 185.

Meredith, W. (1993). Measurement invariance, factor analysis and factorial invariance. Psychometrika, 58, 525-543.

Meredith, W. & Horn, J. L. (2001). The role of factorial invariance in modeling growth and change. In L. M. Collins & A. G. Sayer (Eds.), New methods for the analysis of change (pp. 203 – 240). Washington DC: American Psychological Association.

Horn, J. L., & McArdle, J. J. (1992). A practical and theoretical guide to measurement invariance in aging research. Experimental Aging Research, 18(3), 117-144.

Joreskog, K. G. (1971). Simultaneous factor analysis in several populations. Psychometrika, 36, 409-426.

Vandenberg, R. J., & Lance, C. E. (2000). A review and synthesis of the measurement invariance literature: Suggestions, practices, and recommendations for organizational research. Organizational Research Methods, 3, 4- 69.

 

Non-linear growth models:

Browne, M. W. (1993). Structured latent curve models. In C. M. Cuadras & C. R. Rao (Eds.), Multivariate analysis: Future directions 2 (pp. 171-197). Amsterdam, The Netherlands: Elsevier-North Holland.

Browne, M. W., & Du Toit, S. H. C. (1991). Models for learning data. In L. M. Collins & J. L. Horn (Eds.) Best methods for the analysis of change. Washington, DC: American Psychological Association.

Davidian, M., & Giltinan, D.M. (1995). Nonlinear Models for Repeated Measurement Data. CRC Press.

Hipp, J., Bauer, D.J., Curran, P. J. & Bollen, K. A. (2004). Crimes of opportunity or crimes of emotion: Testing two explanations of seasonal change in crime. Social Forces, 82, 1333-1372.

Vonesh, EF, Chinchilli, VM (1997). Linear and Nonlinear Models for the Analysis of Repeated Measurements. New York, NY: Marcel Dekker.

Zeger, S.L., Liang, K-Y, Albert, P.S. (1988). Models for Longitudinal Data: A Generalized Estimating Equation Approach. Biometrics, 44(4): 1049-1060.

Zeger, S.L., & Liang, K-Y. (1986). Longitudinal Data Analysis for Discrete and Continuous Outcomes. Biometrics, 42(1): 121-130.

 

Multiple group growth models:

McArdle, J.J. (1989). Structural modeling experiments using multiple growth functions.  In P. Ackerman, R. Kanfer & R. Cudeck (Eds.), Learning and individual differences: Abilities, Motivation and Methodology (pp. 71-117).  Hillsdale, NJ: Lawrence Erlbaum Associates.

 

Muthen, B. O., & Curran, P. J. (1997). General longitudinal modeling of individual differences in experimental designs: A latent variable framework for analysis and power estimation. Psychological Methods, 2(4), 371-402.

 

Finite mixture models:

Arminger, G., Stein, P. & Wittenberg, J. (1999). Mixtures of conditional mean- and covariance-structure models. Psychometrika, 64, 475-494.

Bauer, D.J., & Curran, P.J. (2003a). Distributional assumptions of growth mixture models: Implications for overextraction of latent trajectory classes. Psychological Methods, 8, 338-363.

Bauer, D.J., & Curran, P.J. (2003b). Overextraction of latent trajectory classes: Much ado about nothing? Psychological Methods, 8, 384-393.

Bauer, D.J., & Curran, P.J. (2004). The integration of continuous and discrete latent variable models: Potential problems and promising opportunities. Psychological Methods, 9, 3-29.

Jedidi, K., Jagpal, H. S. & DeSarbo, W. S. (1997).  Finite-mixture structural equation models for response-based segmentation and unobserved heterogeneity.  Marketing Science, 16, 39-59.

Muthén, B., & Shedden, K. (1999). Finite mixture modeling with mixture outcomes using the EM algorithm. Biometrics, 55, 463-469.

Muthén, B. O., & Muthén, L. K. (2000). Integrating person-centered and variable-centered analyses: Growth Mixture Modeling with Latent Trajectory Classes. Alcoholism: Clinical and Experimental Research, 24, 882-891.

Muthén, B.O. (2001a). Second-generation structural equation modeling with a combination of categorical and continuous latent variables: New opportunities for latent class/latent growth modeling. In Collins, L.M. & Sayer, A. (Eds.), New Methods for the Analysis of Change (pp. 291-322). Washington, D.C.: APA.

Muthén, B.O. (2001b). Latent variable mixture modeling. In G. A. Marcoulides & R. E. Schumacker (Eds.), New Developments and Techniques in Structural Equation Modeling (pp. 1-33). Lawrence Erlbaum Associates.

Muthén, B. O. (2002). Beyond SEM: General latent variable modeling. Behaviormetrika, 29, 81-117.

Nagin, D. (1999). Analyzing developmental trajectories: A semi-parametric, group-based approach. Psychological Methods, 4, 139-157.

Nagin, D., & Tremblay, R. (2001). Analyzing developmental trajectories of distinct but related behaviors: A group-based method. Psychological Methods, 6, 18-34.

Nagin, D. S. (2005). Group-based modeling of development. Cambridge, MA Harvard University Press.

 

Growth models with discrete repeated measures:

Muthén, B.O. (1996). Growth modeling with binary responses. In A. V. Eye, & C. Clogg (Eds.), Categorical Variables in Developmental Research: Methods of Analysis (pp. 37-54). San Diego, CA: Academic Press.

 

Missing Data

Allison, P. D. (1987). Estimation of Linear Models with Incomplete Data.  In C. Clogg (Ed.), Sociological Methodology 1987 (pp. 71-103). Washington, DC: American Sociological Association.

Allison, P. D. (2000). Multiple Imputation for Missing Data.  Sociological Methods & Research 28: 301-309.

Allison, P.D. (2001). Missing Data. Newbury Park, CA, US: Sage Publications, Inc.

Arbuckle, J.L. (1996). Full information estimation in the presence of incomplete data. In G.A. Marcoulides and R.E. Schumaker (Eds.), Advanced Structural Equation Modeling: Issues and Techniques, pp. 243-278. Lawrence Erlbaum Associates: Mahwah, NJ.

Rubin, D.B. (1976). Inference and Missing Data. Biometrika 63: 581-592.

Rubin, D.B. (1987). Multiple Imputation for Nonresponse in Surveys.  New York:  Wiley.

Schafer, J.L. (1997). Analysis of Incomplete Multivariate Data.  London: Chapman & Hall.

Schafer, J.L. (1999) Multiple imputation: A primer. Statistical Methods in Medical Research, 8, 3–15.

 

Statistical power and sample size:

Snijders, T. A. B. and Bosker, R. J. (1993). Standard errors and sample sizes for two-level research. Journal of Educational Statistics, 18, 237-259.

Raudenbush, S. W. (1997). Statistical analysis and optimal design for cluster randomized trials. Psychological Methods, 2, 173-185.

Raudenbush, S. W. and Liu, X. (2000). Statistical power and optimal design for multisite randomized trials. Psychological Methods, 5, 199-213.