Growth Curve Analysis in Contemporary Psychological Research

The term “growth curve” is used to describe data where: (1) the same entities are repeatedly observed, (2) the same procedures of measurement and scaling of observations are used, and (3) the timing of the observations is known. Growth curves are now common in many areas of psychological research, and some of these are presented here. The term “growth curve analysis” denotes the processes of describing, testing hypotheses, and making scientific inferences about the growth and change patterns in a wide range of time-related phenomena. In this sense, growth curve analyses are a specific form of the larger set of developmental and longitudinal research methods, but the unique features of growth data permit unique kinds of analyses. Formal models for the analysis of growth curves which have been developed in many different substantive domains are described here in five sections: (1) An introduction to growth curves, (2) linear models of growth, (3) multiple groups in growth curve models, (4) aspects of dynamic theory for growth models, and (5) multiple variables in growth curve analyses. We conclude with a discussion of future issues raised by the current growth models. Keywords: growth curves; latent growth models; longitudinal data analysis; mixed models; multilevel models; nonlinear models

[1]  John O. Kangas,et al.  Intelligence at middle age: A thirty-eight year follow-up. , 1971 .

[2]  D. Hedeker,et al.  MIXOR: a computer program for mixed-effects ordinal regression analysis. , 1996, Computer methods and programs in biomedicine.

[3]  Nan M. Laird,et al.  Using the General Linear Mixed Model to Analyse Unbalanced Repeated Measures and Longitudinal Data , 1997 .

[4]  J. Nelder The Fitting of a Generalization of the Logistic Curve , 1961 .

[5]  J. Horn,et al.  A practical and theoretical guide to measurement invariance in aging research. , 1992, Experimental aging research.

[6]  T. Raykov Are Simple Change Scores Obsolete? An Approach to Studying Correlates and Predictors of Change , 1999 .

[7]  John B. Willett,et al.  Understanding correlates of change by modeling individual differences in growth , 1985 .

[8]  S. Embretson The new rules of measurement. , 1996 .

[9]  John B. Willett,et al.  Using covariance structure analysis to detect correlates and predictors of individual change over time , 1994 .

[10]  Terry E. Duncan,et al.  Modeling the processes of development via latent variable growth curve methodology , 1995 .

[11]  J. Mcardle,et al.  Two – Latent Variable Growth Models for Research on Aging , 1990 .

[12]  K. Bradway,et al.  Intelligence at adulthood: A twenty-five year follow-up. , 1962 .

[13]  J. Tisak,et al.  Longitudinal Models of Reliability and Validity: A Latent Curve Approach , 1996 .

[14]  John J. McArdle,et al.  Perspectives on Mathematical/Statistical Model Building (MASMOB) in research on aging. , 1980 .

[15]  S. Stigler,et al.  Regression Toward the Mean and the Study of Change , 1980 .

[16]  R. Darrell Bock,et al.  Statistical Problems of Fitting Individual Growth Curves , 1980 .

[17]  R. Scammon The first seriatim study of human growth , 1927 .

[18]  C. A. McGilchrist,et al.  Stochastic Growth Curve Analysis , 1979 .

[19]  J. Mcardle Structural Models of Developmental Theory in Psychology , 1991 .

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

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

[22]  Donald Hedeker,et al.  Application of random-efiects pattern-mixture models for miss-ing data in longitudinal studies , 1997 .

[23]  R Cudeck,et al.  Mixed-effects Models in the Study of Individual Differences with Repeated Measures Data. , 1996, Multivariate behavioral research.

[24]  J J McArdle,et al.  Age-based construct validation using structural equation modeling. , 1992, Experimental aging research.

[25]  Ledyard R Tucker,et al.  Determination of parameters of a functional relation by factor analysis , 1958 .

[26]  K. Lange,et al.  Extensions to pedigree analysis III. Variance components by the scoring method , 1976, Annals of human genetics.

[27]  J J McArdle,et al.  Latent growth curves within developmental structural equation models. , 1987, Child development.

[28]  Roel Bosker,et al.  Modeled Variance in Two-Level Models , 1994 .

[29]  J J McArdle,et al.  Structural Factor Analysis Experiments with Incomplete Data. , 1994, Multivariate behavioral research.

[30]  Daniel S. Nagin,et al.  Analyzing developmental trajectories: A semiparametric, group-based approach , 1999 .

[31]  J. Mcardle,et al.  Best methods for the analysis of change: Recent advances, unanswered questions, future directions. , 1991 .

[32]  F. J. Richards A Flexible Growth Function for Empirical Use , 1959 .

[33]  James A. Stimson,et al.  Interpreting Polynomial Regression , 1978 .

[34]  D. W. Zimmerman,et al.  Are Simple Gain Scores Obsolete? , 1996 .

[35]  R. Potthoff,et al.  A generalized multivariate analysis of variance model useful especially for growth curve problems , 1964 .

[36]  Fitting Generalized Allometric Models to Multivariate Growth Data , 1984 .

[37]  L. Bertalanffy Quantitative Laws in Metabolism and Growth , 1957 .

[38]  John Wishart,et al.  GROWTH-RATE DETERMINATIONS IN NUTRITION STUDIES WITH THE BACON PIG, AND THEIR ANALYSIS , 1938 .

[39]  J. Mcardle Dynamic but Structural Equation Modeling of Repeated Measures Data , 1988 .

[40]  J R Nesselroade,et al.  "SOMETIMES, IT'S OKAY TO FACTOR DIFFERENCE SCORES"-THE SEPARATION OF STATE AND TRAIT ANXIETY. , 1974, Multivariate behavioral research.

[41]  D. Simonton,et al.  Age and Creative Productivity: Nonlinear Estimation of an Information-Processing Model , 1989, International journal of aging & human development.

[42]  R. Cattell,et al.  Structural Equation Models of Factorial Invariance in Parallel Proportional Profiles and Oblique Confactor Problems. , 1994, Multivariate behavioral research.

[43]  J. Mcardle,et al.  Alternative common factor models for multivariate biometric analyses , 1990, Behavior genetics.

[44]  C. R. Rao,et al.  Some statistical methods for comparison of growth curves. , 1958 .

[45]  Bengt Muthén,et al.  General Longitudinal Modeling of Individual Differences in Experimental Designs: A Latent Variable Framework for Analysis and Power Estimation , 1997 .

[46]  H. Buschke,et al.  Cross-sectional and longitudinal relationships among age, cognition, and processing speed. , 1999, Psychology and aging.

[47]  M. Baines,et al.  A new family of mathematical models describing the human growth curve. , 1978, Annals of human biology.

[48]  J. Horn,et al.  A contemporary method for developmental‐genetic analyses of age changes in intellectual abilities , 1998 .

[49]  J J McArdle,et al.  Modeling incomplete longitudinal and cross-sectional data using latent growth structural models. , 1992, Experimental aging research.

[50]  J. Horn,et al.  STATE, TRAIT AND CHANGE DIMENSIONS OF INTELLIGENCE , 1972 .

[51]  H. V. Roberts [Statisticians Can Matter]: Rejoinder , 1978 .

[52]  S G West,et al.  Putting the individual back into individual growth curves. , 2000, Psychological methods.

[53]  S. Wright The Method of Path Coefficients , 1934 .

[54]  S. Boker,et al.  Statistical vector field analysis applied to mixed cross-sectional and longitudinal data. , 1995, Experimental aging research.

[55]  L. Cronbach,et al.  How we should measure "change": Or should we? , 1970 .

[56]  John J. McArdle,et al.  Expanding test–retest designs to include developmental time-lag components. , 1997 .