A latent curve analysis of unobserved heterogeneity in university achievements


  • Silvia Bianconcini Alma Mater Studiorum - Università di Bologna
  • Silvia Cagnone Alma Mater Studiorum - Università di Bologna
  • Stefania Mignani Alma Mater Studiorum - Università di Bologna
  • Paola Monari Alma Mater Studiorum - Università di Bologna




The aim of this paper is to analyze the academic achievement of a cohort of students enrolled in 2001 at the Faculty of Economics of the University of Bologna by using a latent growth model for longitudinal data. The basic idea of this approach is that individuals differ in their growth over time according to a continuous underlying or latent trajectory.

Random coefficients in the model allow each individual to have a different trajectory. Latent growth models can be incorporated in the Structural Equation Models (SEMs) framework by viewing the random coefficients as latent variables. Hence model identification and estimation are performed according to the conventions of the SEM analysis.

The effects of different covariates in the student temporal behavior is also evaluated.


T.W. ANDERSON, (1963), The use of factor analysis in the statistical analysis of multiple time series,

Psychometrika, 28, pp. 1-25.

M. ARELLANO, (2003), Panel data econometrics, Oxford University press.

G.A. BAKER, (1954), Factor analysis of relative growth, Growth, 18, pp. 137-143.

K.A. BOLLEN, (1989), Structural equations with latent variables, Wiley, New York.

K.A BOLLEN, P.J.CURRAN, (2006), Latent curve models: a structural equation perspective, New York:John Wiley and Sons.

K.A. BOLLEN, J.S LONG, (1993), Testing structural equation models, Newbury Park, CA: Sage.

M.W. BROWNE, S.H.C. DU TOUT, (1991), Models for learning data. In L.M. Collins and J.L. Horn (eds.), Best methods for the analysis of change, pp. 47-68, Washington D.C.: American psychological association.

A.S. BRYK, S.W.RAUDENBUSH, (1989), Towards a more appropriate conceptualization of research on school effects: a three-level hierarchical linear model. In R.D. Bock (ed.), Multilevel analysis of educational data (pp. 159-204), San Diego, CA: Academic press.

P.J. DIGGLE, K.Y. LIANG, S.L. ZEGER, (1994), Analysis of longitudinal data, Oxford: Clarendon press.

M. FEDER, G. NATHAN, D. PFEFFERMAN, (2000), Multilevel model-ing of complex survey longitudinal data with time varying random effects, 20, Survey methodology, vol. 26, n. 1, pp. 53-65.

H. GOLDSTEIN, (2003), Multilevel statistical models (3rd edition), New York: Halstead.

R.E. KIRK, (1982), Experimental design: procedures for the behavioral sciences, 2nd ed., Monterey, CA: Brooks/Cole.

A. LEWBEL, (2006), Modeling heterogeneity,Working paper, Boston College.

J.J. MCARDLE, (1988), Dynamic but structural equation modeling of repeated measures data. In J. R. Nesselroade and R.B. Cattel (eds.), The handbook of multivariate experimental psychology, 2nd ed., pp. 561-614, NewYork: Plenum press.W.

MEREDITH, J. TISAK, (1990), Latent curve analysis, Psychometrika, 55, 1, pp. 107-122.

R.O. MUELLER, (1996), Basic principles of structural equation modeling, Springer-Verlag, New York.

B. MUTHÉN, D. KAPLAN, M. HOLLIS (1987), On structural equation modeling with data that are not missing completely at random. Psychometrika, 42, pp. 431-462.

B. MUTHÉN, S.T. KHOO (1998), Longitudinal Studies of Achievement Growth Using Latent Variable Modeling, Learning and Individual Differences, 10 (2), pp. 73-101.

C.R. RAO, (1958), Some statistical methods for comparison of growth curves, Biometrics, 14, pp. 1-17.

D.R. ROGOSA, J.B. WILLETT, (1985), Understanding correlates of change by modeling individual differences in growth, Psychometrika, 50, pp. 203-228.

C.J. SKINNER, D. HOLMES, (1999), Random effects models for longitudinal survey data, paper presented at the Conference on analysis of survey data, Southampton, United Kingdom.

J.D. SINGER, J.B .WILLETT, (2004), Applied longitudinal data analysis: modeling change and event occurence, New York: Oxford University press.

A. SKRONDAL, S. RABE-HESKET, (2004), Generalized latent variable modeling: multilevel longitudinal and structural equation models. Boca Raton, FL: Chapman and Hall/CRC.

J.M. WOOLDRIDGE, (2000), Econometric analysis of cross section and panel data, Cambridge: MIT press.

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


How to Cite

Bianconcini, S., Cagnone, S., Mignani, S., & Monari, P. (2007). A latent curve analysis of unobserved heterogeneity in university achievements. Statistica, 67(1), 55–67. https://doi.org/10.6092/issn.1973-2201/3497