Methodological Advances in the Analysis of Individual Growth With Relevance to Education Policy

The purpose of this article is to demonstrate how recent methodological developments in the analysis of individual growth can inform important problems in education policy. Specifically, this article focuses on a method referred to as growth mixture modeling. Growth mixture modeling is a relatively new procedure for the analysis of longitudinal data that relaxes many of the assumptions associated with conventional growth curve modeling. In particular, growth mixture modeling tests for the existence of unique growth trajectory classes through a combination of latent class analysis and standard growth curve modeling. Antecedent predictors of the latent classes can be incorporated as well as relations from the latent classes to specific outcomes. This article applies growth mixture modeling to data from the Early Childhood Longitudinal Study-Kindergarten class of 1998-1999. The specific policy question posed in this article focuses on the estimation of latent growth trajectory classes in reading proficiency and the effects of full-day or part-day kindergarten programs on growth within reading trajectory classes. Results identify a 3-class solution corresponding to slow-developing, normal-developing, and fast-developing reading growth in children. The results further show that full-day kindergarten attendance benefits children in the slow-reading development class relative to the normal and fast-reading development class, but the effect is lessened when holding constant socioeconomic status and age of entry into kindergarten. The implications of the method for quantitative education policy analysis are also discussed.

[1]  Jerry West,et al.  America's Kindergartners: Findings from the Early Childhood Longitudinal Study, Kindergarten Class of 1998-99, Fall 1998. , 2000 .

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

[3]  Dominic F. Gullo The Long Term Educational Effects of Half‐Day vs Full‐Day Kindergarten , 2000 .

[4]  S. Mulaik,et al.  Foundations of Factor Analysis , 1975 .

[5]  Bengt Muthén,et al.  Second-generation structural equation modeling with a combination of categorical and continuous latent variables: New opportunities for latent class–latent growth modeling. , 2001 .

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

[7]  L. Shepard,et al.  What Doesn't Work: Explaining Policies of Retention in the Early Grades. , 1987 .

[8]  J. Vermunt Latent Class Models , 2004 .

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

[10]  Bengt Muthén,et al.  Analysis of reading skills development from kindergarten through first grade: An application of growth mixture modeling to sequential processes , 2002 .

[11]  K. Jöreskog A General Method for Estimating a Linear Structural Equation System. , 1970 .

[12]  James Elicker,et al.  What do they do all day? Comprehensive evaluation of a full-day kindergarten , 1997 .

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

[14]  John B. Willett,et al.  Questions and Answers in the Measurement of Change , 1988 .

[15]  B. Muthén BEYOND SEM: GENERAL LATENT VARIABLE MODELING , 2002 .

[16]  S. Kagan Readiness 2000: Rethinking Rhetoric and Responsibility , 2000 .

[17]  Bengt Muthén,et al.  Modeling of Intervention Effects With Noncompliance: A Latent Variable Approach for Randomized Trials , 2001 .

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

[19]  Michael W. Browne,et al.  Best methods for the analysis of change: Recent advances, unanswered questions, future directions. , 1991 .

[20]  B. Muthén Latent Variable Mixture Modeling , 2001 .

[21]  A. Basilevsky,et al.  Factor Analysis as a Statistical Method. , 1964 .

[22]  David Rogosa,et al.  A growth curve approach to the measurement of change. , 1982 .

[23]  Joseph A. Fusaro,et al.  The Effect of Full-Day Kindergarten on Student Achievement: A Meta-Analysis. , 1997 .