title: Integrating developmental theory and methodology: Using derivatives to articulate change theories, models, and inferences.
abstract: Matching theories about growth, development, and change to appropriate statistical models can present a challenge, which can result in misuse, misinterpretation, and underutilization of different analytical approaches. We discuss the use ofderivatives--- the change of a construct with respect to changes in another construct. Derivatives provide a common language linking developmental theory and statistical methods. Conceptualizing change in terms of derivatives allows precise translation of theory into method and highlights commonly overlooked models of change. A wide variety of models can be understood in terms of the level, velocity and acceleration of constructs: the 0th, 1st, and 2ndderivatives, respectively. We introduce the language of derivatives, and highlight the conceptually differing questions that can be addressed in developmental studies. A substantive example is presented to demonstrate how common and unfamiliar statistical methodology can be understood as addressing relations between differing pairs of derivatives.
authors.affiliation: University of Kansas.
authors.forename: Pascal R
authors.initials: PR
authors.lastname: Deboeck
authors.affiliation: University of North Florida.
authors.forename: Jody
authors.initials: J
authors.lastname: Nicholson
authors.affiliation: Southern Methodist University.
authors.forename: Chrystyna
authors.initials: C
authors.lastname: Kouros
authors.affiliation: Texas Tech University.
authors.forename: Todd D
authors.initials: TD
authors.lastname: Little
authors.affiliation: Vanderbilt University.
authors.forename: Judy
authors.initials: J
authors.lastname: Garber
keywords: derivatives; developmental theory; growth curves; hierarchical linear modeling; models of change; theory-method interface