Integrating Developmental Theory and Methodology: Using Derivatives to Articulate Change Theories, Models, and Inferences

Pascal R. Deboeck, Jody Nicholson, Chrystyna Kouros, Todd D. Little, Judy Garber

Research output: Contribution to journalArticle

7 Scopus citations

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 of derivatives: the change of a construct with respect to the change 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 zeroth, first, and second derivatives, 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.

Original languageEnglish
Pages (from-to)217-231
Number of pages15
JournalApplied Developmental Science
Volume19
Issue number4
DOIs
StatePublished - Oct 2 2015

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