Journal
APPLIED DEVELOPMENTAL SCIENCE
Volume 19, Issue 4, Pages 217-231Publisher
ROUTLEDGE JOURNALS, TAYLOR & FRANCIS LTD
DOI: 10.1080/10888691.2015.1021924
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Funding
- National Institute of Mental Health [K02 MH66249, R29 MH45458]
- National Institute of Child Health and Human Development [P30HD15052]
- William T. Grant Foundation [173096]
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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.
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