### 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 language | English |
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Pages (from-to) | 217-231 |

Number of pages | 15 |

Journal | Applied Developmental Science |

Volume | 19 |

Issue number | 4 |

DOIs | |

State | Published - Oct 2 2015 |

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## Cite this

*Applied Developmental Science*,

*19*(4), 217-231. https://doi.org/10.1080/10888691.2015.1021924