## Abstract

Self-determination theory (SDT), introduced by Deci and Ryan, is a popular theory of motivation. Applications of SDT are numerous and include areas like health care, health professions education, and digital health. Over the recent years, the author published a series of quantitative papers on SDT. To the author’s knowledge, these contributions have remained relatively unrecognized in the SDT community. However, the methodology developed therein can be useful to the field. With the present work, the author reviews, exemplifies with data, and mathematically describes that methodology, in a coherent manner. The focus of this chapter is on computational as well as mathematical aspects. For the investigation of motivation internalization and simplex structure, the author recapitulates the convex decomposition, or constrained regression, model and assembles the computation steps of the convex quadratic program. The author also contributes to the mathematical foundations of the methodology. In particular, mathematical definitions are proposed for the in SDT important concepts of theoretical closeness of regulations, cumulative internalities of regulations along the motivation continuum, and simplex structure of motivation. The idea is to consider a linear order on the set of regulations, take the induced geodesic distance, form a linear motivational structure, and posit that these distances, as measure of closeness, are compatible with the shares of the convex decomposition model. By examples, the author shows how the method can be used for the exploratory data analysis of simplex structure. In particular, for a given intermediate regulation, the author employs the method to estimate the theoretically closer regulation of the two neighbor regulations, contiguous to it. In addition, the technique was applied in a systematic empirical study. The study compared science teaching in a classical school class versus an expeditionary outdoor program. Succinctly, the main results of this study are recapped. In the internal and external shares of identified regulation, the science teaching formats did not differ. The teaching formats differed in the internalization of introjected regulation, which was more strongly external motivation in the outdoor program. The simplex structure of SDT could basically be supported in the study data. The statistical computing and graphics environment R is powerful. Throughout this chapter, computations were made in R, with the package SDT. The functions internalization and simplex of the package SDT were used for computations of the internalization shares and simplex structure shares, respectively. Finally, this chapter concludes with a few general ideas about the motivation theory and with personal suggestions for modifications of it.

Original language | English |
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Title of host publication | Accounting, Finance, Sustainability, Governance and Fraud |

Publisher | Springer Nature |

Pages | 129-154 |

Number of pages | 26 |

DOIs | |

State | Published - 2023 |

### Publication series

Name | Accounting, Finance, Sustainability, Governance and Fraud |
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Volume | Part F2015 |

ISSN (Print) | 2509-7873 |

ISSN (Electronic) | 2509-7881 |

## Keywords

- Amotivation
- Basic psychological needs
- Constrained regression
- Convex decomposition
- Geodesic distance
- Indeterminacy in closeness
- Internalization
- Linear motivational structure
- Linear order
- Motivation
- Quadratic program
- R
- Self-determination theory
- Simplex structure