Self-determination theorySelf-Determination Theory (SDT), introduced by Deci and Ryan, is a popular theory of motivationMotivation. 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 SDTSelf-Determination Theory. 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 internalizationInternalizationand simplex structureSimplex structure, the author recapitulates the convex decompositionConvex decomposition, or constrained regressionConstrained regression, model and assembles the computation steps of the convex quadratic programQuadratic 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 motivationMotivation continuum, and simplex structureSimplex structureof motivationMotivation. The idea is to consider a linear orderLinear order on the set of regulations, take the induced geodesic distanceGeodesic distance, form a linear motivational structureLinear motivational structure, and posit that these distances, as measure of closeness, are compatible with the shares of the convex decompositionConvex decomposition model. By examples, the author shows how the method can be used for the exploratory data analysis of simplex structureSimplex 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 internalizationInternalization of introjected regulation, which was more strongly external motivationMotivation in the outdoor program. The simplex structureSimplex structureof SDTSelf-Determination Theory 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 internalizationInternalization and simplex of the package SDT were used for computations of the internalization shares and simplex structureSimplex structure shares, respectively. Finally, this chapter concludes with a few general ideas about the motivation theory and with personal suggestions for modifications of it.


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