simplex: Motivation Simplex Structure Shares
In SDT: Self-Determination Theory Measures

Description Usage Arguments Details Value Author(s) References See Also Examples

simplex computes the shares of a target regulation type in a reference system consisting of three base regulation types to illustrate the self-determination theory postulated simplex structure of motivation.

1 2	simplex(target_regulation, base_regulation_1, base_regulation_2, base_regulation_3)

`target_regulation`	A required numeric vector of either intrinsic, identified, introjected, or external regulation subscale motivation scores. No `NA`, `NaN`, `Inf`, or `-Inf` values are allowed.
`base_regulation_1, base_regulation_2, base_regulation_3`	Required numeric vectors of, depending on the regulation type specified in `target_regulation`, the remaining three regulation subscale motivation scores. No `NA`, `NaN`, `Inf`, or `-Inf` values are allowed. For an example, see ‘Details’.

This function computes the simplex structure shares of a target motivation (e.g., intrinsic regulation) in a reference system consisting of three base regulation types (e.g., identified regulation, introjected regulation, and external regulation). With the function simplex, the self-determination theory postulated simplex structure can be illustrated, where the simplex structure of the theory means that motivation regulation types theoretically closer to one another are more strongly interrelated/correlated. From a theoretical viewpoint, the simplex structure analysis can be viewed as a generalization of the problem of internalization.

The argument target_regulation, the dependent variable of the constrained regression analysis, can be any regulation type, and the arguments base_regulation_1, base_regulation_2, and base_regulation_3, the independent variables of the constrained regression analysis, do represent the remaining regulation types, with respect to which the optimal shares of the target regulation are computed. The function solve.QP of the package quadprog is applied in simplex to solve the self-determination theory related (convex) quadratic program. For details, see Uenlue and Dettweiler (2015).

If the arguments target_regulation, base_regulation_1, base_regulation_2, and base_regulation_3 are of required types, simplex returns a numeric vector containing the following 3 named components base_regulation_1 share, base_regulation_2 share, and base_regulation_3 share of the target_regulation with respect to the remaining base_regulation_1, base_regulation_2, and base_regulation_3 of the theory. The returned object is of the class share and has the attribute analysis set to have the value simplex.

Ali Uenlue <ali.uenlue@icloud.com>

Uenlue, A. and Dettweiler, U. (2015) Motivation internalization and simplex structure in self-determination theory. Psychological Reports, 117(3), 675–691. URL https://doi.org/10.2466/14.PR0.117c25z1.

The two other main functions of the package: internalization for motivation internalization analysis; sdi for the original and adjusted SDI or RAI index. See the methods associated with simplex as the constructor function: plot.share, the S3 method for plotting objects of the class share; print.share, the S3 method for printing objects of the class share. See also SDT-package for general information about this package.

## attach dataset to search path (to use variable names)
attach(learning_motivation)

## simplex structure analysis with intrinsic regulation as target variable
## and identified, introjected, and external regulation as reference system
(simstr <- simplex(intrinsic, identified, introjected, external))

## numeric vector, attribute value, and class
mode(simstr)
attr(simstr, "analysis")
class(simstr)