sdi: Original and Adjusted SDI or RAI Index
In SDT: Self-Determination Theory Measures

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

sdi computes the original SDI or RAI scoring protocol and an adjusted variant of it.

1 2	sdi(intrinsic_regulation, identified_regulation, introjected_regulation, external_regulation, compute.adjusted = TRUE, minscore = 1)

`intrinsic_regulation, identified_regulation, introjected_regulation, external_regulation`	Required numeric vectors of intrinsic regulation, identified regulation, introjected regulation, and external regulation subscale motivation scores, respectively. No `NA`, `NaN`, `Inf`, or `-Inf` values are allowed.
`compute.adjusted`	An optional logical. The default value `TRUE` corresponds to computing the adjusted variant of the SDI or RAI index, and also allows for setting the argument `minscore`. If set to `FALSE`, the original index value is computed, and the argument `minscore` is irrelevant and ignored in this case.
`minscore`	An optional numeric, integer-valued, giving the minimum score used in the scale procedure (typically 1). See also ‘Details’.

This function provides the popular and original scoring protocol called the self-determination index (SDI), also known as the relative autonomy index (RAI). The version of the used index is for instruments assessing extrinsic motivation (excluding integrated regulation) and intrinsic motivation. With the SDI or RAI, the inventory scores are weighted and combined to give a descriptive overall measure of the behavioral self-regulatory style. The formula is, in respective regulation types:

SDI = RAI = (2 * intrinsic + identified) - (2 * external + introjected).

The original SDI or RAI index does not allow one to account for the extent to which the identified and introjected regulation types are internal and external motivation. In particular, in the process of weighting the subscale scores, the same weights are used (1 or -1, respectively).

Correcting adaptations are proposed to accommodate for mixed or confounded internal and external motivation, implemented in the function sdi. This function also computes an adjusted variant of the original SDI or RAI index, which is weighted according to the extent to which the intermediate identified and introjected regulation types are internal and external motivation. For details, including the mathematical formula for the adjusted measure, see Uenlue (2016).

To compute the adjusted variant measure, sdi calls the function internalization. The latter, in turn, uses the function solve.QP of the package quadprog to solve the corresponding constrained regression optimization problem.

The arguments intrinsic_regulation, identified_regulation, introjected_regulation, and external_regulation do represent aggregate subscale scores calculated by averaging the raw-data test items associated with each of the four subscales (i.e., mean over the items that make up a respective subscale). The four subscales are intrinsic regulation, identified regulation, introjected regulation, and external regulation.

The argument minscore only needs to be specified for the adjusted index variant. Translation with ‘- minscore’ and averaging are applied in the adjusted variant to ensure that the instrument variables and the component and index values all range in the same interval (from 0 to, e.g., 4).

If the arguments intrinsic_regulation, identified_regulation, introjected_regulation, external_regulation, compute.adjusted, and minscore are of required types, sdi returns a named list, of the class sdi and with the attribute variant, which consists of 3 components, independent of whether the original index computation (variant is then set to original) or the adjusted index computation (variant is then set to adjusted) was performed.

The original index computation list contains the following first 3 components, the adjusted index computation list the subsequent 3 components:

`confounded_internal_locus`	A numeric vector of the confounded internal locus original SDI or RAI component values.
`confounded_external_locus`	A numeric vector of the confounded external locus original SDI or RAI component values.
`sdi_original`	A numeric vector of the original SDI or RAI overall index values.
`adjusted_internal_locus`	A numeric vector of the adjusted internal locus adjusted SDI or RAI component values.
`adjusted_external_locus`	A numeric vector of the adjusted external locus adjusted SDI or RAI component values.
`sdi_adjusted`	A numeric vector of the adjusted SDI or RAI overall index values.

Ali Uenlue <ali.uenlue@icloud.com>

Uenlue, A. (2016) Adjusting potentially confounded scoring protocols for motivation aggregation in organismic integration theory: An exemplification with the relative autonomy or self-determination index. Frontiers in Educational Psychology, 7(272), 1–4. URL https://doi.org/10.3389/fpsyg.2016.00272.

The two other main functions of the package: internalization for motivation internalization analysis; simplex for motivation simplex structure analysis. See the methods associated with sdi as the constructor function: plot.sdi, the S3 method for plotting objects of the class sdi; print.sdi, the S3 method for printing objects of the class sdi; summary.sdi, the S3 method for summarizing objects of the class sdi. See also SDT-package for general information about this package.

## attach dataset to search path (so a variable can be accessed by name)
attach(learning_motivation)

## adjusted index computation
adj <- sdi(intrinsic, identified, introjected, external)
## first six elements of each list component vector and attributes
lapply(adj, head)
attributes(adj)

## original index computation
orig <- sdi(intrinsic, identified, introjected, external, compute.adjusted = FALSE)
lapply(orig, head)
attributes(orig)

$adjusted_internal_locus
[1] 1.9666013 0.6611796 1.2663977 1.4860787 1.3610451 0.8580979

$adjusted_external_locus
[1] 2.033399 1.105487 1.150269 1.547255 1.222288 1.225235

$sdi_adjusted
[1] -0.06679746 -0.44430747  0.11612865 -0.06117589  0.13875686 -0.36713743

$names
[1] "adjusted_internal_locus" "adjusted_external_locus"
[3] "sdi_adjusted"           

$variant
[1] "adjusted"

$class
[1] "sdi"

$confounded_internal_locus
[1] 12.50  6.10  9.00 10.45  9.50  6.75

$confounded_external_locus
[1] 11.25  8.00  7.50  9.75  7.50  8.25

$sdi_original
[1]  1.25 -1.90  1.50  0.70  2.00 -1.50

$names
[1] "confounded_internal_locus" "confounded_external_locus"
[3] "sdi_original"             

$variant
[1] "original"

$class
[1] "sdi"