The repository contains three files:
1. **helpers.R** - an R script with two functions (the Spearman-Brown prophecy formula, the function for data simulation).
2. **r_range.R** - the **main function** that estimates plausible and admissible reliability coefficients.
3. **simulation and examples.R** - an script with examples and the simulation study from the associated paper.
**An example of r_range function graphical results**
> r_range(mat=mat1, plot. = T, rel=T, true1=la, true2=lb, p1=.5, legend=T, itemplot = T)
@[osf](bsm6q)
**Example of the text output:**
> r_range(mat=mat1, plot. = T, rel=T, true1=la, true2=lb, p1=.5, legend=T, itemplot = T)
$r_admissible
min max
0.667 0.750
$r_plausible
max
0.667 0.683
$loadings
lambda1 lambda2
min.admissible 0.707 0.707
min.plausible 0.856 0.856
optimal.load 1.000 1.000
max.admissible 1.168 1.168
max.plausible 1.414 1.414
optimal.length 0.500 0.500
optimal.ratio 1.000 1.000
$true
[1] 0.75
$r
lambda4 sb rAF beta r_H
0.667 0.667 0.667 0.667 0.667
$admissible
lambda4 sb rAF beta r_H
TRUE TRUE TRUE TRUE TRUE
$plausible
lambda4 sb rAF beta r_H
TRUE TRUE TRUE TRUE TRUE
**Annotation of results:**
- *r_admissible* - boundaries of the admissible reliability range.
- *r_plausible* - boundaries of the plausible reliability range.
- loadings:
- *min.admissible*, *max.admissible* - boundaries of factor loadings (1st and 2nd item), given the admissible reliability.
- *min.plausible*, *max.plausible* - the same for the plausible reliability.
- *optimal load* - loadings estimated using the Angoff-Feltd approach.
- *optimal length* - optimal item lengths as used by the Angoff-Feltd coefficient.
- *optimal ratio* - optimal test lengths as the ratio of lam1/lam2 with a mean(lam1, lam2) = 1.
- *true* - true reliability (if true factor loadings provided).
- *r* - traditional point reliability estimates (*lambda4* is Cronbach alpha, *sb* is Spearman-Brown reliability, *rAF* is Angoff-Feltd coefficient, *beta* is Raju beta, and *r_H* is Horst formula).
- *admissible*, *plausible* - TRUE/FALSE, if the particular coefficient is within the admissible/plausible reliability range.
