| Title: | Cosine-Correlation Coefficient for Vector Variables |
| Version: | 1.0.0 |
| Description: | Computes the cosine-correlation coefficient for measuring the degree of linear dependence among variables in a multidimensional context. The package implements the generalized cosine-correlation theorem for p-1 variables, providing a quantitative assessment of interrelationships within experimental frameworks. This methodology extends classical correlation measures to higher-dimensional spaces using a dimensional exploration approach based on time scale calculus. |
| License: | MIT + file LICENSE |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.3.3 |
| Imports: | stats |
| Suggests: | knitr, rmarkdown, testthat (≥ 3.0.0) |
| VignetteBuilder: | knitr |
| NeedsCompilation: | no |
| Packaged: | 2025-12-09 14:04:21 UTC; mehmet.cankaya |
| Author: | Mehmet Niyazi Cankaya [aut, cre] |
| Maintainer: | Mehmet Niyazi Cankaya <mehmet.cankaya@usak.edu.tr> |
| Repository: | CRAN |
| Date/Publication: | 2025-12-15 17:50:06 UTC |
Cosine-Correlation Coefficient Computation
Description
Computes the cosine-correlation coefficient for a vector of p-1 variables, measuring the degree of linear dependence among variables in a multidimensional context.
Usage
cosCorr(x, na.rm = FALSE)
Arguments
x |
A numeric vector of length p >= 2, where x[1] should be 0 (representing t_1). The remaining elements x[2], x[3], ..., x[p] represent the p-1 variables (t_2, t_3, ..., t_p). |
na.rm |
Logical. If TRUE, NA values are removed before computation. Default is FALSE. |
Details
The cosine-correlation coefficient is defined as:
\rho_{p-1} = \frac{(p-1) \prod_{i=2}^{p} |t_i|}{\sum_{i=2}^{p} |t_i|^{p-1}}
where t_1 = 0 and t_2, \ldots, t_p are the variables within the system.
The coefficient serves as a measure of the degree of linear dependence among
the p-1 variables, providing a quantitative assessment of their interrelationships
within a multidimensional context.
Value
A numeric value representing the cosine-correlation coefficient
\rho_{p-1}.
The coefficient ranges from 0 to 1, where higher values indicate greater
linear dependence among the variables.
Examples
# Example 1: Simple vector
x <- c(0, 2, 3, 4)
cosCorr(x)
# Example 2: Vector with 5 variables
x <- c(0, 1, 2, 3, 4, 5)
cosCorr(x)