| Type: | Package |
| Title: | Inference on the Overlap Coefficient: The Binormal Approach and Alternatives |
| Version: | 0.1.0 |
| Maintainer: | Alba M. Franco-Pereira <albfranc@ucm.es> |
| Description: | Provides functions to construct confidence intervals for the Overlap Coefficient (OVL). OVL measures the similarity between two distributions through the overlapping area of their distribution functions. Given its intuitive description and ease of visual representation by the straightforward depiction of the amount of overlap between the two corresponding histograms based on samples of measurements from each one of the two distributions, the development of accurate methods for confidence interval construction can be useful for applied researchers. Implements methods based on the work of Franco-Pereira, A.M., Nakas, C.T., Reiser, B., and Pardo, M.C. (2021) <doi:10.1177/09622802211046386>. |
| License: | GPL-2 |
| Encoding: | UTF-8 |
| Language: | en-US |
| LazyData: | true |
| RoxygenNote: | 7.2.3 |
| Imports: | ks |
| Depends: | R (≥ 2.10) |
| Suggests: | testthat (≥ 3.0.0) |
| Config/testthat/edition: | 3 |
| NeedsCompilation: | no |
| Packaged: | 2023-11-12 16:53:32 UTC; Alba |
| Author: | Alba M. Franco-Pereira [aut, cre, cph], Christos T. Nakas [aut], Benjamin Reiser [aut], M.Carmen Pardo [aut] |
| Repository: | CRAN |
| Date/Publication: | 2023-11-13 17:43:18 UTC |
OVL.BCAN
Description
Parametric approach using a bootstrap-based approach to estimate the variance
Usage
OVL.BCAN(x, y, alpha = 0.05, B = 100, h_ini = -0.6)
Arguments
x |
controls |
y |
cases |
alpha |
confidence level |
B |
bootstrap size |
h_ini |
initial value in the optimization problem |
Value
confidence interval
Examples
controls = rnorm(50,6,1)
cases = rnorm(100,6.5,0.5)
OVL.BCAN (controls,cases)
OVL.BCPB
Description
Parametric approach using a bootstrap percentil approach to estimate the variance
Usage
OVL.BCPB(x, y, alpha = 0.05, B = 100, h_ini = -0.6)
Arguments
x |
controls |
y |
cases |
alpha |
confidence level |
B |
bootstrap size |
h_ini |
initial value in the optimization problem |
Value
confidence interval
Examples
controls = rnorm(50,6,1)
cases = rnorm(100,6.5,0.5)
OVL.BCPB (controls,cases)
OVL.BCbias
Description
Parametric approach using a bootstrap bias-corrected approach
Usage
OVL.BCbias(x, y, alpha = 0.05, B = 100, h_ini = -0.6)
Arguments
x |
controls |
y |
cases |
alpha |
confidence level |
B |
bootstrap size |
h_ini |
initial value in the optimization problem |
Value
confidence interval
Examples
controls = rnorm(50,6,1)
cases = rnorm(100,6.5,0.5)
OVL.BCAN (controls,cases)
OVL.D
Description
Parametric approach using the delta method
Usage
OVL.D(x, y, alpha = 0.05)
Arguments
x |
controls |
y |
cases |
alpha |
confidence level |
Value
confidence interval
Examples
controls = rnorm(50,6,1)
cases = rnorm(100,6.5,0.5)
OVL.D (controls,cases)
OVL.DBC
Description
Parametric approach using the delta method after the Box-Cox transformation
Usage
OVL.DBC(x, y, alpha = 0.05, h_ini = -0.6)
Arguments
x |
controls |
y |
cases |
alpha |
confidence level |
h_ini |
initial value in the optimization problem |
Value
confidence interval
Examples
controls = rnorm(50,6,1)
cases = rnorm(100,6.5,0.5)
OVL.DBC (controls,cases)
OVL.DBCL
Description
Parametric approach using the delta method after the Box-Cox transformation taking into account the variability of the estimated transformation parameter
Usage
OVL.DBCL(x, y, alpha = 0.05, h_ini = -0.6)
Arguments
x |
controls |
y |
cases |
alpha |
confidence level |
h_ini |
initial value in the optimization problem |
Value
confidence interval
Examples
controls = rnorm(50,6,1)
cases = rnorm(100,6.5,0.5)
OVL.DBCL (controls,cases)
OVL.K
Description
Kernel approach estimating the variance via bootstrap
Usage
OVL.K(x, y, alpha = 0.05, B = 100, k = 1, h = 1)
Arguments
x |
controls |
y |
cases |
alpha |
confidence level |
B |
bootstrap size |
k |
kernel. When k=1 (default value) the kernel used in the estimation is the Gaussian kernel. Otherwise, the Epanechnikov kernel is used instead. |
h |
bandwidth. When h=1 (default value) the cross-validation bandwidth is chosen. Otherwise, the bandwidth considered by Schmid and Schmidt (2006) is used instead. |
Value
confidence interval
Examples
controls = rnorm(50,6,1)
cases = rnorm(100,6.5,0.5)
OVL.K (controls,cases)
OVL.KPB
Description
Kernel approach using a bootstrap percentile approach
Usage
OVL.KPB(x, y, alpha = 0.05, B = 100, k = 1, h = 1)
Arguments
x |
controls |
y |
cases |
alpha |
confidence level |
B |
bootstrap size |
k |
kernel. When k=1 (default value) the kernel used in the estimation is the Gaussian kernel. Otherwise, the Epanechnikov kernel is used instead. |
h |
bandwidth. When h=1 (default value) the cross-validation bandwidth is chosen. Otherwise, the bandwidth considered by Schmid and Schmidt (2006) is used instead. |
Value
confidence interval
Examples
controls = rnorm(50,6,1)
cases = rnorm(100,6.5,0.5)
OVL.KPB (controls,cases)
OVL.LogitBCAN
Description
BCAN procedure carried out in the logit scale and back-transformed
Usage
OVL.LogitBCAN(x, y, alpha = 0.05, B = 100, h_ini = -0.6)
Arguments
x |
controls |
y |
cases |
alpha |
confidence level |
B |
bootstrap size |
h_ini |
initial value in the optimization problem |
Value
confidence interval
Examples
controls = rnorm(50,6,1)
cases = rnorm(100,6.5,0.5)
OVL.LogitBCAN (controls,cases)
OVL.LogitD
Description
Parametric approach using the delta method after switching to a logit scale and then transforming back
Usage
OVL.LogitD(x, y, alpha = 0.05)
Arguments
x |
controls |
y |
cases |
alpha |
confidence level |
Value
confidence interval
Examples
controls = rnorm(50,6,1)
cases = rnorm(100,6.5,0.5)
OVL.LogitD (controls,cases)
OVL.LogitDBC
Description
Parametric approach using the delta method after the Box-Cox transformation after switching to a logit scale and then transforming back
Usage
OVL.LogitDBC(x, y, alpha = 0.05, h_ini = -0.6)
Arguments
x |
controls |
y |
cases |
alpha |
confidence level |
h_ini |
initial value in the optimization problem |
Value
confidence interval
Examples
controls = rnorm(50,6,1)
cases = rnorm(100,6.5,0.5)
OVL.LogitDBC (controls,cases)
OVL.LogitDBCL
Description
Parametric approach using the delta method after the Box-Cox transformation in the logit scale and back-transformed considering the variability of the estimated transformation parameter
Usage
OVL.LogitDBCL(x, y, alpha = 0.05, h_ini = -0.6)
Arguments
x |
controls |
y |
cases |
alpha |
confidence level |
h_ini |
initial value in the optimization problem |
Value
confidence interval
Examples
controls = rnorm(50,6,1)
cases = rnorm(100,6.5,0.5)
OVL.LogitDBCL (controls,cases)
OVL.LogitK
Description
Kernel approach estimating the variance via bootstrap in the logit scale and back-transformed
Usage
OVL.LogitK(x, y, alpha = 0.05, B = 100, k = 1, h = 1)
Arguments
x |
controls |
y |
cases |
alpha |
confidence level |
B |
bootstrap size |
k |
kernel. When k=1 (default value) the kernel used in the estimation is the Gaussian kernel. Otherwise, the Epanechnikov kernel is used instead. |
h |
bandwidth. When h=1 (default value) the cross-validation bandwidth is chosen. Otherwise, the bandwidth considered by Schmid and Schmidt (2006) is used instead. |
Value
confidence interval
Examples
controls = rnorm(50,6,1)
cases = rnorm(100,6.5,0.5)
OVL.LogitK (controls,cases)
Auxiliary function
Description
Evaluates an auxiliary function
Usage
U(mu1, mu2, sigma1, sigma2)
Arguments
mu1 |
sample mean of a vector x |
mu2 |
sample mean of a vector y |
sigma1 |
sample standard deviation of a vector x |
sigma2 |
sample standard deviation of a vector y |
Value
evaluation of an auxiliary function
Examples
U(1,2,1,1)
Epanechnikov kernel
Description
Evaluates the Epanechnikov kernel
Usage
kernel.e(u)
Arguments
u |
vector of observations |
Value
evaluation of the Epanechnikov kernel
Examples
x = rnorm(100,1,2)
kernel.e(x)
Epanechnikov kernel density estimation
Description
Estimates the density function using the Epanechnikov kernel
Usage
kernel.e.density(data, points, h)
Arguments
data |
vector of observations |
points |
in which the function is evaluated |
h |
bandwidth |
Value
density estimation
Examples
x = rnorm(100,1,2)
gridd = seq(-5,5,length.out=1000)
h = (4/3)^(1/5)*sd(x)*length(x)^(-1/5)
kernel.e.density (x,gridd,h)
Gaussian kernel
Description
Evaluates the Gaussian kernel
Usage
kernel.g(u)
Arguments
u |
vector of observations |
Value
evaluation of the Gaussian kernel
Examples
x = rnorm(100,1,2)
kernel.g(x)
Gaussian kernel density estimation
Description
Estimates the density function using the Gaussian kernel
Usage
kernel.g.density(data, points, h)
Arguments
data |
vector of observations |
points |
in which the function is evaluated |
h |
bandwidth |
Value
density estimation
Examples
x = rnorm(100,1,2)
gridd = seq(-5,5,length.out=1000)
h = (4/3)^(1/5)*sd(x)*length(x)^(-1/5)
kernel.g.density (x,gridd,h)
Likelihood function of the BoxCox transformation
Description
Computation of the likelihood function of the BoxCox transformation
Usage
likbox(h, data, n)
Arguments
h |
parameter of the Box-Cox transformation |
data |
joint vector of controls (first) and cases |
n |
length of the vector of controls |
Value
the likelihood function of the BoxCox transformation
Examples
h=-1.6
controls=rnorm(50,6,1)
cases=rnorm(100,6.5,0.5)
likbox(h,c(controls,cases),n=length(controls))
Sample variance computation
Description
Computes the sample variance of a vector of observations
Usage
ssdd(x)
Arguments
x |
vector of observations |
Value
the sample variance
Examples
x = rnorm(100,1,2)
ssdd(x)
Simulated data with normal distributions to showcase the CI'S Overlap Coefficient (OVL) calculation
Description
Contains controls and cases data from normal distributions
Usage
data(test_data)
Format
A data frame with 100 rows and 2 variables:
- controls
Simulated data from a N(10,1)distribution for the control group
- cases
Simulated data from a N(10.5,0.5)distribution for the case group
References
This data set was artificially created for the OVL.CI package.
Examples
data(test_data)