| Title: | Interval Estimation by Likelihood Method |
| Version: | 0.1.2 |
| Description: | Currently used CI method has its limitation when the test statistics are asymmetrical (chi-square test, F-test) or the model functions are non-linear. It can be overcome by using the likelihood functions for the interval estimation. 'inteli' package now supports interval estimation for the mean, variance, variance ratio, binomial distribution, Poisson distribution, odds ratio, risk difference, relative risk and their likelihood function plots. Testing functions are also provided. |
| License: | GPL (≥ 3) |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.3.3 |
| Imports: | graphics, stats |
| NeedsCompilation: | no |
| Packaged: | 2025-12-26 02:47:08 UTC; mkim |
| Author: | Minkyu Kim [aut, cre],
Kyun-Seop Bae 
[aut] |
| Maintainer: | Minkyu Kim <mkim@acr.kr> |
| Repository: | CRAN |
| Date/Publication: | 2026-01-08 00:00:08 UTC |
Interval Estimation by Likelihood Method
Description
Parameter estimation via likelihood interval (LI) compared to conventional method (CI).
Details
Currently used CI method has its limitation when the test statistics are asymmetrical (chi-square test, F-test) or the model functions are non-linear. It can be overcome by using the likelihood functions for the interval estimation. 'inteli' package now supports interval estimation for the mean, variance, variance ratio, binomial distribution, Poisson distribution, odds ratio, risk difference, relative risk and their likelihood function plots. Testing functions are also provided.
Author(s)
Maintainer: Minkyu Kim mkim@acr.kr
Authors:
Minkyu Kim mkim@acr.kr
References
Wilks SS. The Large-sample Distribution of the Likelihood Ratio for Testing Composite Hypotheses. Ann Math Stat. 1938;9(1):60-62.
Edwards AWF. Likelihood. 1972.
Fisher RA. Statistical Methods and Scientific Inference. 3e. 1973.
Bates DM, Watts DG. Nonlinear Regression Analysis and its Application. 1988.
Ruppert D, Cressie N, Carroll RJ. A Transformation/Weighting Model for Estimating Michaelis-Menten Parameters. Cornell University Technical Report 796. 1988.
Royall R. Statistical Evidence. 1997.
Pinheiro JC, Bates DM. Mixed Effects Models in S and S-PLUS. 2000.
Pawitan Y. In All Likelihood: Statistical Modelling and Inference Using Likelihood. 2001.
Lehmann EL. Fisher, Nayman, and the Creation of Classical Statistics. 2011.
Rohde CA. Introductory Statistical Inference with the Likelihood Function. 2014.
Held L, Bove DS. Likelihood and Bayesian Inference. 2020.
Lee MH, Bae KS. Likelihood interval for nonlinear regression. 2023.
Likelihood Interval for Probability of Single Sample from Binomial Distribution
Description
Likelihood interval for probability of single sample assuming binomial distribution. Likelihood function plot is also shown. For faster calculation speed, plot option '0' is recommended.
Arguments
event |
number of events from observed data; a numeric vector |
total |
total number of trials from observed data; a numeric vector |
plot |
likelihood function plots by LI; default is "all" |
conf.level |
confidence level for the interval estimation |
eps |
machine epsilon value; default is 1e-08 |
k |
cutoff value for likelihood interval. If not specified, F-test is used. |
Value
demo |
basic demographics of data |
LI |
estimated interval of probability (y/n) by LI |
CI |
estimated interval of probability (y/n) by CI |
plot |
likelihood-related plots |
Author(s)
Kyun-Seop Bae <k@acr.kr>, Minkyu Kim <mkim@acr.kr>
Examples
lib(8, 10)
Likelihood Interval for Mean of Single Sample from Normal Distribution
Description
Likelihood interval for mean of single sample assuming normal distribution. Likelihood function plot is also shown. Likelihood function plot is also shown. For faster calculation speed, plot option '0' is recommended.
Arguments
data |
a numeric vector of data values; mandatory |
plot |
likelihood function plots by LI; default is "all". 'OBJ', 'O1', '1' is objective function plot; 'OFV', 'O2', '2' is log likelihood function plot; 'LRT', 'O3', '3' is log LRT function plot. |
conf.level |
confidence level for the interval estimation |
df |
degree of freedom for likelihood interval; default is 1 |
k |
cutoff value for likelihood interval. If not specified, F-test is used. |
Value
demo |
basic demographics of data |
LI |
estimated interval of mean by LI |
CI |
estimated interval of mean by CI |
plot |
likelihood-related plots |
Author(s)
Kyun-Seop Bae <k@acr.kr>, Minkyu Kim <mkim@acr.kr>
Examples
lim(rnorm(20, 0, 1))
Likelihood Interval for Odds Ratio of 2-by-2 Contingency Table.
Description
Likelihood interval for odds ratio of 2-by-2 contingency table. Likelihood function plot is also shown. For faster calculation speed, plot option '0' is recommended.
Arguments
exposure.O_event.O |
a numeric vector of exposure (+) and event (+), 'a' of 2-by-2 table; mandatory |
exposure.O_TOTAL |
a numeric vector of exposure (+), 'a' + 'b' of 2-by-2 table; mandatory |
exposure.X_event.O |
a numeric vector of exposure (-) and event (-), 'c' of 2-by-2 table; mandatory |
exposure.X_TOTAL |
a numeric vector of exposure (-), 'c' + 'd' of 2-by-2 table; mandatory |
plot |
likelihood function plots by LI; default is "all". 'OBJ', 'O1', '1' is objective function plot; 'OFV', 'O2', '2' is log likelihood function plot; 'LRT', 'O3', '3' is log LRT function plot. |
conf.level |
confidence level for the interval estimation |
eps |
machine epsilon value; default is 1e-08 |
k |
cutoff value for likelihood interval. If not specified, F-test is used. |
Value
demo |
basic demographics of data |
contin_2x2 |
2-by-2 contingency table |
LI |
estimated interval of odds ratio by LI |
CI |
estimated interval of odds ratio by CI |
plot |
likelihood-related plots |
Author(s)
Kyun-Seop Bae <k@acr.kr>, Minkyu Kim <mkim@acr.kr>
Examples
liod(21, 43, 16, 67)
liod(21, 43, 16, 67, plot = 0) # faster calculation
Likelihood Interval for Poisson Mean of Single Sample from Poisson Distribution
Description
Likelihood interval for Poisson mean of single sample assuming Poisson distribution. Likelihood function plot is also shown. For faster calculation speed, plot option '0' is recommended.
Arguments
event |
number of events; a numeric vector |
unit.time |
unit time for Poisson mean; default is 1 |
data.size |
sample size. If not specified, size is assumed to be 1. For LI being more precise, sample size must be considered. |
conf.level |
confidence level for the interval estimation |
eps |
machine epsilon value; default is 1e-08 |
k |
cutoff value for likelihood interval. If not specified, F-test is used. |
Value
demo |
basic demographics of data |
LI |
estimated interval of Poisson mean by LI |
CI |
estimated interval of Poisson mean by CI |
plot |
likelihood-related plots |
Author(s)
Kyun-Seop Bae <k@acr.kr>, Minkyu Kim <mkim@acr.kr>
Examples
lipois(8)
lipois(event = 8, unit.time = 3)
lipois(event = 8, unit.time = 3, data.size = 6)
Likelihood Interval for Variance Ratio of Two Samples from Normal Distribution
Description
Likelihood interval for variance ratio of two samples assuming normal distribution. Likelihood function plot is also shown. For faster calculation speed, plot option '0' is recommended. Sample size is not allocated.
Arguments
num.data |
a numeric vector of data values, variance value at the numerator position; mandatory |
denom.data |
a numeric vector of data values, variance value at the denominator position; mandatory |
plot |
likelihood function plots by LI; default is "all". 'OBJ', 'O1', '1' is objective function plot; 'OFV', 'O2', '2' is log likelihood function plot; 'LRT', 'O3', '3' is log LRT function plot. |
conf.level |
confidence level for the interval estimation |
df |
degree of freedom for likelihood interval; default is 2.4 |
k |
cutoff value for likelihood interval. If not specified, F-test is used. |
Value
demo |
basic demographics of data |
LI |
estimated interval of variance ratio by LI |
LI.sdR |
estimated interval of standard deviation ratio by LI |
CI |
estimated interval of variance by CI |
plot |
likelihood-related plots |
Author(s)
Kyun-Seop Bae <k@acr.kr>, Minkyu Kim <mkim@acr.kr>
Examples
lir(rnorm(30, 0, 1), rnorm(20, 0, 1))
Likelihood Interval for Risk Difference of 2-by-2 Contingency Table.
Description
Likelihood interval for risk difference of 2-by-2 contingency table. Likelihood function plot is also shown. For faster calculation speed, plot option '0' is recommended.
Arguments
exposure.O_event.O |
a numeric vector of exposure (+) and event (+), 'a' of 2-by-2 table; mandatory |
exposure.O_TOTAL |
a numeric vector of exposure (+), 'a' + 'b' of 2-by-2 table; mandatory |
exposure.X_event.O |
a numeric vector of exposure (-) and event (-), 'c' of 2-by-2 table; mandatory |
exposure.X_TOTAL |
a numeric vector of exposure (-), 'c' + 'd' of 2-by-2 table; mandatory |
plot |
likelihood function plots by LI; default is "all". 'OBJ', 'O1', '1' is objective function plot; 'OFV', 'O2', '2' is log likelihood function plot; 'LRT', 'O3', '3' is log LRT function plot. |
conf.level |
confidence level for the interval estimation |
eps |
machine epsilon value; default is 1e-08 |
k |
cutoff value for likelihood interval. If not specified, F-test is used. |
Value
demo |
basic demographics of data |
contin_2x2 |
2-by-2 contingency table |
LI |
estimated interval of risk difference by LI |
CI |
estimated interval of risk difference by CI |
plot |
likelihood-related plots |
Author(s)
Kyun-Seop Bae <k@acr.kr>, Minkyu Kim <mkim@acr.kr>
Examples
lird(21, 43, 16, 67)
lird(21, 43, 16, 67, plot = 0) # faster calculation
Likelihood Interval for Relative Risk of 2-by-2 Contingency Table.
Description
Likelihood interval for relative risk of 2-by-2 contingency table. Likelihood function plot is also shown. For faster calculation speed, plot option '0' is recommended.
Arguments
exposure.O_event.O |
a numeric vector of exposure (+) and event (+), 'a' of 2-by-2 table; mandatory |
exposure.O_TOTAL |
a numeric vector of exposure (+), 'a' + 'b' of 2-by-2 table; mandatory |
exposure.X_event.O |
a numeric vector of exposure (-) and event (-), 'c' of 2-by-2 table; mandatory |
exposure.X_TOTAL |
a numeric vector of exposure (-), 'c' + 'd' of 2-by-2 table; mandatory |
plot |
likelihood function plots by LI; default is "all". 'OBJ', 'O1', '1' is objective function plot; 'OFV', 'O2', '2' is log likelihood function plot; 'LRT', 'O3', '3' is log LRT function plot. |
conf.level |
confidence level for the interval estimation |
eps |
machine epsilon value; default is 1e-08 |
k |
cutoff value for likelihood interval. If not specified, F-test is used. |
Value
demo |
basic demographics of data |
contin_2x2 |
2-by-2 contingency table |
LI |
estimated interval of relative risk by LI |
CI |
estimated interval of relative risk by CI |
plot |
likelihood-related plots |
Author(s)
Kyun-Seop Bae <k@acr.kr>, Minkyu Kim <mkim@acr.kr>
Examples
lirr(21, 43, 16, 67)
lirr(21, 43, 16, 67, plot = 0) # faster calculation
Likelihood Interval for Variance of Single Sample from Normal Distribution
Description
Likelihood interval for variance of single sample assuming normal distribution. Likelihood function plot is also shown. For faster calculation speed, plot option '0' is recommended.
Arguments
data |
a numeric vector of data values; mandatory |
plot |
likelihood function plots by LI; default is "all". 'OBJ', 'O1', '1' is objective function plot; 'OFV', 'O2', '2' is log likelihood function plot; 'LRT', 'O3', '3' is log LRT function plot. |
conf.level |
confidence level for the interval estimation |
df |
degree of freedom for likelihood interval; default is 1.2 |
k |
cutoff value for likelihood interval. If not specified, F-test is used. |
Value
demo |
basic demographics of data |
LI |
estimated interval of variance by LI |
LI.sd |
estimated interval of standard deviation by LI |
CI |
estimated interval of variance by CI |
plot |
likelihood-related plots |
Author(s)
Kyun-Seop Bae <k@acr.kr>, Minkyu Kim <mkim@acr.kr>
Examples
liv(rnorm(30, 0, 1))
Testing Function for Probability from Binomial Distribution
Description
Testing function for variance ratio of two samples assuming normal distribution by LI method. O2 type likelihood function plot is also shown.
Arguments
event |
number of events from observed data; a numeric vector |
total |
total number of trials from observed data; a numeric vector |
test.val |
a numeric vector of testing value for probability |
conf.level |
confidence level for the interval estimation |
eps |
machine epsilon value; default is 1e-08 |
k |
cutoff value for likelihood interval. If not specified, F-test is used. |
Value
demo |
basic demographics of data |
interval |
estimated interval by LI and CI. |
stat |
statistical values, such as p-value and likelihood ratio |
verdict |
estimation result as a sentence |
plot |
log likelihood function plot (O2 type) |
Author(s)
Kyun-Seop Bae <k@acr.kr>, Minkyu Kim <mkim@acr.kr>
Examples
qlib(8, 13, 0.7)
qlib(3, 10, 0.8)
Testing Function for Mean Difference of Two Samples from Normal Distribution by LI Method
Description
Testing function for mean difference of two samples assuming normal distribution by LI method. O2 type likelihood function plot is also shown.
Arguments
set.a |
a numeric vector of former data values; mandatory |
set.b |
a numeric vector of latter data values; mandatory |
conf.level |
confidence level for the interval estimation |
df |
degree of freedom for likelihood interval; default is 1 |
k |
cutoff value for likelihood interval. If not specified, F-test is used. |
Value
demo |
basic demographics of data |
interval |
estimated interval by LI and CI. PE is mean(set.a) - mean(set.b). |
stat |
statistical values, such as p-value and likelihood ratio |
verdict |
estimation result as a sentence |
plot |
log likelihood function plot (O2 type) |
Author(s)
Kyun-Seop Bae <k@acr.kr>, Minkyu Kim <mkim@acr.kr>
Examples
x <- rnorm(30, 0, 1)
y <- rnorm(20, 0, 1)
qlim(x, y)
Testing Function for Poisson Mean from Poisson Distribution
Description
Testing function for Poisson mean of single sample assuming Poisson distribution by LI method. O2 type likelihood function plot is also shown.
Arguments
data |
a numeric vector of data values; mandatory |
test.val |
a numeric vector of testing value for Poisson mean; mandatory |
conf.level |
confidence level for the interval estimation |
eps |
machine epsilon value; default is 1e-08 |
k |
cutoff value for likelihood interval. If not specified, F-test is used. |
Value
demo |
basic demographics of data |
interval |
estimated interval by LI and CI. |
stat |
statistical values, such as p-value and likelihood ratio |
verdict |
estimation result as a sentence |
plot |
log likelihood function plot (O2 type) |
Author(s)
Kyun-Seop Bae <k@acr.kr>, Minkyu Kim <mkim@acr.kr>
Examples
qlipois(rnorm(20, 1, 1), 1)
Testing Function for Variance Ratio of Two Samples from Normal Distribution
Description
Testing function for variance ratio of two samples assuming normal distribution by LI method. O2 type likelihood function plot is also shown. Smaller sample is allocated to be in the nominator for more accurate and precise estimation.
Arguments
set.a |
a numeric vector of data values; mandatory, pre-allocation |
set.b |
a numeric vector of data values; mandatory, pre-allocation |
conf.level |
confidence level for the interval estimation |
df |
degree of freedom for likelihood interval; default is 2.4 |
k |
cutoff value for likelihood interval. If not specified, F-test is used. |
Value
demo |
basic demographics of data |
interval |
estimated interval by LI and CI. |
stat |
statistical values, such as p-value and likelihood ratio |
verdict |
estimation result as a sentence |
plot |
log likelihood function plot (O2 type) |
Author(s)
Kyun-Seop Bae <k@acr.kr>, Minkyu Kim <mkim@acr.kr>
Examples
x <- rnorm(30, 0, 1)
y <- rnorm(20, 0, 1)
qliv(x, y) # x placed in the denominator