Interval Estimation by Likelihoodist (LI) Compared to Frequentist (CI)

Description

Parameter estimation via likelihood interval (LI) compared to traditional method (CI). This is the expanded version for 'LBI'- and 'wnl'-package, formulated by Kyun-Seop Bae <k@acr.kr>.

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 variance and variance ratio, and their likelihood function plots. Further estimating methods (especially for non-linear model functions) are upcoming.

Author(s)

Minkyu Kim <mkim@acr.kr>

References

1. Wilks SS. The Large-sample Distribution of the Likelihood Ratio for Testing Composite Hypotheses. Ann Math Stat. 1938;9(1):60-62.

2. Ruppert D, Cressie N, Carroll RJ. A Transformation/Weighting Model for Estimating Michaelis-Menten Parameters. Cornell University Technical Report 796. 1988.

3. Pawitan Y. In All Likelihood: Statistical Modelling and Inference Using Likelihood. 2001.

4. Lee MH, Bae KS. Likelihood interval for nonlinear regression. Transl Clin Pharmacol. 2023.

Examples

x <- rnorm(20, 0, 1)
y <- rnorm(40, 0, 1)

varE(x)
varEplot(x, FALSE)
varEplot(x, TRUE)

varR(x, y)
varRplot(x, y, FALSE)
varRplot(x, y, TRUE)

varE: Calculate Variance Estimate

Description

This function computes the interval estimation for a single group variance by both LI and CI method.

Usage

varE(data, conf.level = 0.95, df = 1.2, lower = 1e-08, upper = 1e+06, k)

Arguments

Value

Point Estimate (PE), lower limit/bound (LL/LB), upper limit/bound (UL/UB), width, sample size, cutoff value k and maximum log-likelihood function value are calculated.

Examples

x <- rnorm(20, 0, 1)
varE(x)

y <- rnorm(40, 0, 1)
varE(y)

varEplot: Plot of Variance Estimate by Likelihood Method

Description

This function plots a graph of interval estimation for a single group variance by LI method, either in the log-likelihood function or the normalized log-likelihood value.

Usage

varEplot(
  data,
  logLRT = FALSE,
  conf.level = 0.95,
  df = 1.2,
  low.scale = 3,
  up.scale = 5,
  k
)

Arguments

Value

Plotted graph, either in the log-likelihood function or the normalized log-likelihood value.

Examples

x <- rnorm(20, 0, 1)
varEplot(x, FALSE)
varEplot(x, TRUE)

y <- rnorm(40, 0, 1)
varEplot(y, FALSE)
varEplot(y, TRUE)

varR: Calculate Variance Ratio Estimate

Description

This function computes the interval estimation for a two group variance ratio by both LI and CI method.

Usage

varR(
  num.data,
  denom.data,
  conf.level = 0.95,
  df = 2.4,
  lower = 1e-08,
  upper = 1e+06,
  k
)

Arguments

Value

Point Estimate (PE), lower limit/bound (LL/LB), upper limit/bound (UL/UB), width, sample size, cutoff value k and maximum log-likelihood function value are calculated.

Examples

x <- rnorm(20, 0, 1)
y <- rnorm(40, 0, 1)
varR(x, y)

varRplot: Plot of Variance Ratio Estimate by Likelihood Method

Description

This function plots a graph of interval estimation for a two group variance ratio by LI method, either in the log-likelihood function or the normalized log-likelihood value.

Usage

varRplot(
  num.data,
  denom.data,
  logLRT = FALSE,
  conf.level = 0.95,
  df = 2.4,
  low.scale = 5,
  up.scale = 5,
  k
)

Arguments

Value

Plotted graph, either in the log-likelihood function or the normalized log-likelihood value

Examples

x <- rnorm(20, 0, 1)
y <- rnorm(40, 0, 1)
varRplot(x, y, FALSE)
varRplot(x, y, TRUE)