Overview
Empirical likelihood enables a nonparametric, likelihood-driven style of inference without relying on assumptions frequently made in parametric models. Empirical likelihood-based tests are asymptotically pivotal and thus avoid explicit studentization. For this reason it is challenging to incorporate empirical likelihood methods directly into other packages that perform inferences for parametric models. The R package melt aims to bridge the gap and provide a unified framework for data analysis with empirical likelihood methods. A collection of functions are available to perform multiple empirical likelihood tests and construct confidence intervals for linear and generalized linear models in R. The package offers an easy-to-use interface and flexibility in specifying hypotheses and calibration methods, extending the framework to simultaneous inferences. The core computational routines are implemented with the Eigen C++ library and RcppEigen interface, with OpenMP for parallel computation. Details of the testing procedures are given in Kim, MacEachern, and Peruggia (2023). This work was supported by the U.S. National Science Foundation under Grants No. SES-1921523 and DMS-2015552.
Installation
You can install the latest stable release from CRAN.
install.packages("melt")You can install the latest development version from GitHub or R-universe.
# install.packages("devtools")
devtools::install_github("ropensci/melt")
install.packages("melt", repos = "https://ropensci.r-universe.dev")Main functions
melt provides an intuitive API for performing the most common data analysis tasks:
-
el_lm()fits a linear model with empirical likelihood. -
el_glm()fits a generalized linear model with empirical likelihood. -
confint()computes confidence intervals for model parameters. -
confreg()computes confidence region for model parameters. -
elt()tests a linear hypothesis. -
elmt()performs multiple testing simultaneously.
Usage
library(melt)
set.seed(971112)
## Test for the mean
data("precip")
el_mean(precip, par = 30)
#>
#> Empirical Likelihood
#>
#> Model: mean
#>
#> Maximum EL estimates:
#> [1] 34.89
#>
#> Chisq: 8.285, df: 1, Pr(>Chisq): 0.003998
#> EL evaluation: converged
## Linear model
data("mtcars")
fit_lm <- el_lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
summary(fit_lm)
#>
#> Empirical Likelihood
#>
#> Model: lm
#>
#> Call:
#> el_lm(formula = mpg ~ disp + hp + wt + qsec, data = mtcars)
#>
#> Number of observations: 32
#> Number of parameters: 5
#>
#> Parameter values under the null hypothesis:
#> (Intercept) disp hp wt qsec
#> 29.04 0.00 0.00 0.00 0.00
#>
#> Lagrange multipliers:
#> [1] -260.167 -2.365 1.324 -59.781 25.175
#>
#> Maximum EL estimates:
#> (Intercept) disp hp wt qsec
#> 27.329638 0.002666 -0.018666 -4.609123 0.544160
#>
#> logL: -327.6 , logLR: -216.7
#> Chisq: 433.4, df: 4, Pr(>Chisq): < 2.2e-16
#> Constrained EL: converged
#>
#> Coefficients:
#> Estimate Chisq Pr(>Chisq)
#> (Intercept) 27.329638 443.208 < 2e-16 ***
#> disp 0.002666 0.365 0.54575
#> hp -0.018666 10.730 0.00105 **
#> wt -4.609123 439.232 < 2e-16 ***
#> qsec 0.544160 440.583 < 2e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
cr <- confreg(fit_lm, parm = c("disp", "hp"), npoints = 200)
plot(cr)
data("clothianidin")
fit2_lm <- el_lm(clo ~ -1 + trt, data = clothianidin)
summary(fit2_lm)
#>
#> Empirical Likelihood
#>
#> Model: lm
#>
#> Call:
#> el_lm(formula = clo ~ -1 + trt, data = clothianidin)
#>
#> Number of observations: 102
#> Number of parameters: 4
#>
#> Parameter values under the null hypothesis:
#> trtNaked trtFungicide trtLow trtHigh
#> 0 0 0 0
#>
#> Lagrange multipliers:
#> [1] -4.116e+06 -7.329e-01 -1.751e+00 -1.418e-01
#>
#> Maximum EL estimates:
#> trtNaked trtFungicide trtLow trtHigh
#> -4.479 -3.427 -2.800 -1.307
#>
#> logL: -918.9 , logLR: -447.2
#> Chisq: 894.4, df: 4, Pr(>Chisq): < 2.2e-16
#> EL evaluation: maximum iterations reached
#>
#> Coefficients:
#> Estimate Chisq Pr(>Chisq)
#> trtNaked -4.479 411.072 < 2e-16 ***
#> trtFungicide -3.427 59.486 1.23e-14 ***
#> trtLow -2.800 62.955 2.11e-15 ***
#> trtHigh -1.307 4.653 0.031 *
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
confint(fit2_lm)
#> lower upper
#> trtNaked -5.002118 -3.9198229
#> trtFungicide -4.109816 -2.6069870
#> trtLow -3.681837 -1.9031795
#> trtHigh -2.499165 -0.1157222
## Generalized linear model
data("thiamethoxam")
fit_glm <- el_glm(visit ~ log(mass) + fruit + foliage + var + trt,
family = quasipoisson(link = "log"), data = thiamethoxam,
control = el_control(maxit = 100, tol = 1e-08, nthreads = 4)
)
summary(fit_glm)
#>
#> Empirical Likelihood
#>
#> Model: glm (quasipoisson family with log link)
#>
#> Call:
#> el_glm(formula = visit ~ log(mass) + fruit + foliage + var +
#> trt, family = quasipoisson(link = "log"), data = thiamethoxam,
#> control = el_control(maxit = 100, tol = 1e-08, nthreads = 4))
#>
#> Number of observations: 165
#> Number of parameters: 8
#>
#> Parameter values under the null hypothesis:
#> (Intercept) log(mass) fruit foliage varGZ trtSpray
#> -0.1098 0.0000 0.0000 0.0000 0.0000 0.0000
#> trtFurrow trtSeed phi
#> 0.0000 0.0000 1.4623
#>
#> Lagrange multipliers:
#> [1] 1319.19 210.54 -12.99 -24069.07 -318.90 -189.14 -53.35
#> [8] 262.32 -170.21
#>
#> Maximum EL estimates:
#> (Intercept) log(mass) fruit foliage varGZ trtSpray
#> -0.10977 0.24750 0.04654 -19.40632 -0.25760 0.06724
#> trtFurrow trtSeed
#> -0.03634 0.34790
#>
#> logL: -2272 , logLR: -1429
#> Chisq: 2859, df: 7, Pr(>Chisq): < 2.2e-16
#> Constrained EL: initialization failed
#>
#> Coefficients:
#> Estimate Chisq Pr(>Chisq)
#> (Intercept) -0.10977 0.090 0.763757
#> log(mass) 0.24750 425.859 < 2e-16 ***
#> fruit 0.04654 11.584 0.000665 ***
#> foliage -19.40632 65.181 6.83e-16 ***
#> varGZ -0.25760 17.308 3.18e-05 ***
#> trtSpray 0.06724 0.860 0.353820
#> trtFurrow -0.03634 0.217 0.641379
#> trtSeed 0.34790 19.271 1.13e-05 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Dispersion for quasipoisson family: 1.462288
## Test of no treatment effect
contrast <- c(
"trtNaked - trtFungicide", "trtFungicide - trtLow", "trtLow - trtHigh"
)
elt(fit2_lm, lhs = contrast)
#>
#> Empirical Likelihood Test
#>
#> Hypothesis:
#> trtNaked - trtFungicide = 0
#> trtFungicide - trtLow = 0
#> trtLow - trtHigh = 0
#>
#> Significance level: 0.05, Calibration: Chi-square
#>
#> Statistic: 26.6, Critical value: 7.815
#> p-value: 7.148e-06
#> Constrained EL: converged
## Multiple testing
contrast2 <- rbind(
c(0, 0, 0, 0, 0, 1, 0, 0),
c(0, 0, 0, 0, 0, 0, 1, 0),
c(0, 0, 0, 0, 0, 0, 0, 1)
)
elmt(fit_glm, lhs = contrast2)
#>
#> Empirical Likelihood Multiple Tests
#>
#> Overall significance level: 0.05
#>
#> Calibration: Multivariate chi-square
#>
#> Hypotheses:
#> Estimate Chisq Df
#> trtSpray = 0 0.06724 0.860 1
#> trtFurrow = 0 -0.03634 0.217 1
#> trtSeed = 0 0.34790 19.271 1Please note that this package is released with a Contributor Code of Conduct. By contributing to this project, you agree to abide by its terms.