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melt

Overview

melt provides a unified framework for data analysis with empiricallikelihood methods. A collection of functions is available to performmultiple empirical likelihood tests and construct confidence intervalsfor various models in ‘R’. melt offers an easy-to-use interface andflexibility in specifying hypotheses and calibration methods, extendingthe framework to simultaneous inferences. The core computationalroutines are implemented with the ‘Eigen’ ‘C++’ library and ‘RcppEigen’interface, with ‘OpenMP’ for parallel computation. Details of thetesting procedures are provided inKim, MacEachern, and Peruggia(2023). The package hasa companion paper byKim, MacEachern, and Peruggia(2024). This work was supportedby the U.S. National Science Foundation under GrantsNo. SES-1921523andDMS-2015552.

Installation

You can install the latest stable release of melt from CRAN.

install.packages("melt")

You can install the development version of melt from GitHub orR-universe.

# install.packages("pak")pak::pak("ropensci/melt")

install.packages("melt",repos="https://ropensci.r-universe.dev")

Main functions

melt provides an intuitive API for performing the most common dataanalysis tasks:

el_mean() computes empirical likelihood for the mean.
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 hypothesis with various calibration options.
elmt() performs multiple testing simultaneously.

Usage

library(melt)set.seed(971112)## Test for the meandata("precip")(fit<- 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## Adjusted empirical likelihood calibrationelt(fit,rhs=30,calibrate="ael")#>#>  Empirical Likelihood Test#>#> Hypothesis:#> par = 30#>#> Significance level: 0.05, Calibration: Adjusted EL#>#> Statistic: 7.744, Critical value: 3.841#> p-value: 0.005389#> EL evaluation: converged## Bootstrap calibrationelt(fit,rhs=30,calibrate="boot")#>#>  Empirical Likelihood Test#>#> Hypothesis:#> par = 30#>#> Significance level: 0.05, Calibration: Bootstrap#>#> Statistic: 8.285, Critical value: 3.84#> p-value: 0.0041#> EL evaluation: converged## F calibrationelt(fit,rhs=30,calibrate="f")#>#>  Empirical Likelihood Test#>#> Hypothesis:#> par = 30#>#> Significance level: 0.05, Calibration: F#>#> Statistic: 8.285, Critical value: 3.98#> p-value: 0.005318#> EL evaluation: converged## Linear modeldata("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 ' ' 1cr<- 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 ' ' 1confint(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 modeldata("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      0.764#> log(mass)     0.24750 425.859    < 2e-16 ***#> fruit         0.04654  29.024   7.15e-08 ***#> foliage     -19.40632  65.181   6.83e-16 ***#> varGZ        -0.25760  17.308   3.18e-05 ***#> trtSpray      0.06724   0.860      0.354#> trtFurrow    -0.03634   0.217      0.641#> 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 effectcontrast<- 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 testingcontrast2<- 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  1