Title:	Measurement Error Modelling using MCEM
Version:	1.3.1
Description:	Fits measurement error models using Monte Carlo Expectation Maximization (MCEM). For specific details on the methodology, see: Greg C. G. Wei & Martin A. Tanner (1990) A Monte Carlo Implementation of the EM Algorithm and the Poor Man's Data Augmentation Algorithms, Journal of the American Statistical Association, 85:411, 699-704 <doi:10.1080/01621459.1990.10474930> For more examples on measurement error modelling using MCEM, see the 'RMarkdown' vignette: "'refitME' R-package tutorial".
Depends:	R (≥ 4.4.0)
Imports:	MASS, mgcv, VGAM, VGAMdata, caret, expm, mvtnorm, sandwich, stats, dplyr, scales
License:	GPL-2
Encoding:	UTF-8
LazyData:	true
RoxygenNote:	7.3.2
NeedsCompilation:	no
Packaged:	2025-04-13 02:29:48 UTC; User
Author:	Jakub Stoklosa [aut, cre], Wenhan Hwang [aut, ctb], David Warton [aut, ctb]
Maintainer:	Jakub Stoklosa <j.stoklosa@unsw.edu.au>
Repository:	CRAN
Date/Publication:	2025-04-13 05:00:02 UTC

The Corymbia eximia presence-only data set

Description

Data set consisting of presence-only records for the plant species Corymbia eximia, site coordinates 5 covariates for each site.

Usage

Corymbiaeximiadata

Format

A data set that contains: 8 columns with 86,316 observations (or sites). The columns are defined as follows:

X

Longitude coordinate.

Y

Latitude coordinate.

FC

Recorded number of fire counts for each site.

MNT

Recorded minimum temperatures for each site.

MXT

Recorded maximum temperature for each site.

Rain

Recorded rainfall for each site.

D.Main

Recorded distance from nearest major road.

Y.obs

Presences for the plant species Corymbia eximia for each site.

Source

See Renner and Warton (2013) for full details on the data and study.

References

Renner, I. W. and Warton, D. I. (2013). Equivalence of MAXENT and Poisson point process models for species distribution modeling in ecology. Biometrics, 69, 274–281.

Examples

# Load the data.

data(Corymbiaeximiadata)

The Framingham heart study data set

Description

Data set consisting of records of male patients with coronary heart disease collected from the Framingham heart study. The Framinghamdata data consists of binary responses and four predictor variables collected on 'n = 1615' patients.

Usage

Framinghamdata

Format

A data set that contains: 5 columns with 1,615 observations. The columns are defined as follows:

Y

Response indicator (binary variable) of first evidence of CHD status of patient.

z1

Serum cholesterol level of patient.

z2

Age of patient.

z3

Smoking indicator - whether the patient smokes.

w1

Systolic blood pressure (SBP) of patient - this is the error contaminated variable, calculated from mean scores. The measurement error is 0.00630, see pp. 112 of Carroll et al. (2006).

Source

See Carroll et al. (2006) for full details on the data and study. Also, see https://github.com/JakubStats/refitME for an RMarkdown vignette of an example that uses the data.

References

Carroll, R. J., Ruppert, D., Stefanski, L. A., and Crainiceanu, C. M. (2006). Measurement Error in Nonlinear Models: A Modern Perspective. 2nd Ed. London: Chapman & Hall/CRC.

Examples

# Load the data.

data(Framinghamdata)

Function for fitting VGAM capture-recapture (CR) model using the MCEM algorithm

Description

Function for fitting VGAM capture-recapture (CR) model using the MCEM algorithm where covariates have measurement error.

Usage

MCEMfit_CR(mod, sigma.sq.u, B = 50, epsilon = 1e-05, silent = FALSE)

Arguments

Value

MCEMfit_CR returns model coefficient and population size estimates with standard errors and the effective sample size.

Warning

This function is still under development. Currently the function can only fit the CR model used in the manuscript. IT DOES NOT SUPPORT ALL VGAM families.

Author(s)

Jakub Stoklosa, Wen-Han Hwang and David I. Warton.

Source

See https://github.com/JakubStats/refitME for an RMarkdown vignette with examples.

References

Stoklosa, J., Hwang, W-H., and Warton, D.I. refitME: Measurement Error Modelling using Monte Carlo Expectation Maximization in R.

See Also

MCEMfit_glm

Examples

# A VGAM example using the Prinia flaviventris capture-recapture data.

library(refitME)
library(VGAM)

data(Priniadata)

tau <- 17   # No. of capture occasions.
w1 <- Priniadata$w1 # Bird wing length predictor.

CR_naiv <- vglm(cbind(cap, noncap) ~ w1,
   VGAM::posbinomial(omit.constant = TRUE, parallel = TRUE ~ w1),
   data = Priniadata, trace = FALSE)

sigma.sq.u <- 0.37 # ME variance.

CR_MCEM <- refitME(CR_naiv, sigma.sq.u)

detach(package:VGAM)

Function for wrapping the MCEM algorithm on gam objects

Description

Function for wrapping the MCEM algorithm on GAMs where predictors are subject to measurement error/error-in-variables.

Usage

MCEMfit_gam(
  mod,
  family,
  sigma.sq.u,
  B = 50,
  epsilon = 1e-05,
  silent = FALSE,
  ...
)

Arguments

Value

MCEMfit_gam returns the original naive fitted model object but coefficient estimates and the covariance matrix have been replaced with the final MCEM model fit. Standard errors and the effective sample size (which diagnose how closely the proposal distribution matches the posterior, see equation (2) of Stoklosa, Hwang and Warton) have also been included as outputs.

Author(s)

Jakub Stoklosa, Wen-Han Hwang and David I. Warton.

Source

See https://github.com/JakubStats/refitME for an RMarkdown vignette with examples. With permission from Matt Wand, we have now made these data available in the refitME R-package.

References

Ganguli, B, Staudenmayer, J., and Wand, M. P. (2005). Additive models with predictors subject to measurement error. Australian & New Zealand Journal of Statistics, 47, 193–202.

Stoklosa, J., Hwang, W-H., and Warton, D.I. refitME: Measurement Error Modelling using Monte Carlo Expectation Maximization in R.

See Also

MCEMfit_glm

Examples

# A GAM example using the air pollution data set from the SemiPar package.

library(refitME)
library(mgcv)
library(dplyr)

data(Milanmortdata)

dat.air <- sample_n(Milanmortdata, 100) # Takes a random sample of size 100.

Y <- dat.air[, 6]  # Mortality counts.

n <- length(Y)

z1 <- (dat.air[, 1])
z2 <- (dat.air[, 4])
z3 <- (dat.air[, 5])
w1 <- log(dat.air[, 9])  # The error-contaminated predictor (total suspended particles).

dat <- data.frame(cbind(Y, w1, z1, z2, z3))

gam_naiv <- gam(Y ~ s(w1), family = "poisson", data = dat)

sigma.sq.u <- 0.0915 # Measurement error variance.

B <- 10  # Consider increasing this if you want a more accurate answer.

gam_MCEM <- refitME(gam_naiv, sigma.sq.u, B)

plot(gam_MCEM, select = 1)

detach(package:mgcv)

Function for fitting any likelihood-based model using the MCEM algorithm

Description

Function for wrapping the MCEM algorithm on any likelihood-based model where predictors are subject to measurement error/error-in-variables.

Usage

MCEMfit_gen(
  mod,
  family,
  sigma.sq.u,
  B = 50,
  epsilon = 1e-05,
  silent = FALSE,
  theta.est = 1,
  shape.est = 1,
  ...
)

Arguments

Value

MCEMfit_gen returns the original naive fitted model object but coefficient estimates and residuals have been replaced with the final MCEM model fit. Standard errors are included and returned, if mod is a class of object accepted by the sandwich package (such as glm, gam, survreg and many more).

Author(s)

Jakub Stoklosa, Wen-Han Hwang and David I. Warton.

References

Carroll, R. J., Ruppert, D., Stefanski, L. A., and Crainiceanu, C. M. (2006). Measurement Error in Nonlinear Models: A Modern Perspective. 2nd Ed. London: Chapman & Hall/CRC.

Stoklosa, J., Hwang, W-H., and Warton, D.I. refitME: Measurement Error Modelling using Monte Carlo Expectation Maximization in R.

See Also

MCEMfit_glm and MCEMfit_gam

Function for wrapping the MCEM algorithm on lm or glm objects

Description

Function for wrapping the MCEM algorithm on GLMs where predictors are subject to measurement error/error-in-variables.

Usage

MCEMfit_glm(
  mod,
  family,
  sigma.sq.u,
  B = 50,
  epsilon = 1e-05,
  silent = FALSE,
  ...
)

Arguments

Value

MCEMfit_glm returns the naive fitted model object where coefficient estimates, the covariance matrix, fitted values, the log-likelihood, and residuals have been replaced with the final MCEM model fit. Standard errors and the effective sample size (which diagnose how closely the proposal distribution matches the posterior, see equation (2) of Stoklosa, Hwang and Warton) have also been included as outputs.

Author(s)

Jakub Stoklosa, Wen-Han Hwang and David I. Warton.

Source

See https://github.com/JakubStats/refitME for an RMarkdown vignette with examples.

References

Carroll, R. J., Ruppert, D., Stefanski, L. A., and Crainiceanu, C. M. (2006). Measurement Error in Nonlinear Models: A Modern Perspective. 2nd Ed. London: Chapman & Hall/CRC.

Stoklosa, J., Hwang, W-H., and Warton, D.I. refitME: Measurement Error Modelling using Monte Carlo Expectation Maximization in R.

See Also

MCEMfit_gam

Examples

# A GLM example I - binary response data.

library(refitME)

data(Framinghamdata)

glm_naiv <- glm(Y ~ w1 + z1 + z2 + z3, x = TRUE, family = binomial, data = Framinghamdata)

# The error-contaminated predictor in this example is systolic blood pressure (w1).

sigma.sq.u <- 0.006295  # ME variance, as obtained from Carroll et al. (2006) monograph.

B <- 50 # The number of Monte Carlo replication values.

glm_MCEM <- refitME(glm_naiv, sigma.sq.u, B)

The Milan mortality data set

Description

The Milanmortdata data frame has data on 3652 consecutive days (10 consecutive years: 1st January, 1980 to 30th December, 1989) for the city of Milan, Italy. Note that this data set was originally contained and available from the now discontinued SemiPar R-package. With the permission of Matt Wand we have made these data (now called Milanmortdata) available in the refitME R-package.

Usage

Milanmortdata

Format

This data frame contains the following columns:

day.num

number of days since 31st December, 1979.

day.of.week

1 = Monday, 2 = Tuesday, 3 = Wednesday, 4 = Thursday, 5 = Friday, 6 = Saturday, 7 = Sunday.

holiday

indicator of public holiday: 1 = public holiday, 0 = otherwise.

mean.temp

mean daily temperature in degrees Celcius.

rel.humid

relative humidity.

tot.mort

total number of deaths.

resp.mort

total number of respiratory deaths.

SO2

measure of sulphur dioxide level in ambient air.

TSP

total suspended particles in ambient air.

Source

Vigotti, M.A., Rossi, G., Bisanti, L., Zanobetti, A. and Schwartz, J. (1996). Short term effect of urban air pollution on respiratory health in Milan, Italy, 1980-1989. Journal of Epidemiology and Community Health, 50, S71-S75.

References

Ruppert, D., Wand, M.P. and Carroll, R.J. (2003). Semiparametric Regression Cambridge University Press.

Examples

# Load the data.

data(Milanmortdata)
pairs(Milanmortdata, pch = ".")

The yellow-bellied Prinia Prinia flaviventris capture-recapture data

Description

Data set consisting of capture-recapture histories 164 uniquely captured birds across 17 weekly capture occasions. Bird wing lengths were also measured in the study.

Usage

Priniadata

Format

A data set that contains: 3 columns with 164 observations. The columns are defined as follows:

w1

Bird wing lengths.

cap

Number of times the individual was captured.

noncap

Number of times the individual was not captured.

Source

See Hwang, Huang and Wang (2007) for full details on the data and study.

References

Hwang, W. H., Huang, S. Y. H., and Wang, C. (2007). Effects of measurement error and conditional score estimation in capture–recapture models. Statistica Sinica, 17, 301-316.

Examples

# Load the data.

data(Priniadata)

An ANOVA function for fitted refitME objects

Description

An ANOVA function for fitted refitME objects.

Usage

## S3 method for class 'refitME'
anova(object, ..., dispersion = NULL, test = NULL)

Arguments

Value

anova.refitME produces output identical to anova.lm, anova.glm or anova.gam.

Author(s)

Jakub Stoklosa, Wen-Han Hwang and David I. Warton.

See Also

anova

An ANOVA function for fitted MCEMfit_glm objects

Description

An ANOVA function for fitted MCEMfit_glm objects.

Usage

anova_MCEMfit_glm(object, ..., dispersion = NULL, test = NULL)

Arguments

Value

anova_MCEMfit_glm produces output identical to anova.glm.

Author(s)

Jakub Stoklosa, Wen-Han Hwang and David I. Warton.

See Also

anova.glm

Extract log-Likelihoods for refitME model objects

Description

Extract log-Likelihoods for refitME model objects. This function subtracts the entropy term from the observed likelihood.

Usage

## S3 method for class 'refitME'
logLik(object, ...)

Arguments

Value

logLik.refitME produces identical output to logLik but for refitME model objects.

Author(s)

Jakub Stoklosa, Wen-Han Hwang and David I. Warton.

See Also

logLik

Extract log-Likelihoods for MCEMfit_lm model objects

Description

Extract log-Likelihoods for MCEMfit_lm model objects. This function subtracts the entropy term from the observed likelihood.

Usage

logLik_MCEMfit_lm(object, REML = FALSE, ...)

Arguments

Value

logLik_MCEMfit_lm produces output identical to logLik.

Author(s)

Jakub Stoklosa, Wen-Han Hwang and David I. Warton.

See Also

logLik

A wrapper function for correcting measurement error in predictor variables via the MCEM algorithm

Description

Function that extracts the fitted (naive) model object and wraps the MCEM algorithm to correct for measurement error/error-in-variables in predictors.

Usage

refitME(mod, sigma.sq.u, B = 50, epsilon = 1e-05, silent = FALSE, ...)

Arguments

Value

refitME returns the naive fitted model object where coefficient estimates, the covariance matrix, fitted values, the log-likelihood, and residuals have been replaced with the final MCEM model fit. Standard errors are included and returned, if mod is a class of object accepted by the sandwich package (such as glm, gam, survreg and many more). The effective sample size (which diagnose how closely the proposal distribution matches the posterior, see equation (2) of Stoklosa, Hwang and Warton) have also been included as outputs.

Author(s)

Jakub Stoklosa, Wen-Han Hwang and David I. Warton.

Source

See https://github.com/JakubStats/refitME for an RMarkdown vignette with examples.

References

Carroll, R. J., Ruppert, D., Stefanski, L. A., and Crainiceanu, C. M. (2006). Measurement Error in Nonlinear Models: A Modern Perspective. 2nd Ed. London: Chapman & Hall/CRC.

Stoklosa, J., Hwang, W-H., and Warton, D.I. refitME: Measurement Error Modelling using Monte Carlo Expectation Maximization in R.

See Also

MCEMfit_glm, MCEMfit_gam and MCEMfit_gen

Examples

# A GLM example I - binary response data.

library(refitME)

data(Framinghamdata)

glm_naiv <- glm(Y ~ w1 + z1 + z2 + z3, x = TRUE, family = binomial, data = Framinghamdata)

# The error-contaminated predictor variable in this example is systolic blood pressure (w1).

sigma.sq.u <- 0.01259/2 # ME variance, as obtained from Carroll et al. (2006) monograph.

B <- 50  # The number of Monte Carlo replication values.

glm_MCEM <- refitME(glm_naiv, sigma.sq.u, B)

Function that replaces NA with zero for a matrix

Description

This function replaces NA with zero for a matrix.

Usage

## S3 method for class 'na'
sqrt(x)

Arguments

Value

sqrt.na returns a matrix.

Author(s)

Jakub Stoklosa

Function that calculates a weighted variance

Description

This function that calculates a weighted variance for a given vector.

Usage

wt.var(x, w)

Arguments

Value

wt.var returns a single value from analysis requested.

Source

The developer of this function is Jeremy VanDerWal. See https://rdrr.io/cran/SDMTools/src/R/wt.mean.R

Examples

# Define simple data
x = 1:25 # Set of numbers.
wt = runif(25) # Some arbitrary weights.

# Display variances (unweighted and then weighted).
var(x)
wt.var(x, wt)