Package {malp}

Data on body fat

Description

Lists estimates of the percentage of body fat determined by underwater weighing and various body circumference measurements for 252 men.

Usage

data("bodyFat")

Format

A data frame with 252 observations on the following 15 variables.

BD

Density determined from underwater weighing

PBF

Percent body fat from Siri's (1956) equation

Age

Age (years)

WGT

Weight (lbs)

HGT

Height (inches)

NCK

Neck circumference (cm)

CST

Chest circumference (cm)

ABD

Abdomen 2 circumference (cm)

Hip

Hip circumference (cm)

TGH

Thigh circumference (cm)

KN

Knee circumference (cm)

ANK

Ankle circumference (cm)

BCP

Biceps (extended) circumference (cm)

FA

Forearm circumference (cm)

WRT

Wrist circumference (cm)

Source

Statlib.

https://lib.stat.cmu.edu/datasets/bodyfat

Concordance correlation coefficient

Description

This is a measure of agreement, which evaluates how close the linear relationship between two random variables is from the 45 degree line.

Usage

ccc(x, y, type="Lin")

Arguments

Value

A numeric vector of length 1.

References

Lin, L. (1989). A concordance correlation coefficient to evaluate reproducibility. Biometrics, 45, 255–268.

Examples

## High concordance: almost y=x
set.seed(112233)
x <- rnorm(100)
u <- rnorm(100, sd=0.1)
y1 <- x + u
ccc(x,y1)

## Lower concordance: almost y=1+x
y2 <- 1+x+u
ccc(x,y2)

## But same Pearson correlation
cor(x,y2)

Data on Optical Coherence Tomography (OCT)

Description

Eye measurements used in Abedi et al. (2011). The original dataset contains two type of measurement for 46 individuals (1 measurement per eye). The data is then filtered to include only observations for which the signal strength is greater or equal to 6 for both measurement methods.

Usage

data("eye")

Format

A data frame with 56 observations on the following 3 variables.

Eye

OD for right eye and OS for left eye.

Stratus

time-domain Stratus OCT.

Cirrus

spectral-domain Cirrus OCT

References

Abedi, G. and Patal, P. and Doros, G. and Subramanian, M.L. (2011). Transitioning from stratus OCT to cirrus OCT: a comparison and a proposed equation to convert central subfield macular thickness measurements in healthy subjects. Graefe's Archive for Clinical and Experimental Ophthalmology, 249, 1353–1357.

K-fold cross-validation for Maximum Agreement Linear Predictor

Description

It returns some goodness of fit measures using the k-fold cross-validation method.

Usage

kFoldMalp(obj, k=5, repeated=1)

Arguments

Value

A numeric named vector with three goodness of fit measures: the Pearson correlation (PCC) and the concordance correlation (CCC) coefficients between the predictions and observed observations, and the mean squared error (MSE).

References

Kim, T. & Chausse, P & Matteo Bottai & Doros, G. & Giurcanu, M. & Luta, G. & Pena, E.A. (2026). “Maximum Agreement Linear Predictors.” Electronic Journal of Statistics, 20(2), 2892–2942. doi:10.1214/26-EJS2550

Examples

## Stratus VS Cirrus OCT (optimal coherence tomography)

# Left eye
data(eye)
fitL <- malp(Stratus~Cirrus, data=subset(eye, Eye=="OS"))
kFoldMalp(fitL)

# Right eye
fitR <- malp(Stratus~Cirrus, data=subset(eye, Eye=="OD"))
kFoldMalp(fitR)

Maximum Agreement Linear Predictor

Description

This is the main function to estimate the maximum agreement linear predictor. Instead of estimating the predictor directly, as in Kim et al. (2026), the coefficients are estimated like linear models fitted by lm and saved in the "malp" object created by this function.

Usage

malp(formula, data, obj=TRUE)

Arguments

Value

malp returns an object of class "malp", with the following components:

The print method for this object is like the method for objects of class "lm". It prints the call and coefficient estimates.

References

Kim, T. & Chausse, P & Matteo Bottai & Doros, G. & Giurcanu, M. & Luta, G. & Pena, E.A. (2026). “Maximum Agreement Linear Predictors.” Electronic Journal of Statistics, 20(2), 2892–2942. doi:10.1214/26-EJS2550

Examples

## Stratus VS Cirrus OCT (optimal coherence tomography)

# Left eye
data(eye)
fitL <- malp(Stratus~Cirrus, data=subset(eye, Eye=="OS"))
fitL
# Right eye
fitR <- malp(Stratus~Cirrus, data=subset(eye, Eye=="OD"))
fitR

## Body fat

data(bodyFat)
fit <- malp(PBF~ABD+WGT+FA+WRT+Age+TGH+NCK+Hip, bodyFat)
fit

Plot method for objects of class "malp"

Description

The function plots the dependent variable against the fitted values from the maximum agreement method. The purpose is to compare the fit with the 45 degree line representing the absolute agreement.

Usage

## S3 method for class 'malp'
plot(x, y=NULL, which=c("MALP", "LSLP", "Both"),
                       pch=21:22, col=2:3, bg=2:3, ...)

Arguments

Value

No value is returned. This method is called for producing a plot. It invisibly returns NULL.

References

Kim, T. & Chausse, P & Matteo Bottai & Doros, G. & Giurcanu, M. & Luta, G. & Pena, E.A. (2026). “Maximum Agreement Linear Predictors.” Electronic Journal of Statistics, 20(2), 2892–2942. doi:10.1214/26-EJS2550

Examples

## Eye data example (see reference)

data(eye)
fitL <- malp(Stratus~Cirrus, data=subset(eye, Eye=="OS"))
plot(fitL, which="Both")

## Body fat (see reference)

data(bodyFat)
fit <- malp(PBF~ABD+WGT+FA+WRT+Age+TGH+NCK+Hip, bodyFat)
plot(fit, which="Both")

Predict method for objects of class "malp"

Description

The function predicts the dependent variable using models estimated by the maximum agreement method.

Usage

## S3 method for class 'malp'
predict(object, newdata = NULL, se.fit = FALSE,
                          interval = c("none", "confidence", "prediction"), level = 0.95,
                          includeLS = FALSE, LSdfCorr = FALSE, 
                          vcovMet = c("Asymptotic", "Normal", "Boot", "Jackknife"),
                          bootInterval=FALSE,
                          bootIntType=c("all", "norm", "basic",
                                        "stud", "perc", "bca"),
                          Bse.=100, B.=300,
                          parallel = c("no", "multicore", "snow"),
                          ncpus = getOption("boot.ncpus", 1L), cl =
                          NULL, ...) 

Arguments

Details

By default, standard errors are computed using the Delta Method, which relies on a linear approximation of the solution. This approach is asymptotically valid under weak regularity conditions. However, its accuracy may be poor in small samples, in which case simulation-based methods may provide more reliable standard error estimates.

If you are willing to assume joint normality, you can set vcovMet to "Normal", in which case the exact expression for the standard error of the predictor is used. This method is valid only under the joint normality assumption.

Value

The following applies to all types of prediction. If includeLS is set to TRUE, the returned value is a list with components LS (least squares) and MALP (maximum agreement), each containing the prediction object described below. Otherwise, the prediction object itself is returned.

If interval = "none" and se.fit = FALSE, the prediction object is a numeric vector of predictions.

If interval = "none" and se.fit = TRUE, the prediction object is a list with components fit, containing the numeric vector of predictions, and se.fit, containing the corresponding estimated standard errors.

If interval is set to either "confidence" or "predict", the prediction object is a numeric matrix whose first column contains the predictions, the second the lower bound of the confidence or prediction interval, and the third the upper bound.

Thus, for each type of prediction, the return value follows the same conventions as predict.lm.

References

Kim, T. & Chausse, P & Matteo Bottai & Doros, G. & Giurcanu, M. & Luta, G. & Pena, E.A. (2026). “Maximum Agreement Linear Predictors.” Electronic Journal of Statistics, 20(2), 2892–2942. doi:10.1214/26-EJS2550

Examples

## Stratus VS Cirrus OCT (optimal coherence tomography)

# Left eye

data(eye)
fitL <- malp(Stratus~Cirrus, data=subset(eye, Eye=="OS"))
newd <- data.frame(Cirrus=200:205)
pr <- predict(fitL, newdata=newd, interval="confidence", includeLS=TRUE)
pr

## Body fat

data(bodyFat)
fit <- malp(PBF~ABD+WGT+FA+WRT+Age+TGH+NCK+Hip, bodyFat)
newd <- data.frame(Age=20:25, ABD=85, WGT=155, FA=27, WRT=17, TGH=60,
NCK=40, Hip=100)
pr <- predict(fit, newdata=newd, se.fit=TRUE)
pr

Summary for objects of class "malp"

Description

The method computes a coefficient matrix similar to the summary method for "lm" objects.

Usage

## S3 method for class 'malp'
summary(object,
                       vcovMet=c("Asymptotic", "Normal", "Boot", "Jackknife"),
                       se=TRUE, LSdfCorr=FALSE, ...)

Arguments

Value

symmary.malp returns an object of class "summary.malp", with the following components:

A print method is also available for this class of objects.

References

Kim, T. & Chausse, P & Matteo Bottai & Doros, G. & Giurcanu, M. & Luta, G. & Pena, E.A. (2026). “Maximum Agreement Linear Predictors.” Electronic Journal of Statistics, 20(2), 2892–2942. doi:10.1214/26-EJS2550

Examples

## Stratus VS Cirrus OCT (optimal coherence tomography)

# Left eye
data(eye)
fitL <- malp(Stratus~Cirrus, data=subset(eye, Eye=="OS"))
summary(fitL)
# Right eye
fitR <- malp(Stratus~Cirrus, data=subset(eye, Eye=="OD"))
summary(fitR)

## Body fat

data(bodyFat)
fit <- malp(PBF~ABD+WGT+FA+WRT+Age+TGH+NCK+Hip, bodyFat)
summary(fit)

Covariance estimation method for objects of class malp

Description

It returns the covariance matrix of the coefficients obtained using the maximum agreement method.

Usage

## S3 method for class 'malp'
vcov(object, method=c("Asymptotic", "Normal", "Boot", "Jackknife"),
                    B=400, LSdfCorr=FALSE, ...)

Arguments

Details

Kim et al. (2026) derive expressions for the standard errors of the predictor directly, rather than for the covariance matrix of the estimated coefficients. The different methods available for estimating these standard errors are described in the Details section of predict.

The covariance matrix of the estimated coefficients is obtained by deriving an expression from the predictor variance formula presented in Kim et al. (2026).

Value

It returns the variance covariance matrix of the coefficient

References

Kim, T. & Chausse, P & Matteo Bottai & Doros, G. & Giurcanu, M. & Luta, G. & Pena, E.A. (2026). “Maximum Agreement Linear Predictors.” Electronic Journal of Statistics, 20(2), 2892–2942. doi:10.1214/26-EJS2550

Examples

## Stratus VS Cirrus OCT (optimal coherence tomography)

# Left eye
data(eye)
fitL <- malp(Stratus~Cirrus, data=subset(eye, Eye=="OS"))
vcov(fitL)