Type: Package
Title: Longitudinal Concordance Correlation
Version: 1.1.4
Author: Thiago de Paula Oliveira ORCID iD [aut, cre], Rafael de Andrade Moral ORCID iD [aut], Silvio Sandoval Zocchi ORCID iD [ctb], Clarice Garcia Borges Demetrio ORCID iD [ctb], John Hinde ORCID iD [aut]
Maintainer: Thiago de Paula Oliveira <thiago.paula.oliveira@alumni.usp.br>
Description: Estimates the longitudinal concordance correlation to access the longitudinal agreement profile. The estimation approach implemented is variance components approach based on polynomial mixed effects regression model, as proposed by Oliveira, Hinde and Zocchi (2018) <doi:10.1007/s13253-018-0321-1>. In addition, non-parametric confidence intervals were implemented using percentile method or normal-approximation based on Fisher Z-transformation.
Date: 2022-08-23
Depends: R (≥ 3.2.3), nlme (≥ 3.1-124), ggplot2 (≥ 2.2.1)
Imports: hnp, parallel, doSNOW, doRNG, foreach
Suggests: roxygen2 (≥ 3.0.0), covr, testthat, MASS
License: GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
Encoding: UTF-8
Repository: CRAN
NeedsCompilation: yes
LazyData: true
RoxygenNote: 7.1.2
Packaged: 2022-08-24 20:25:40 UTC; thiago
Date/Publication: 2022-08-25 09:00:02 UTC

Akaike and Bayesian Information Criteria for an lcc Object.

Description

Calculate the Akaike's 'An Information Criterion' or the BIC or SBC (Schwarz's Bayesian criterion) for an object of class lcc.

Usage

## S3 method for class 'lcc'
AIC(object, ..., k = 2)

## S3 method for class 'lcc'
BIC(object, ...)

Arguments

object

an object inheriting from class lcc, representing a fitted longitudinal concordance correlation function.

...

optional arguments passed to the AIC function.

k

numeric value, use as penalty coefficient for the number of parameters in the fitted model; the default k = 2 is the classical AIC.

Value

A numeric value with the corresponding AIC or BIC value. See methods for AIC objects to get more details.

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

See Also

lcc, summary.lcc, coef.lcc, vcov.lcc

Examples

## Not run: 
attach(simulated_hue)
fm6 <- lcc(data = simulated_hue, subject = "Fruit",
           resp = "Hue", method = "Method", time = "Time",
           qf = 2, qr = 1, components = TRUE,
           time_lcc = list(n=50, from=min(Time), to=max(Time)))
AIC(fm6)
BIC(fm6)

## End(Not run)

Internal Function to Compute the Sampled Concordance Correlation Values.

Description

This is an internally called functions used to compute the sampled concordance correlation values.

Value

No return value, called for side effects

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

Internal Function to Estimate the Sampled Concordance Correlation Coefficient.

Description

This is an internally called function used to estimate the sampled concordance correlation coefficient.

Value

No return value, called for side effects

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

Internal Function to Estimate the Sampled Pearson Correlation.

Description

This is an internally called functions used to estimate the sampled Pearson correlation.

Value

No return value, called for side effects

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

Compare Likelihoods of Fitted Models from an lcc Object

Description

Compare Likelihoods of Fitted Models from an lcc Object

Usage

## S3 method for class 'lcc'
anova(object, ..., test, type, adjustSigma,
  verbose)

Arguments

object

an object inheriting from class lcc or lme, representing a fitted longitudinal concordance correlation function.

...

other optional fitted model objects inheriting from classes "lcc", or "lme".

test

an optional logical value controlling whether likelihood ratio tests should be used to compare the fitted models represented by object and the objects in .... Defaults to TRUE.

type

an optional character string specifying the type of sum of squares to be used in F-tests for the terms in the model. If sequential, the sequential sum of squares obtained by including the terms in the order they appear in the model is used; else, if marginal, the marginal sum of squares obtained by deleting a term from the model at a time is used. This argument is only used when a single fitted object is passed to the function. Partial matching of arguments is used, so only the first character needs to be provided. Defaults to sequential.

adjustSigma

an optional logical value. If TRUE and the estimation method used to obtain object was maximum likelihood, the residual standard error is multiplied by sqrt(nobs/(nobs - npar)), converting it to a REML-like estimate. This argument is only used when a single fitted object is passed to the function. Default is TRUE.

verbose

an optional logical value. If TRUE, the calling sequences for each fitted model object are printed with the rest of the output, being omitted if verbose = FALSE. Defaults to FALSE.

Details

This function is an adaptation from the anova.lme. For more details see methods for nlme.

Value

If just one lcc model object is declared, a data frame with the numerator degrees of freedom, denominator degrees of freedom, F-values, and P-values for the fixed terms in the model. Otherwise, when multiple lcc fitted objects are being compared, a data frame with the degrees of freedom, the (restricted) log-likelihood, the Akaike Information Criterion (AIC), and the Bayesian Information Criterion (BIC) of each object is returned.

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

See Also

lcc, summary.lcc

Examples

## Not run: 
## Testing random effects
fm1.aov <- lcc(data = hue, subject = "Fruit", resp = "H_mean",
               method = "Method", time = "Time", qf = 2, qr = 1)
fm2.aov <- update(fm1.aov,  qr = 2)
anova(fm1.aov, fm2.aov)

## End(Not run)

## Not run: 
# Testing fixed effects
fm3.aov <- update(fm2.aov,  REML = FALSE)
fm4.aov <- update(fm2.aov,  REML = FALSE,  qf = 3)
anova(fm3.aov, fm4.aov)

## End(Not run)

## Not run: 
# Comparing the 3 lcc models
fm5.aov <- update(fm2.aov,  var.class = varExp, weights.form = "time")
anova(fm1.aov, fm2.aov, fm5.aov)

## End(Not run)

Internal functions to estimate fixed effects and variance components.

Description

This is an internally called functions used to estimate fixed effects and variance components for each bootstrap sample.

Value

No return value, called for side effects

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

Internal Function to Prepare the ciCompute Function.

Description

This is an internally called function used to prepare the ciCompute function.

Value

No return value, called for side effects

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

Internal Function to Compute the Non-Parametric Bootstrap Interval.

Description

This is an internally called function used to compute the non-parametric bootstrap interval.

Value

returns a matrix or list of matrix containing the non-parametric bootstrap interval.

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

Extract Model Coefficients

Description

The fixed effects estimated and corresponding random effects estimates are obtained at subject levels less or equal to i. The resulting estimates are returned as a data frame, with rows corresponding to subject levels and columns to coefficients.

Usage

## S3 method for class 'lcc'
coef(object, ...)

Arguments

object

an object inheriting from class lcc, representing a fitted longitudinal concordance correlation function.

...

optional arguments passed to the coef.lme function.

Details

See methods for nlme objects to get more details.

Value

Coefficients extracted from the model object.

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

See Also

lcc, summary.lcc, lccPlot, vcov.lcc

Examples


## Not run: 
fm1<-lcc(data = hue, subject = "Fruit", resp = "H_mean",
         method = "Method", time = "Time", qf = 2, qr = 2)
coef(fm1)

## End(Not run)

Internal Functions to Generate Bootstrap Samples Based on Dataset.

Description

This is an internally called functions used to generate bootstrap samples.

Value

No return value, called for side effects

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

Internal Function to Prepare the Dataset for lcc Objects

Description

This is an internally called function used to prepare the dataset for lcc objects

Value

No return value, called for side effects

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

Extract lcc Fitted Values

Description

Fitted values from object of class lcc returned by modeling functions.

Usage

## S3 method for class 'lcc'
fitted(object, type, digits, ...)

Arguments

object

an object inheriting from class lcc, representing a fitted longitudinal concordance correlation function.

type

an optional character string specifying the type of output to be returned. If type="lcc", prints the fitted longitudinal concordance correlation. If type="lpc", prints the fitted longitudinal Pearson correlation. If type="la", prints the fitted longitudinal accuracy. Defaults to type="lcc".

digits

a non-null value for digits specifies the minimum number of significant digits to be printed in values. The default, NULL.

...

not used.

Value

A data frame with columns given by methods, time, and fitted values.

No return value, called for side effects

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

See Also

lcc, summary.lcc, lccPlot

Examples

data(hue)
## Second degree polynomial model with random intercept, slope and
## quadratic term
## Not run: 
fm1 <- lcc(data = hue, subject = "Fruit", resp = "H_mean",
           method = "Method", time = "Time", qf = 2, qr = 2,
           components = TRUE)
fitted(fm1)
fitted(fm1, type="lpc")
fitted(fm1, type="la")

## End(Not run)

Internal Function to Build Fitted Values for lcc Objects

Description

This is an internally called function used to build fitted values.

Value

No return value, called for side effects

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

Internal Function to Extract Variance Components Estimates.

Description

This is an internally called function used to extract variance components estimate of \Sigma matrix based on specified structure.

Value

No return value, called for side effects

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br and Rafael de Andrade Moral, rafael_moral@yahoo.com.br

Extract Variance Components from a Fitted Model

Description

Extract Variance Components from a Fitted Model

Usage

## S3 method for class 'lcc'
getVarCov(obj, type, ...)

Arguments

obj

an object inheriting from class lcc, representing a fitted longitudinal concordance correlation function.

type

specifies the type of variance covariance matrix. If type = "random.effects", the default, extract the random-effects variance-covariance; if type = "conditional" extract the conditional variance-covariance of the responses; and if type = "marginal" extracts the the marginal variance-covariance of the responses.

...

optional arguments passed to the getVarCov function.

Details

See methods for nlme objects to get more details.

Value

Returns the variance-covariance matrix of a fitted lcc model object.

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

See Also

lcc, summary.lcc, coef.lcc, vcov.lcc

Examples


## Not run: 
fm1<-lcc(data = hue, subject = "Fruit", resp = "H_mean",
         method = "Method", time = "Time", qf = 2, qr = 2)
getVarCov(fm1)

## End(Not run)

Hue color data

Description

An observational study conducted at the Vegetable Production Department at "Luiz de Queiroz" College of Agriculture/University of São Paulo in 2010/2011 to evaluate the peel color of 20 papaya fruits cv. Sunrise Solo over time. The color hue was measured on the equatorial region of each fruit using four points observed by the colorimeter and 1,000 points observed by the scanner. Thus, the circular mean hue was calculated for each fruit by each device at time t. The aim of the agreement study was to assess how well the colorimeter agreed with the scanner over time.

Usage

data(hue)

Format

A data frame with 554 observations on the mean hue variable. The format is:

H_mean numeric; mean hue of papaya's peel
Method a factor with levels Colorimeter, Scanner
Time integer; time in days
Fruit a factor with 20 levels; from 1 to 20
where each level is represented by one fruit.

Source

Oliveira, T.P.; Hinde, J.; Zocchi S.S. Longitudinal Concordance Correlation Function Based on Variance Components: An Application in Fruit Color Analysis. Journal of Agricultural, Biological, and Environmental Statistics, v. 23, n. 2, 233–254, 2018.

Oliveira, T.P.; Zocchi S.S.; Jacomino, A.P. Measuring color hue in 'Sunrise Solo' papaya using a flatbed scanner. Rev. Bras. Frutic., v. 39, n. 2, e-911, 2017.

References

Oliveira, T.P.; Hinde, J.; Zocchi S.S. Longitudinal Concordance Correlation Function Based on Variance Components: An Application in Fruit Color Analysis. Journal of Agricultural, Biological, and Environmental Statistics, v. 23, n. 2, 233–254, 2018.

See Also

lcc.

Examples

data(hue)
summary(hue)
str(hue)
## Second degree polynomial model with random intercept, slope and
## quadratic term including an exponential variance function using
## time as covariate.
model<-lcc(data = hue, subject = "Fruit", resp = "H_mean",
          method = "Method", time = "Time", qf = 2, qr = 2,
          components = TRUE, time_lcc = list(from = min(hue$Time),
          to = max(hue$Time), n=40), var.class=varExp,
          weights.form="time")
summary(model, type="model")
summary(model, type="lcc")
## for discussion on the analysis of complete data set,
## see Oliveira et al. (2018)

Internal Function to Prepare lccModel Function

Description

This is an internally called function used to verify the specification of variance-covariance matrices and likelihood based method.

Value

No return value, called for side effects

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

Reports whether x is a lcc object

Description

Reports whether x is a lcc object

Usage

is.lcc(x)

Arguments

x

An object to test

Value

Returns if the object belongs to lcc class

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

Internal functions to generate longitudinal accuracy samples.

Description

This is an internally called functions used to generate longitudinal caccuracy samples.

Value

No return value, called for side effects

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

Internal Function to Estimate the Longitudinal Accuracy.

Description

This is an internally called function used to estimate the longitudinal accuracy (LA).

Value

returns a vector or list containing the longitudinal accuracy estimates.

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

Internal Function to Prepare the laBuilder Function

Description

This is an internally called function used to prepare the laBuilder function.

Details

returns a vector or list containing the longitudinal accuracy estimates.

Value

No return value, called for side effects

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

Longitudinal Concordance Correlation (LCC) Estimated by Fixed Effects and Variance Components using a Polynomial Mixed-Effects Regression Model

Description

The lcc function gives fitted values and non-parametric bootstrap confidence intervals for LCC, longitudinal Pearson correlation (LPC), and longitudinal accuracy (LA) statistics. These statistics can be estimated using different structures for the variance-covariance matrix for random effects and variance functions to model heteroscedasticity among the within-group errors using or not the time as a covariate.

Usage

lcc(data, resp, subject, method, time, interaction, qf,
    qr, covar, gs, pdmat, var.class, weights.form, time_lcc, ci,
    percentileMet, alpha, nboot, show.warnings, components,
    REML, lme.control, numCore)

Arguments

data

an object of class data.frame.

resp

character string. Name of the response variable in the data set.

subject

character string. Name of the subject variable in the data set.

method

character string. Name of the method variable in the data set. The first level of method is used as the gold-standard method.

time

character string. Name of the time variable in the data set.

interaction

an option to estimate the interaction effect between method and time. If TRUE, the default, interaction effect is estimated. If FALSE only the main effects of time and method are estimated.

qf

an integer specifying the degree time polynomial trends, normally 1, 2 or 3. (Degree 0 is not allowed). Default is qf=1

qr

an integer specifying random effects terms to account for subject-to-subject variation. Note that qr=0 specifies a random intercept (form ~ 1|subject); qr=1 specifies random intercept and slope (form ~ time|subject). If qr=qf=q, with q \ge 1, random effects at subject level are added to all terms of the time polynomial regression (form ~ poly(time, q, raw = TRUE)|subject). Default is qr=0.

covar

character vector. Name of the covariates to be included in the model as fixed effects. Default to NULL, never include.

gs

character string. Name of method level which represents the gold-standard. Default is the first level of method.

pdmat

standard classes of positive-definite matrix structures defined in the pdClasses function. The different positive-definite matrices structures available in the lcc function are pdSymm, the default, pdLogChol, pdDiag, pdIdent, pdCompSymm, and pdNatural.

var.class

standard classes of variance functions to model the variance structure of within-group errors using covariates, see varClasses. Default to NULL, correspond to homoscedastic within-group errors. Available standard classes:

varIdent:

allows different variances according to the levels of the stratification variable.

varExp:

exponential function of the variance covariate; see varExp.

weights.form

character string. An one-sided formula specifying a variance covariate and, optionally, a grouping factor for the variance parameters in the var.class. If var.class=varIdent, the option “method”, form ~1|method or “time.ident”, form ~1|time, must be used in the weights.form argument. If var.class=varExp, the option “time”, form ~time, or “both”, form ~time|method, must be used in the weights.form argument.

time_lcc

regular sequence for time variable merged with specific or experimental time values used for LCC, LPC, and LA predictions. Default is NULL. The list may contain the following components:

time:

a vector of specific or experimental time values of given length. The experimental time values are used as default.

from:

the starting (minimum) value of time variable.

to:

the end (maximum) value of time variable.

n:

an integer specifying the desired length of the sequence. Generally, n between 30 and 50 is adequate.

ci

an optional non-parametric boostrap confidence interval calculated for the LCC, LPC and LA statistics. If TRUE confidence intervals are calculated and printed in the output. Default is FALSE.

percentileMet

an optional method for calculating the non-parametric bootstrap intervals. If FALSE, the default, is the normal approximation method. If TRUE, the percentile method is used instead.

alpha

significance level. Default is 0.05.

nboot

an integer specifying the number of bootstrap samples. Default is 5,000.

show.warnings

an optional argument that shows the number of convergence errors in the bootstrap samples. If TRUE shows in which bootstrap sample the error occurred. If FALSE, the default, shows the total number of convergence errors.

components

an option to print LPC and LA statistics. If TRUE the estimates and confidence intervals for LPC and LA are printed in the output. If FALSE, the default, provides estimates and confidence interval only for the LCC statistic.

REML

if TRUE, the default, the model is fit by maximizing the restricted log-likelihood. If FALSE the log-likelihood is maximized.

lme.control

a list of control values for the estimation algorithm to replace the default values of the function lmeControl available in the nlme package. Defaults to an empty list. The returned list is used as the control argument for the lme function.

numCore

number of cores used in parallel during bootstrapping computation. Default is 1.

Value

an object of class lcc. The output is a list with the following components:

model

summary of the polynomial mixed-effects regression model.

Summary.lcc

fitted values for the LCC or LCC, LPC and LA (if components=TRUE); concordance correlation coefficient (CCC) between methods for each level of time as sampled values, and the CCC between mixed-effects model predicted values and observed values from data as goodness of fit (gof)

data

the input dataset.

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br, Rafael de Andrade Moral, John Hinde

References

Lin, L. A Concordance Correlation Coefficient to Evaluate Reproducibility. Biometrics, 45, n. 1, 255-268, 1989.

Oliveira, T.P.; Hinde, J.; Zocchi S.S. Longitudinal Concordance Correlation Function Based on Variance Components: An Application in Fruit Color Analysis. Journal of Agricultural, Biological, and Environmental Statistics, v. 23, n. 2, 233–254, 2018.

Oliveira, T.P.; Moral, R.A.; Zocchi, S.S.; Demetrio, C.G.B.; Hinde, J. lcc: an R packageto estimate the concordance correlation, Pearson correlation, and accuracy over time. PeerJ, 8:c9850, 2020. DOI:10.7717/peerj.9850

See Also

summary.lcc, fitted.lcc, print.lcc, lccPlot, plot.lcc, coef.lcc, ranef.lcc, vcov.lcc, getVarCov.lcc, residuals.lcc, AIC.lcc

Examples

data(hue)
## Second degree polynomial model with random intercept, slope and
## quadratic term
fm1 <- lcc(data = hue, subject = "Fruit", resp = "H_mean",
           method = "Method", time = "Time", qf = 2, qr = 2)
print(fm1)
summary(fm1)
summary(fm1, type="model")
lccPlot(fm1) +
 ylim(0,1) +
 geom_hline(yintercept = 1, linetype = "dashed") +
 scale_x_continuous(breaks = seq(1,max(hue$Time),2))

## Estimating longitudinal Pearson correlation and longitudinal
## accuracy
fm2 <- update(fm1, components = TRUE)
summary(fm2)
lccPlot(fm2) +
 ylim(0,1) +
 geom_hline(yintercept = 1, linetype = "dashed") +
 scale_x_continuous(breaks = seq(1,max(hue$Time),2)) +
 theme_bw()

## A grid of points as the Time variable for prediction
fm3 <- update(fm2, time_lcc = list(from = min(hue$Time),
           to = max(hue$Time), n=40))
summary(fm3)
lccPlot(fm3) +
 ylim(0,1) +
 geom_hline(yintercept = 1, linetype = "dashed") +
 scale_x_continuous(breaks = seq(1,max(hue$Time),2)) +
 theme_bw()

## Not run: 
## Including an exponential variance function using time as a
## covariate.
fm4 <- update(fm2,time_lcc = list(from = min(hue$Time),
              to = max(hue$Time), n=30), var.class=varExp,
              weights.form="time")
summary(fm4,  type="model")
fitted(fm4)
fitted(fm4, type = "lpc")
fitted(fm4, type = "la")
lccPlot(fm4) +
 geom_hline(yintercept = 1, linetype = "dashed")
lccPlot(fm4, type = "lpc") +
 geom_hline(yintercept = 1, linetype = "dashed")
lccPlot(fm4, type = "la") +
 geom_hline(yintercept = 1, linetype = "dashed")

## Non-parametric confidence interval with 500 bootstrap samples
fm5 <- update(fm1, ci = TRUE, nboot = 500)
summary(fm5)
lccPlot(fm5) +
 geom_hline(yintercept = 1, linetype = "dashed")


## Considering three methods of color evaluation
data(simulated_hue)
attach(simulated_hue)
fm6 <- lcc(data = simulated_hue, subject = "Fruit",
           resp = "Hue", method = "Method", time = "Time",
           qf = 2, qr = 1, components = TRUE,
           time_lcc = list(n=50, from=min(Time), to=max(Time)))
summary(fm6)
lccPlot(fm6, scales = "free")
lccPlot(fm6, type="lpc", scales = "free")
lccPlot(fm6, type="la", scales = "free")
detach(simulated_hue)

## Including an additional covariate in the linear predictor
## (randomized block design)
data(simulated_hue_block)
attach(simulated_hue_block)
fm7 <- lcc(data = simulated_hue_block, subject = "Fruit",
           resp = "Hue", method = "Method",time = "Time",
           qf = 2, qr = 1, components = TRUE, covar = c("Block"),
           time_lcc = list(n=50, from=min(Time), to=max(Time)))
summary(fm7)
lccPlot(fm7, scales="free")
detach(simulated_hue_block)

## Testing interaction effect between time and method
fm8 <- update(fm1, interaction = FALSE)
anova(fm1, fm8)

## Using parallel computing with 3 cores, and a set.seed(123)
## to verify model reproducibility.
set.seed(123)
fm9 <- lcc(data = hue, subject = "Fruit", resp = "H_mean",
              method = "Method", time = "Time", qf = 2, qr = 2,
              ci=TRUE, nboot = 30, numCore = 3)

# Repeating same model with same set seed.
set.seed(123)
fm10 <- lcc(data = hue, subject = "Fruit", resp = "H_mean",
              method = "Method", time = "Time", qf = 2, qr = 2,
              ci=TRUE, nboot = 30, numCore = 3)

## Verifying if both fitted values and confidence intervals
## are identical
identical(fm9$Summary.lcc$fitted,fm10$Summary.lcc$fitted)

## End(Not run)

Internal functions to generate longitudinal concordance correlation samples.

Description

This is an internally called functions used to generate longitudinal concordance correlation samples.

Value

No return value, called for side effects

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

Internal Function to Estimate the Longitudinal Concordance Correlation.

Description

This is an internally called function used to estimate the longitudinal concordance correlation (LCC).

Value

returns a vector or list containing the longitudinal concordance correlation estimates.

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

Internal Function to Prepare lcc Objects

Description

This is an internally called function used to prepare lcc objects for calculate the longitudinal concordance correlation, longitudinal Pearson correlation, longitudinal bias corrector, and plotting

Value

No return value, called for side effects

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br and Rafael de Andrade Moral, rafael_moral@yahoo.com.br

Internal Function to Fits a Linear Mixed-Effects Model in the Formulation Described in Laird and Ware (1982).

Description

This is an internally called function used to fits a linear mixed-effects model; see lme.

Value

No return value, called for side effects

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

References

Laird, N.M. and Ware, J.H. (1982) Random-Effects Models for Longitudinal Data, Biometrics, 38, 963–974.

Pinheiro, J.C. and Bates., D.M. (1996) Unconstrained Parametrizations for Variance-Covariance Matrices, Statistics and Computing, 6, 289–296.

Pinheiro, J.C., and Bates, D.M. (2000) Mixed-Effects Models in S and S-PLUS, Springer.

Plot Fitted Curves from an lcc Object.

Description

A plot of predictions versus the time covariate is generated. Predicted values are joined by lines while sampled observations are represented by circles. If the argument components=TRUE is considered in the lcc object, single plots of each statistics are returned on differents pages.

Usage

lccPlot(obj, type, control, ...)

Arguments

obj

an object inheriting from class "lcc", representing a fitted lcc model.

type

character string. If type = "lcc", the output is the LCC plot; if type = "lpc", the output is the LPC plot; and if type = "la" the output is the LA plot. Types "lpc" and "la" are available only if components = TRUE.

control

a list of control values or character strings returned by the function plotControl. Defaults to an empty list. The list may contain the following components:

shape:

draw points considering a shape parameter. Possible shape values are the numbers 0 to 25, and 32 to 127; see aes_linetype_size_shape. Default is 1.

colour:

specification for lines color. Default is "black".

size:

specification for lines size. Should be specified with a numerical value (in millimetres); see aes_linetype_size_shape. Default is 0.5.

xlab:

title for the x axis. Default is "Time".

ylab:

title for the y axis. Default is "LCC", "LPC", or "LA"

scale_y_continuous:

numeric vector of length two providing limits of the scale. Default is c(0,1).

all.plot:

viewport functions for the lcc class. If TRUE, the default, returns an object created by the viewport function with multiple plots on a single page. If FALSE returns a single ggplot object by different pages using the marrangeGrob function.

...

arguments to be passed to facet_wrap function

Value

No return value, called for side effects

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

References

Lin, L. A Concordance Correlation Coefficient to Evaluate Reproducibility. Biometrics, 45, n. 1, 255-268, 1989.

Oliveira, T.P.; Hinde, J.; Zocchi S.S. Longitudinal Concordance Correlation Function Based on Variance Components: An Application in Fruit Color Analysis. Journal of Agricultural, Biological, and Environmental Statistics, v. 23, n. 2, 233–254, 2018.

See Also

lcc.

Examples


data(hue)
## Second degree polynomial model with random intercept, slope and
## quadratic term
fm1<-lcc(data = hue, subject = "Fruit", resp = "H_mean",
         method = "Method", time = "Time", qf = 2, qr = 2,
         components=TRUE)
lccPlot(fm1, type="lcc")
lccPlot(fm1, type="lpc")
lccPlot(fm1, type="la")

## Using themes of ggplot2 package
lccPlot(fm1, type = "lpc")+
 ylim(0,1) +
 geom_hline(yintercept = 1, linetype = "dashed") +
 scale_x_continuous(breaks = seq(1,max(hue$Time),2))+
 theme_bw() +
 theme(legend.position = "none", aspect.ratio = 1,
  axis.line.x = element_line(color="black", size = 0.5),
  axis.line.y = element_line(color="black", size = 0.5),
  axis.title.x = element_text(size=14),
  axis.title.y = element_text(size=14),
  axis.text.x = element_text(size = 14, face = "plain"),
  axis.text.y = element_text(size = 14, face = "plain"))

## Using the key (+) to constructing sophisticated graphics
lccPlot(fm1, type="lcc") +
 scale_y_continuous(limits=c(-1, 1)) +
 labs(title="My title",
 y ="Longitudinal Concordance Correlation",
 x = "Time (Days)")

## Runing all.plots = FALSE and saving plots as pdf
## Not run: 
data(simulated_hue_block)
attach(simulated_hue_block)
fm2<-lcc(data = simulated_hue_block, subject = "Fruit",
         resp = "Hue", method = "Method",time = "Time",
         qf = 2, qr = 1, components = TRUE, covar = c("Block"),
         time_lcc = list(n=50, from=min(Time), to=max(Time)))
ggsave("myplots.pdf",
       lccPlot(fm2, type="lcc", scales = "free"))

## End(Not run)

Internal Function to Summarize Fitted and Sampled Values for lcc Objects

Description

This is an internally called function used to summarize fitted and sampled values, and the concordance correlation coefficient between them for lcc objects.

Value

No return value, called for side effects

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

Internal Function to Prepare the lccBuilder Function

Description

This is an internally called function used to prepare the lccBuilder function.

Value

returns a vector or list containing the longitudinal concordance correlation estimates.

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

Internal Functions to Compute the Non-Parametric Confidence Intervals for LCC.

Description

This is an internally called functions used to compute the non-parametric confidence intervals for LCC.

Value

No return value, called for side effects

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

Extract Log-Likelihood of an lcc Object

Description

Extract Log-Likelihood of an lcc Object

Usage

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

Arguments

object

an object inheriting from class lcc, representing a fitted longitudinal concordance correlation function.

...

further arguments passed to logLik.

REML

an optional logical value. If TRUE the restricted log-likelihood is returned, else, if FALSE, the log-likelihood is returned.

Details

See methods for nlme objects to get more details.

Value

If REML=TRUE, the default, returns the restricted log-likelihood value of the linear mixed-effects model; else the log-likelihood value

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

See Also

lcc, summary.lcc

Examples


## Not run: 
fm1<-lcc(data = hue, subject = "Fruit", resp = "H_mean",
         method = "Method", time = "Time", qf = 2, qr = 2)
logLik(fm1)

## End(Not run)

Internal functions to generate longitudinal Pearson correlation samples.

Description

This is an internally called functions used to generate longitudinal Pearson correlation samples.

Value

No return value, called for side effects

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

Internal Function to Estimate the Longitudinal Pearson Correlation.

Description

This is an internally called function used to estimate the longitudinal Pearson correlation (LPC).

Value

returns a vector or list containing the longitudinal Pearson correlation estimates.

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

Internal Function to Prepare the lpcBuilder Function

Description

This is an internally called function used toprepare the lpcBuilder function.

Value

returns a vector or list containing the longitudinal Pearson correlation estimates.

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

Diagnostic Plots of an lcc Object.

Description

Diagnostic plots for conditional error and random effects from the linear mixed-effects fit are obtained. Six plots plots (selectable by 'which') are currently available: a plot of residuals against fitted values, a plot of residuals against time variable, a boxplot of residuals by subject, a plot of observerd values against fitted values, a normal Q-Q plot with simulation envelopes based on conditional error, and a normal Q-Q plot with simulation envelopes based on the random effects. By default, all plots are provided.

Usage

## S3 method for class 'lcc'
plot(x, which = c(1L:6L),
     caption = list("Residuals vs Fitted",
                    "Residuals vs Time",
                    "Residuals by Subject",
                    "Observed values vs Fitted values",
                    "Normal Q-Q Plot (Conditional residuals)",
                    "Normal Q-Q Plot (Random effects)"),
     sub.caption =  NULL,  main = NULL,
     panel = if(add.smooth) panel.smooth else points,
     add.smooth = TRUE, ask = TRUE,
     id.n = 3, labels.id = names(residuals(x)),
     label.pos = c(4, 2), cex.id = 0.75, cex.caption = 1,
     cex.oma.man = 1.25, ...)

Arguments

x

an object inheriting from class lcc, representing a fitted longitudinal concordance correlation function.

which

if a subset of the plots is required, specify a subset of the numbers from 1 to 6.

caption

captions to appear above the plots. Vector or list of valid graphics annotations is required. All captions can be supressed using '""' or NA.

sub.caption

common sub-title (at bottom). Default to NULL.

main

The main title (on top) above the caption.

panel

panel function. If add.smooth = TRUE, panel.smooth is used rather than points.

add.smooth

logical indicating if smoother should be added to most plots; see also panel above. Defaults to TRUE.

ask

logical; if TRUE, the default, the user is _ask_ed before each plot, see par.

id.n

number of points to be labelled is the first three plots, starting with the most extreme.

labels.id

vector of labels, from which the labels for extreme points will be chosen. Default to NULL (uses observation numbers).

label.pos

positioning of labels, for the left half and right half of the graph respectively, for plots 1-3.

cex.id

magnification of point label.

cex.caption

controls the size of caption.

cex.oma.man

controls the size of the sub.caption only if that is _above_ the figures when there is more than one.

...

further graphical parameters from 'par'.

Details

The Q-Q plot uses the normalized residuals. The standardized residuals is pre-multiplied by the inverse square-root factor of the estimated error correlation matrix while the random effects is pre-multiplied by the inverse square root of the estimated variances obtained from matrix G. The simulate envelopes are obtained from package hnp (Moral et al., 2018).

Code partially adapted from plot.lm.

Value

Return plots for conditional error and random effects from the linear mixed-effects

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

See Also

lccPlot, lcc, mtext, text, plotmath

Examples


## Second degree polynomial model with random intercept, slope and
## quadratic term
fm1 <- lcc(data = hue, subject = "Fruit", resp = "H_mean",
           method = "Method", time = "Time", qf = 2, qr = 2)
plot(fm1)

Internal Function to Produces a Longitudinal Accuracy Plot.

Description

This is an internally called function used to produces a longitudinal accuracy plot from fitted ans sampled values with or not non-parametric confidence intervals.

Details

returns a inital plot for the longitudinal accuracy correlation.

Value

No return value, called for side effects

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

Internal Function to Produces a Longitudinal Concordance Correlation Plot.

Description

This is an internally called function used to produces a longitudinal concordance correlation plot from fitted ans sampled values with or not non-parametric confidence intervals.

Details

returns a inital plot for the longitudinal concordance correlation.

Value

No return value, called for side effects

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

Internal Function to Produces a Longitudinal Perason Correlation Plot.

Description

This is an internally called function used to produces a longitudinal Perason correlation plot from fitted ans sampled values with or not non-parametric confidence intervals.

Details

returns a inital plot for the longitudinal Pearson correlation.

Value

No return value, called for side effects

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

Specifying Graphical Control Values for lcc Class

Description

The values supplied in the plotControl() call replace the defaults, and a list with all settings is returned.

Usage

plotControl(
  plot = TRUE,
  shape = 1,
  colour = "black",
  size = 0.5,
  xlab = "Time",
  ylab = "LCC"
)

Arguments

plot

an optional to include an initial plot. If TRUE, the default, returns a ggplot object with a initial plot for lcc class. If FALSE never includes.

shape

Draw points considering a shape parameter. Legal shape values are the numbers 0 to 25, and 32 to 127; see aes_linetype_size_shape. Default is 1.

colour

an specification for lines color. Default is "black".

size

an specification for lines size. Should be specified with a numerical value (in millimetres); see aes_linetype_size_shape. Default is 0.5.

xlab

a title for the x axis. Default is "Time".

ylab

title for the y axis. Default is "LCC".

Value

a list with components for each of the possible arguments.

No return value, called for side effects

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

Internal Function to Prepare the plotBuilder_la Function.

Description

This is an internally called functions used to prepare the plotBuilder_la function.

Value

No return value, called for side effects

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

Internal function to prepare the plotBuilder_lcc function.

Description

This is an internally called function used to prepare the plotBuilder_lcc function.

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

Internal function to prepare the plotBuilder_lpc function.

Description

This is an internally called functions used to prepare the plotBuilder_lpc function.

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

Print the Anova of an lcc Object

Description

Method print for the anova.lcc.

Usage

## S3 method for class 'anova.lcc'
print(x, verbose, ...)

Arguments

x

an object inheriting from class anova.lcc, representing a fitted longitudinal concordance correlation function.

verbose

an optional logical value used to control the amount of printed output. If TRUE, the calling sequences for each fitted model object are printed with the rest of the output, being omitted if verbose = FALSE. Defaults to FALSE.

...

further arguments passed to print.

Details

Modified from anova.lme. For more details see methods for nlme.

Value

Return no value, called for side effects

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

See Also

summary.lcc, lccPlot, lcc

Examples


## Not run: 
## Second degree polynomial model with random intercept, slope and
## quadratic term
fm1<-lcc(data = hue, subject = "Fruit", resp = "H_mean",
         method = "Method", time = "Time", qf = 2, qr = 2)
print(anova(fm1))

## End(Not run)

Print an lcc Object

Description

Prints information about the longitudinal concordance correlation represented by an object of class lcc. The returned object has a print method.

Usage

## S3 method for class 'lcc'
print(x, digits, ...)

Arguments

x

an object inheriting from class lcc, representing a fitted longitudinal concordance correlation function.

digits

a non-null value for digits specifies the minimum number of significant digits to be printed in values. The default, NULL.

...

further arguments passed to {print}.

Value

an object inheriting from class print.lcc.

No return value, called for side effects

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

See Also

lcc, summary.lcc

Examples

## Not run: 
## Second degree polynomial model with random intercept, slope and
## quadratic term
fm1<-lcc(data = hue, subject = "Fruit", resp = "H_mean",
         method = "Method", time = "Time", qf = 2, qr = 2)
print(fm1)

## End(Not run)

Print the Summary of an lcc Object

Description

Information summarizing the fitted longitudinal concordance correlation is printed. This includes the AIC, BIC, and log-likelihood at convergence. If type = "lcc", prints the fitted values while type = "model" prints the fixed effects estimates and their standard errors, standard deviations, correlations for the random effects, within-group correlation, and variance function parameters.

Usage

## S3 method for class 'summary.lcc'
print(x, verbose, digits, ...)

Arguments

x

an object inheriting from class summary.lcc, representing a fitted longitudinal concordance correlation function.

verbose

an optional logical value used to control the amount of printed output when type = "model". Defaults to FALSE

digits

a non-null value for digits specifies the minimum number of significant digits to be printed in values. The default, NULL.

...

further arguments passed to print.

Value

No return value, called for side effects

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

See Also

summary.lcc, lccPlot, lcc

Examples

## Not run: 
## Second degree polynomial model with random intercept, slope and
## quadratic term
fm1<-lcc(data = hue, subject = "Fruit", resp = "H_mean",
         method = "Method", time = "Time", qf = 2, qr = 2)
print(summary(fm1, type="model"))

## End(Not run)

Extract Model Random Effects

Description

Extract the estimated random effects at level i.

Usage

## S3 method for class 'lcc'
ranef(object, ...)

Arguments

object

an object inheriting from class lcc, representing a fitted longitudinal concordance correlation function.

...

optional arguments passed to the ranef.lme function.

Details

See methods for nlme objects to get more details.

Value

A data frame with rows given by the different groups at that level and columns given by the random effects.

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

See Also

lcc, coef.lcc,

Examples

## Not run: 
fm1<-lcc(data = hue, subject = "Fruit", resp = "H_mean",
         method = "Method", time = "Time", qf = 2, qr = 2)
ranef(fm1)

## End(Not run)

Internal Function to Prepare lccModel Function

Description

This is an internally called function used to verify the specification of variance-covariance matrices and likelihood based method.

Author(s)

Code by Don MacQueen

Extract Model Residuals

Description

Extract the residulas from the model used to estimate the longitudinal concordance correlation function.

Usage

## S3 method for class 'lcc'
residuals(object, type, ...)

Arguments

object

an object inheriting from class lcc, representing a fitted longitudinal concordance correlation function.

type

an optional character string specifying the type of residulas to be used. If type = "response", the default, the residuals at level i are obtained by subtracting the fitted values at that level from the response vector. If type = "pearson", the "response" residuals is divided by the estimated within-group standard error. If type = "normalized", the normalized residuals are used. Partial matching of arguments is used, so only the first character needs to be provided.

...

optional arguments passed to the residuals.lme function.

Details

See methods for nlme objects to get more details.

Value

Return no value, called for side effects

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

See Also

lcc, summary.lcc, coef.lcc, vcov.lcc

Examples


## Not run: 
fm1<-lcc(data = hue, subject = "Fruit", resp = "H_mean",
         method = "Method", time = "Time", qf = 2, qr = 2)
getVarCov(fm1)

## End(Not run)

Hue color simulated data

Description

Simulated hue data set based on papaya's maturation over time considering three methods of measurement.

Usage

data(simulated_hue)

Format

A simulated data frame with 6,000 observations on the mean hue variable. The format is:

Hue numeric; mean hue of papaya's peel
Method a factor with levels labelled from Method 1 to Method 3
Time integer; time in days from 0 to 19
Fruit a factor with 100 levels labelled from 1 to 100
where each level is represented by one fruit.

Details

A total of 100 fruits were observed over 20 days by three methods to evaluate the mean hue of fruit's peel. The aim of the agreement study was to assess how well the methods 2, and 3 agreed with method 1 over time.

See Also

lcc.

Examples

data(simulated_hue)
summary(simulated_hue)
str(simulated_hue)

Hue color simulated data in a randomized block design

Description

Simulated hue data set based on papaya's maturation over time considering four methods of measurement in a randomized block design.

Usage

data(simulated_hue_block)

Format

A simulated data frame with 24,000 observations on the mean hue variable. The format is:

Hue numeric; mean hue of papaya's peel
Block factor with levels labelled from 1 to 3
Method a factor with levels labelled from Method 1, to Method 4
Time integer; time in days from 0 to 19
Fruit a factor with 300 levels labelled from 1 to 300
where each level is represented by one fruit.

Details

A total of 100 fruits by block were observed over 20 days by four methods to evaluate the mean hue of fruit's peel. We considered three blocks in this simulation. The aim of the agreement study was to assess how well the methods 2, 3, and 4 agreed with method 1 over time.

See Also

lcc.

Examples

data(simulated_hue_block)
summary(simulated_hue_block)
str(simulated_hue_block)

Summarize an lcc Object

Description

Additional information about the fit of longitudinal concordance correlation, longitudinal Pearson correlation, and longitudinal accuracy represented by an object of class lcc. The returned object has a print method.

Usage

## S3 method for class 'lcc'
summary(object, type, adjustSigma, verbose, ...)

Arguments

object

an object inheriting from class lcc, representing a fitted longitudinal concordance correlation function.

type

an optional character string specifying the type of output to be returned. If type="model", prints the summary of the polynomial mixed-effects regression model. If type="lcc", prints the summary of the fitted and sampled values for LCC, LPC, and LA as well as the concordance correlation coefficient between fitted values from the model and observed values as goodness of fit (gof) measurement. Defaults to type="model".

adjustSigma

an optional logical value used when type = model. If TRUE and the estimation method used to obtain object was maximum likelihood, the residual standard error is multiplied by sqrt(nobs/(nobs - npar)). See summary.lme for more information. Default is TRUE.

verbose

an optional logical value used to control the amount of output in the print.summary.lme method when type = model is used. Defaults to FALSE.

...

not used.

Value

an object inheriting from class summary.lcc including:

fitted

the fitted values extracted from the lcc object.

gof

the goodness of fit (gof) measurement is calculated using the concordance correlation coefficient between fitted and observed values. Value of 1 denote perfect concordance.

AIC

the Akaike Information Criterion corresponding to object.

BIC

the Bayesian Information Criterion corresponding to object.

logLik

If REML=FALSE, returns the log-likelihood value of the linear mixed-effects model; otherwise, the restricted log-likelihood is returned

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

See Also

AIC, BIC, print.summary.lcc, lcc

Examples


## Second degree polynomial model with random intercept, slope and
## quadratic term
fm1<-lcc(data = hue, subject = "Fruit", resp = "H_mean",
         method = "Method", time = "Time", qf = 2, qr = 2)
summary(fm1, type="model")
summary(fm1, type="lcc")

Regular Sequence for the Time Variable

Description

An list specifying control arguments to generate a regular sequence for the time variable returned by the function time_lcc, which is used to constructed the LCC, LPC and LA curves and its simultaneous confidence intervals. Default is NULL.

Usage

time_lcc(time, from, to, n)

Arguments

time

unique values of time variable

from

the starting (minimal) value of time variable.

to

the end (maximal) value of time variable.

n

an integer specifying the desired length of the sequence. Generally, n between 30 and 50 is adequate.

Value

Return a regular sequence used to create the time variable

Examples

data(hue)
attach(hue)
time_lcc(time=Time, from=min(Time), to=max(Time), n=30)
detach(hue)

Extract Variance-Covariance Matrix of the Fixed Effects

Description

Extract Variance-Covariance Matrix of the Fixed Effects

Usage

## S3 method for class 'lcc'
vcov(object, ...)

Arguments

object

an object inheriting from class lcc, representing a fitted longitudinal concordance correlation function.

...

optional arguments passed to the vcov.lme function.

Details

See methods for nlme objects to get more details.

Value

Returns the variance-covariance matrix of a fitted lcc model object.

Author(s)

Thiago de Paula Oliveira, thiago.paula.oliveira@alumni.usp.br

See Also

summary.lcc, lccPlot, lcc, coef.lcc

Examples

## Not run: 
fm1<-lcc(data = hue, subject = "Fruit", resp = "H_mean",
         method = "Method", time = "Time", qf = 2, qr = 2)
vcov(fm1)

## End(Not run)

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