Package 'lcc'

Title: Longitudinal Concordance Correlation
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.
Authors: Thiago de Paula Oliveira [aut, cre] , Rafael de Andrade Moral [aut] , Silvio Sandoval Zocchi [ctb] , Clarice Garcia Borges Demetrio [ctb] , John Hinde [aut]
Maintainer: Thiago de Paula Oliveira <[email protected]>
License: GPL (>= 2)
Version: 2.0.0
Built: 2024-11-21 03:35:08 UTC
Source: https://github.com/prof-thiagooliveira/lcc

Help Index

Akaike and Bayesian Information Criteria for an lcc Object

Description

Calculates the Akaike Information Criterion (AIC) or the Bayesian Information Criterion (BIC) for a fitted longitudinal concordance correlation model represented by an lcc object.

Calculates the Bayesian Information Criterion (BIC) for a fitted longitudinal concordance correlation model represented by an lcc object. BIC is used for model selection, with lower values indicating a better model.

Usage

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

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

Arguments

object

An object of class lcc, representing a fitted longitudinal concordance correlation function.
...

Optional arguments passed to the underlying BIC function from the stats package.
k

Numeric value used as a penalty coefficient for the number of parameters in the fitted model; the default k = 2 corresponds to the classical AIC.

Details

The function computes AIC or BIC values as a measure of the relative quality of statistical models for a given set of data. Lower AIC or BIC values indicate a better model fit with fewer parameters. For more information, refer to the methods for AIC objects.

The function computes BIC as a measure of the trade-off between model fit and complexity. It is particularly useful for comparing models with different numbers of parameters. For more information, refer to the documentation for BIC.

See Also

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

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

Examples

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

## End(Not run)

## 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)

Compare Likelihoods of Fitted Models from an lcc Object

Description

Compares the fit of different longitudinal concordance correlation models (lcc objects). When comparing multiple models, the function returns a data frame with degrees of freedom, log-likelihood, AIC, and BIC for each model. For a single model, it returns F-values and P-values for fixed terms in the model.

Usage

## S3 method for class 'lcc'
anova(object, ..., test = TRUE, type = c("sequential", "marginal"), 
  adjustSigma = TRUE, verbose = FALSE)

Arguments

object

An object inheriting from class lcc or lme.
...

Other optional fitted model objects inheriting from classes "lcc" or "lme".
test

Logical; if TRUE, performs likelihood ratio tests to compare models. Defaults to TRUE.
type

Character string specifying the type of sum of squares for F-tests. Options are "sequential" or "marginal". Defaults to "sequential".
adjustSigma

Logical; if TRUE, adjusts the residual standard error for maximum likelihood estimation. Defaults to TRUE.
verbose

Logical; if TRUE, prints additional model details. Defaults to FALSE.

Details

This function is an adaptation from anova.lme. It assesses whether the addition of terms significantly improves model fit.

See Also

lcc, summary.lcc

Examples

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

## End(Not run)

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.

Author(s)

Thiago de Paula Oliveira, [email protected]

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)

Extract Fitted Values from an lcc Object

Description

Extracts and prints the fitted values from an object of class lcc, as returned by modeling functions. The function allows selection of different types of fitted values based on longitudinal data analysis.

Usage

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

Arguments

object

An object of class lcc, representing a fitted longitudinal concordance correlation model.
type

The type of fitted values to extract: "lcc" for longitudinal concordance correlation, "lpc" for longitudinal Pearson correlation, or "la" for longitudinal accuracy. Defaults to "lcc".
digits

Minimum number of significant digits to be printed. Default is NULL, which uses the default precision.
...

Additional arguments (currently not used).

Value

The function prints the fitted values and returns them as a data frame.

See Also

lcc, summary.lcc, lccPlot

Examples

data(hue)
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")

Format Columns for Print

Description

This internal helper function is used to format the columns of a data frame for printing, specifically for use within the 'print.anova.lcc' function. It applies special formatting rules based on the column name, such as rounding and special handling of small p-values.

Usage

formatColumn(column, colName)

Arguments

column

A vector representing a column from a data frame.
colName

A string indicating the name of the column, which determines the formatting rules to be applied.

Details

The function specifically handles the following columns: - "p-value": Rounds the values to four decimal places, and represents values less than 0.0001 as "<.0001". - "AIC", "BIC", "logLik", "L.Ratio": Applies 'zapsmall' for formatting. Other columns are returned without changes.

Value

A vector with the same length as 'column', where each element has been formatted according to the column-specific rules.

Examples

data <- data.frame(
  pvalue = c(0.00005, 0.0234, 0.5),
  AIC = c(123.4567, 234.5678, 345.6789)
)
data$pvalue <- formatColumn(data$pvalue, "p-value")
data$AIC <- formatColumn(data$AIC, "AIC")

Extract Variance Components from a Fitted lcc Model

Description

Retrieves the variance-covariance matrix of the specified component from a fitted lcc model object. The function can extract different types of variance-covariance matrices based on the specified component type.

Usage

## S3 method for class 'lcc'
getVarCov(obj, type = "random.effects", ...)

Arguments

obj

An object of class lcc, representing a fitted longitudinal concordance correlation model.
type

Specifies the type of variance-covariance matrix to extract. Options are "random.effects" for random-effects variance-covariance, "conditional" for conditional variance-covariance of the responses, and "marginal" for marginal variance-covariance of the responses. Default is "random.effects".
...

Optional arguments passed to the underlying getVarCov function from the nlme package.

Details

This function is useful for detailed inspection of the variance components in different aspects of the model. For more information on the types of variance-covariance matrices and their interpretations, refer to the documentation of the nlme package.

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 tt. 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)

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≥1q \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, [email protected], 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()

## Not run: 
## 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()

## End(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")

## Not run: 
## 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")

## End(Not run)

## Considering three methods of color evaluation
## Not run: 
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)

## End(Not run)

## Including an additional covariate in the linear predictor
## (randomized block design)
## Not run: 
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)

## End(Not run)

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

## Not run: 
## 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)

Plot Fitted Curves from an lcc Object

Description

This function generates a plot of predictions versus the time covariate for an lcc object. Predicted values are connected by lines, while actual observations are denoted by circles. If components=TRUE was used in the lcc object, individual plots for each statistic (LCC, LPC, and LA) are produced on separate pages.

Usage

lccPlot(obj, type = "lcc", control = list(), ...)

Arguments

obj

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

Character string specifying the type of plot to generate.

  • "lcc": Produces the LCC plot.

  • "lpc": Produces the LPC plot. Available only if components = TRUE.

  • "la": Produces the LA plot. Available only if components = TRUE.

control

A list of graphical control values or character strings returned by the plotControl function. Defaults to an empty list. The list can contain components like shape, colour, size, xlab, ylab, scale_y_continuous, and all.plot.
...

Additional arguments passed to the facet_wrap function.

Value

An object of class ggplot or viewport, depending on the all.plot setting in control.

Author(s)

Thiago de Paula Oliveira, [email protected]

See Also

lcc, plotControl

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 ggplot2 themes
lccPlot(fm1, type = "lpc") + theme_bw() + labs(x = "Time (Days)", y = "LPC Value")

# Generating and saving plots
## Not run: 
  ggsave("lccPlot.pdf", lccPlot(fm1, type = "lcc"))

## End(Not run)

Extract Log-Likelihood of an lcc Object

Description

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

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.

Author(s)

Thiago de Paula Oliveira, [email protected]

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)

Diagnostic Plots for an lcc Object

Description

Generates a series of diagnostic plots for evaluating the fit of a linear mixed-effects model represented by an lcc object. This function provides six types of plots, including residual plots, fitted value comparisons, and normal Q-Q plots. Users can select specific plots or display all by default.

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 of class lcc, representing a fitted longitudinal concordance correlation function.
which

A numeric vector specifying which plots to display. The valid range is c(1L:6L), corresponding to the plot types.
caption

Captions for the plots, provided as a vector or list of valid graphics annotations. Default captions are provided for each plot.
sub.caption

A common sub-title for all plots; defaults to NULL.
main

The main title for the plots, displayed above the captions.
panel

Panel function to be used for adding points to the plots. Defaults to panel.smooth if add.smooth is TRUE, otherwise points.
add.smooth

Logical; indicates whether a smoother should be added to most plots. Defaults to TRUE.
ask

Logical; if TRUE, prompts the user before displaying each plot in a multi-plot layout. Defaults to TRUE.
id.n

Number of extreme points to label in the first three plots.
labels.id

Labels for the extreme points, defaulting to observation numbers if NULL.
label.pos

Positioning of labels in the left and right halves of the graph, applicable for plots 1-3.
cex.id

Magnification factor for point labels.
cex.caption

Size of the plot captions.
cex.oma.man

Size of the overall margin annotation (applies only if sub.caption is above the figures in multi-plot layouts).
...

Additional graphical parameters passed to par.

Details

The Q-Q plots use normalized residuals. Standardized residuals are pre-multiplied by the inverse square-root factor of the estimated error correlation matrix, while random effects are adjusted using the estimated variances from matrix G. Simulation envelopes in Q-Q plots are generated using the hnp package.

The function is partly adapted from plot.lm.

Author(s)

Thiago de Paula Oliveira, [email protected]

See Also

lccPlot, lcc, mtext, text, plotmath

Examples

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

## End(Not run)

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.

Author(s)

Thiago de Paula Oliveira, [email protected]

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 Method for lcc Objects

Description

Prints detailed information about the fitted longitudinal concordance correlation model contained in an lcc object.

Usage

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

Arguments

x

An object of class lcc, representing a fitted longitudinal concordance correlation model.
digits

Minimum number of significant digits to be printed in values. Default is NULL, which uses the default precision.
...

Further arguments passed to print.

Value

The function is used for its side effect of printing and returns the input lcc object invisibly.

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)
print(fm1)

## End(Not run)

Print Summary of an lcc Object

Description

Provides a detailed summary of a fitted longitudinal concordance correlation model, including AIC, BIC, log-likelihood, and other relevant statistics. The function supports detailed output for different types of model fits.

Usage

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

Arguments

x

An object of class summary.lcc, representing a summarized longitudinal concordance correlation function.
verbose

Logical value to control the amount of printed output for model details. Defaults to FALSE.
digits

Specifies the minimum number of significant digits to be printed in values. Default is NULL.
...

Further arguments passed to print.

See Also

summary.lcc, lccPlot, lcc

Examples

## Not run: 
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 Random Effects from an lcc Model

Description

Extracts the estimated random effects from a fitted longitudinal concordance correlation model represented by an lcc object. The function returns a data frame with rows corresponding to different groups at a specified level and columns representing the random effects.

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 from the nlme package.

Details

This function is useful for examining the random effects associated with groups or subjects in the model. For a detailed explanation of these effects, see the documentation for nlme objects.

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)

Extract Residuals from a Fitted lcc Model

Description

Extracts residuals from the fitted longitudinal concordance correlation model represented by an lcc object. Different types of residuals can be obtained based on the specified type.

Usage

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

Arguments

object

An object of class lcc, representing a fitted longitudinal concordance correlation function.
type

A character string specifying the type of residuals to extract. Options are "response" for residuals obtained by subtracting the fitted values from the response (default), "pearson" for "response" residuals divided by the estimated within-group standard error, and "normalized" for normalized residuals. Partial matching is used, so only the first character of the type is necessary.
...

Optional arguments passed to the residuals.lme function from the nlme package.

Details

The function provides a convenient way to examine the differences between observed and predicted values in the model. Understanding these residuals can be crucial for model diagnostics and validation. For more information, refer to the methods for nlme objects.

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)
residuals(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, [email protected]

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")

Extract Variance-Covariance Matrix of the Fixed Effects for an lcc Object

Description

Extracts the variance-covariance matrix of the fixed effects from a fitted lcc model object. This function provides insights into the variability and covariance structure of the fixed effects in the model.

Usage

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

Arguments

object

An object of class lcc, representing a fitted longitudinal concordance correlation model.
...

Optional arguments passed to the vcov.lme function from the nlme package.

Details

The function specifically retrieves the variance-covariance matrix associated with the fixed effects of the lcc object, which is useful for understanding the relationship between these effects. For more details on variance-covariance matrices, refer to the methods for nlme objects.

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)