| Title: | Measuring Agreement Using Sklar's Omega Coefficient |
|---|---|
| Description: | Provides tools for applying Sklar's Omega (Hughes, 2018) <arXiv:1803.02734> methodology to nominal scores, ordinal scores, percentages, counts, amounts (i.e., non-negative real numbers), and balances (i.e., any real number). The framework can accommodate any number of units, any number of coders, and missingness; and can be used to measure agreement with a gold standard, intra-coder agreement, and/or inter-coder agreement. Frequentist inference is supported for all levels of measurement. Bayesian inference is supported for continuous scores only. |
| Authors: | John Hughes <[email protected]> |
| Maintainer: | John Hughes <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 3.0-2 |
| Built: | 2024-10-27 04:04:19 UTC |
| Source: | https://github.com/cran/sklarsomega |
Produce a Bland-Altman plot.
baplot( x, y, pch = 20, col = "black", bg = "black", main = "", xlab = "Mean", ylab = "Difference", lwd1 = 1, lwd2 = 1, cex = 1, lcol = "black" )baplot( x, y, pch = 20, col = "black", bg = "black", main = "", xlab = "Mean", ylab = "Difference", lwd1 = 1, lwd2 = 1, cex = 1, lcol = "black" )
x |
the first vector of outcomes. |
y |
the second vector of outcomes. |
pch |
the plotting character. Defaults to 20, a bullet. |
col |
the foreground color. Defaults to black. |
bg |
the background color. Defaults to black. |
main |
a title for the plot. Defaults to no title, i.e., |
xlab |
a title for the x axis. Defaults to |
ylab |
a title for the y axis. Defaults to |
lwd1 |
the line width for the scatter plot. Defaults to 1. |
lwd2 |
the line width for the confidence band. Defaults to 1. |
cex |
scaling factor for the scatter plot. Defaults to 1. |
lcol |
line color for the confidence band. Defaults to black. |
This function produces rather customizable Bland-Altman plots, using the plot and abline functions. The former is used to create the scatter plot. The latter is used to display the confidence band.
Altman, D. G. and Bland, J. M. (1983). Measurement in medicine: The analysis of method comparison studies. The Statistician, 307–317.
Nissi, M. J., Mortazavi, S., Hughes, J., Morgan, P., and Ellermann, J. (2015). T2* relaxation time of acetabular and femoral cartilage with and without intra-articular Gd-DTPA2 in patients with femoroacetabular impingement. American Journal of Roentgenology, 204(6), W695.
# Produce a Bland-Altman plot for the cartilage dataset. data(cartilage) baplot(cartilage$pre, cartilage$post, pch = 21, col = "navy", bg = "darkorange", lwd1 = 2, lwd2 = 2, lcol = "navy")# Produce a Bland-Altman plot for the cartilage dataset. data(cartilage) baplot(cartilage$pre, cartilage$post, pch = 21, col = "navy", bg = "darkorange", lwd1 = 2, lwd2 = 2, lcol = "navy")
Build a Sklar's Omega correlation matrix.
build.R(data)build.R(data)
data |
a matrix of scores. Each row corresponds to a unit, each column a coder. |
This function accepts a data matrix and uses its column names to build the appropriate block-diagonal correlation matrix. If gold-standard scores are included, they should be in the first column of the matrix, and that column should be named 'g'. For a given coder, the column name should begin with 'c', and then the coder number and score number should follow, separated by '.' (so that multi-digit numbers can be accommodated). For example, 'c.12.2' denotes the second score for coder 12.
Note that this function is called by sklars.omega and so is not a user-level
function, per se. We expose the function so that interested users can more easily carry out
simulation studies.
build.R returns a list comprising two elements.
R |
the correlation matrix. |
onames |
a character vector that contains names for the parameters of the correlation matrix. |
This data frame has exactly two columns. The first column contains raw T2* values, the second column contrast-enhanced T2* values.
data(cartilage)data(cartilage)
Nissi, M. J., Mortazavi, S., Hughes, J., Morgan, P., and Ellermann, J. (2015). T2* relaxation time of acetabular and femoral cartilage with and without intra-articular Gd-DTPA2 in patients with femoroacetabular impingement. American Journal of Roentgenology, 204(6), W695.
data(cartilage)data(cartilage)
Check the column names of a Sklar's Omega data matrix for correctness.
check.colnames(data)check.colnames(data)
data |
a matrix of scores. Each row corresponds to a unit, each column a coder. |
This function performs a somewhat rudimentary validation of the column names. At most one column may be labeled 'g', and said column must be the first. The only other valid format is 'c.C.S', where 'C' denotes coder number and 'S' denotes the Sth score for coder C (both positive whole numbers). It is up to the user to ensure that the coder and score indices make sense and are ordered correctly, i.e., coders, and scores for a given coder, are numbered consecutively.
check.colnames returns a list comprising two elements.
success |
logical; if TRUE, the column names passed the test. |
cols |
if |
Krippendorff, K. (2013). Computing Krippendorff's alpha-reliability. Technical report, University of Pennsylvania.
# The following data were presented in Krippendorff (2013). data.nom = matrix(c(1,2,3,3,2,1,4,1,2,NA,NA,NA, 1,2,3,3,2,2,4,1,2,5,NA,3, NA,3,3,3,2,3,4,2,2,5,1,NA, 1,2,3,3,2,4,4,1,2,5,1,NA), 12, 4) colnames(data.nom) = c("c.1.1", "c.2.1", "c.3.1", "c.4.1") data.nom (check.colnames(data.nom)) # Introduce errors for columns 1 and 4. colnames(data.nom) = c("c.a.1", "c.2.1", "c.3.1", "C.4.1") (check.colnames(data.nom)) # The following scenario passes the check but is illogical. colnames(data.nom) = c("g", "c.2.1", "c.1.47", "c.2.1") (check.colnames(data.nom))# The following data were presented in Krippendorff (2013). data.nom = matrix(c(1,2,3,3,2,1,4,1,2,NA,NA,NA, 1,2,3,3,2,2,4,1,2,5,NA,3, NA,3,3,3,2,3,4,2,2,5,1,NA, 1,2,3,3,2,4,4,1,2,5,1,NA), 12, 4) colnames(data.nom) = c("c.1.1", "c.2.1", "c.3.1", "c.4.1") data.nom (check.colnames(data.nom)) # Introduce errors for columns 1 and 4. colnames(data.nom) = c("c.a.1", "c.2.1", "c.3.1", "C.4.1") (check.colnames(data.nom)) # The following scenario passes the check but is illogical. colnames(data.nom) = c("g", "c.2.1", "c.1.47", "c.2.1") (check.colnames(data.nom))
Compute confidence/credible intervals for Sklar's Omega.
## S3 method for class 'sklarsomega' confint(object, parm, level = 0.95, ...)## S3 method for class 'sklarsomega' confint(object, parm, level = 0.95, ...)
object |
an object of class |
parm |
a specification of which parameters are to be given confidence intervals, either a vector of numbers or a vector of names. If missing, all parameters are considered. |
level |
the desired confidence level for the interval. The default value is 0.95. |
... |
additional arguments. These are passed to |
This function computes confidence/credible intervals for a Sklar's Omega fit.
A vector with entries giving lower and upper confidence limits. These will be labelled as (1 - level) / 2 and 1 - (1 - level) / 2.
Nissi, M. J., Mortazavi, S., Hughes, J., Morgan, P., and Ellermann, J. (2015). T2* relaxation time of acetabular and femoral cartilage with and without intra-articular Gd-DTPA2 in patients with femoroacetabular impingement. American Journal of Roentgenology, 204(6), W695.
# Fit a subset of the cartilage data, assuming a Laplace marginal distribution. Compute # confidence intervals in the usual ML way (observed information matrix). Note that # calling function sklars.omega with confint = bootstrap will lead to bootstrap sampling, # in which case confidence intervals will be bootstrap intervals. data(cartilage) data.cart = as.matrix(cartilage)[1:100, ] colnames(data.cart) = c("c.1.1", "c.2.1") fit.lap = sklars.omega(data.cart, level = "balance", confint = "asymptotic", control = list(dist = "laplace")) summary(fit.lap) confint(fit.lap, level = 0.99)# Fit a subset of the cartilage data, assuming a Laplace marginal distribution. Compute # confidence intervals in the usual ML way (observed information matrix). Note that # calling function sklars.omega with confint = bootstrap will lead to bootstrap sampling, # in which case confidence intervals will be bootstrap intervals. data(cartilage) data.cart = as.matrix(cartilage)[1:100, ] colnames(data.cart) = c("c.1.1", "c.2.1") fit.lap = sklars.omega(data.cart, level = "balance", confint = "asymptotic", control = list(dist = "laplace")) summary(fit.lap) confint(fit.lap, level = 0.99)
Compute DFBETAs for units and/or coders.
## S3 method for class 'sklarsomega' influence(model, units, coders, ...)## S3 method for class 'sklarsomega' influence(model, units, coders, ...)
model |
a fitted model object. |
units |
a vector of integers. A DFBETA will be computed for each of the corresponding units. |
coders |
a vector of integers. A DFBETA will be computed for each of the corresponding coders. |
... |
additional arguments. |
This function computes DFBETAs for one or more units and/or one or more coders.
A list comprising at most two elements.
dfbeta.units |
a matrix, the columns of which contain DFBETAs for the units specified via argument |
dfbeta.coders |
a matrix, the columns of which contain DFBETAs for the coders specified via argument |
Young, D. S. (2017). Handbook of Regression Methods. CRC Press.
Krippendorff, K. (2013). Computing Krippendorff's alpha-reliability. Technical report, University of Pennsylvania.
# The following data were presented in Krippendorff (2013). After # analyzing the data and displaying a summary of the fit, compute # and display DFBETAs for unit 11 and coders 2 and 3. data.nom = matrix(c(1,2,3,3,2,1,4,1,2,NA,NA,NA, 1,2,3,3,2,2,4,1,2,5,NA,3, NA,3,3,3,2,3,4,2,2,5,1,NA, 1,2,3,3,2,4,4,1,2,5,1,NA), 12, 4) colnames(data.nom) = c("c.1.1", "c.2.1", "c.3.1", "c.4.1") fit.nom = sklars.omega(data.nom, level = "nominal", confint = "none") summary(fit.nom) (inf = influence(fit.nom, units = 11, coders = c(2, 3)))# The following data were presented in Krippendorff (2013). After # analyzing the data and displaying a summary of the fit, compute # and display DFBETAs for unit 11 and coders 2 and 3. data.nom = matrix(c(1,2,3,3,2,1,4,1,2,NA,NA,NA, 1,2,3,3,2,2,4,1,2,5,NA,3, NA,3,3,3,2,3,4,2,2,5,1,NA, 1,2,3,3,2,4,4,1,2,5,1,NA), 12, 4) colnames(data.nom) = c("c.1.1", "c.2.1", "c.3.1", "c.4.1") fit.nom = sklars.omega(data.nom, level = "nominal", confint = "none") summary(fit.nom) (inf = influence(fit.nom, units = 11, coders = c(2, 3)))
Return the maximum of the Sklar's Omega log objective function.
## S3 method for class 'sklarsomega' logLik(object, ...)## S3 method for class 'sklarsomega' logLik(object, ...)
object |
a fitted model object. |
... |
additional arguments. |
This function extracts the maximum value of the log objective function from a model fit, and is principally intended to be used in computing information criteria.
This function returns an object of class logLik. This is a number with at least one attribute, "df" (degrees of freedom), giving the number of estimated parameters in the model.
Return the number of observations for a Sklar's Omega fit.
## S3 method for class 'sklarsomega' nobs(object, ...)## S3 method for class 'sklarsomega' nobs(object, ...)
object |
a fitted model object. |
... |
additional arguments. |
This function extracts the number of observations from a model fit, and is principally intended to be used in computing information criteria.
An integer.
Compute the cumulative distribution function for a categorical distribution.
pcat(q, p)pcat(q, p)
q |
vector of quantiles. |
p |
vector of probabilities. |
This function uses dcat to compute the cdf for the categorical distribution with support and probabilities .
pcat returns a probability or a vector of probabilities, depending on the dimension of q.
Compute the quantile function for a categorical distribution.
qcat(pr, p, lower.tail = TRUE, log.pr = FALSE)qcat(pr, p, lower.tail = TRUE, log.pr = FALSE)
pr |
vector of probabilities. |
p |
vector of proabilities. |
lower.tail |
logical; if TRUE (default), probabilities are |
log.pr |
logical; if TRUE, probabilities |
This function computes quantiles for the categorical distribution with support and probabilities .
qcat returns a vector of quantiles.
Extract model residuals.
## S3 method for class 'sklarsomega' residuals(object, ...)## S3 method for class 'sklarsomega' residuals(object, ...)
object |
an object of class |
... |
additional arguments. |
Although residuals may not be terribly useful in this context, we provide residuals nonetheless. Said residuals are computed by first applying the probability integral transform, then applying the inverse probability integral transform, then pre-multiplying by the inverse of the square root of the (fitted) copula correlation matrix. For nominal or ordinal scores, the distributional transform approximation is used.
A vector of residuals.
Nissi, M. J., Mortazavi, S., Hughes, J., Morgan, P., and Ellermann, J. (2015). T2* relaxation time of acetabular and femoral cartilage with and without intra-articular Gd-DTPA2 in patients with femoroacetabular impingement. American Journal of Roentgenology, 204(6), W695.
# Fit a subset of the cartilage data, assuming a Laplace marginal distribution. # Produce a normal probability plot of the residuals, and overlay the line y = x. data(cartilage) data.cart = as.matrix(cartilage)[1:100, ] colnames(data.cart) = c("c.1.1", "c.2.1") fit.lap = sklars.omega(data.cart, level = "balance", control = list(dist = "laplace")) summary(fit.lap) res = residuals(fit.lap) qqnorm(res, pch = 20) abline(0, 1, col = "blue", lwd = 2)# Fit a subset of the cartilage data, assuming a Laplace marginal distribution. # Produce a normal probability plot of the residuals, and overlay the line y = x. data(cartilage) data.cart = as.matrix(cartilage)[1:100, ] colnames(data.cart) = c("c.1.1", "c.2.1") fit.lap = sklars.omega(data.cart, level = "balance", control = list(dist = "laplace")) summary(fit.lap) res = residuals(fit.lap) qqnorm(res, pch = 20) abline(0, 1, col = "blue", lwd = 2)
Simulate a Sklar's Omega dataset(s).
## S3 method for class 'sklarsomega' simulate(object, nsim = 1, seed = NULL, ...)## S3 method for class 'sklarsomega' simulate(object, nsim = 1, seed = NULL, ...)
object |
a fitted model object. |
nsim |
number of datasets to simulate. Defaults to 1. |
seed |
either |
... |
additional arguments. |
This function simulates one or more responses distributed according to the fitted model.
A data frame having nsim columns, each of which contains a simulated response vector. Said data frame has a "seed" attribute, which takes the value of the seed argument or the value of .Random.seed.
# Fit a subset of the cartilage data, assuming a Laplace marginal distribution. data(cartilage) data.cart = as.matrix(cartilage)[1:100, ] colnames(data.cart) = c("c.1.1", "c.2.1") fit.lap = sklars.omega(data.cart, level = "balance", confint = "none", control = list(dist = "laplace")) summary(fit.lap) # Simulate three datasets from the fitted model, and then display the # head of the first dataset in matrix form. sim = simulate(fit.lap, nsim = 3, seed = 42) data.sim = t(fit.lap$data) data.sim[! is.na(data.sim)] = sim[, 1] data.sim = t(data.sim) head(data.sim)# Fit a subset of the cartilage data, assuming a Laplace marginal distribution. data(cartilage) data.cart = as.matrix(cartilage)[1:100, ] colnames(data.cart) = c("c.1.1", "c.2.1") fit.lap = sklars.omega(data.cart, level = "balance", confint = "none", control = list(dist = "laplace")) summary(fit.lap) # Simulate three datasets from the fitted model, and then display the # head of the first dataset in matrix form. sim = simulate(fit.lap, nsim = 3, seed = 42) data.sim = t(fit.lap$data) data.sim[! is.na(data.sim)] = sim[, 1] data.sim = t(data.sim) head(data.sim)
Apply Sklar's Omega.
sklars.omega( data, level = c("nominal", "ordinal", "count", "percentage", "amount", "balance"), confint = c("none", "bootstrap", "asymptotic"), verbose = FALSE, control = list() )sklars.omega( data, level = c("nominal", "ordinal", "count", "percentage", "amount", "balance"), confint = c("none", "bootstrap", "asymptotic"), verbose = FALSE, control = list() )
data |
a matrix of scores. Each row corresponds to a unit, each column a coder. The columns must be named appropriately so that the correct copula correlation matrix can be constructed. See |
level |
the level of measurement, one of |
confint |
the method for computing confidence intervals, one of |
verbose |
logical; if TRUE, various messages may be printed to the console. |
control |
a list of control parameters.
|
This is the package's flagship function. It applies the Sklar's Omega methodology to nominal, ordinal, count, amount, balance, or percentage outcomes, and, if desired, produces confidence intervals. Parallel computing is supported, when applicable, and other measures (e.g., sparse matrix operations) are taken in the interest of computational efficiency.
If the level of measurement is nominal or ordinal, the scores (which must take values in ) are assumed to share a common categorical marginal distribution. A composite marginal likelihood (CML) approach is used for categorical scores. Only parametric bootstrap intervals are supported for categorical outcomes since sandwich estimation tends to lead to inflated standard errors.
If the scores are counts, control parameter dist must be used to select a marginal distribution of "poisson" or "negbinomial". For counts a distributional transform (DT) approximation of the likelihood is employed. Either bootstrap or sandwich intervals are available: confint = "bootstrap" or confint = "asymptotic".
If the level of measurement is balance or amount or percentage, control parameter dist must be used to select a marginal distribution from among "gaussian", "laplace", "t", and "empirical"; or from among "gamma" and "empirical"; or from among "beta" or "kumaraswamy", respectively. The method of maximum likelihood (ML) is used unless dist = "empirical", in which case conditional maximum likelihood is used, i.e., the copula parameters are estimated conditional on the sample distribution function of the scores. For the ML method, both bootstrap and asymptotic confidence intervals are available. When dist = "empirical", only bootstrap intervals are available.
When applicable, functions of appropriate sample quantities are used as starting values for marginal parameters, regardless of the level of measurement.
Function sklars.omega returns an object of class "sklarsomega", which is a list comprising the following elements.
AIC |
the value of AIC for the fit, if |
BIC |
the value of BIC for the fit, if |
boot.sample |
when applicable, the bootstrap sample. |
call |
the matched call. |
coefficients |
a named vector of parameter estimates. |
confint |
the value of argument |
control |
the list of control parameters. |
convergence |
unless optimization failed, the value of |
cov.hat |
if |
data |
the matrix of scores, perhaps altered to remove rows (units) containing fewer than two scores. |
iter |
if optimization converged, the number of iterations required to optimize the objective function. |
level |
the level of measurement. |
message |
if applicable, the value of |
method |
the approach to inference, one of |
mpar |
the number of marginal parameters. |
npar |
the total number of parameters. |
optim.method |
the method used to optimize the objective function. The L-BFGS-B method is attempted first. If L-BFGS-B fails, a second attempt is made using the bounded Hooke-Jeeves algorithm. |
R |
the initial value of the copula correlation matrix. |
R.hat |
the estimated value of the copula correlation matrix. |
residuals |
the residuals. |
root.R.hat |
a square root of the estimated copula correlation matrix. This is used for simulation and to compute the residuals. |
value |
the minimum of the log objective function. |
verbose |
the value of argument |
y |
the scores as a vector, perhaps altered to remove rows (units) containing only one score. |
Hughes, J. (2018). Sklar's Omega: A Gaussian copula-based framework for assessing agreement. ArXiv e-prints, March.
Nissi, M. J., Mortazavi, S., Hughes, J., Morgan, P., and Ellermann, J. (2015). T2* relaxation time of acetabular and femoral cartilage with and without intra-articular Gd-DTPA2 in patients with femoroacetabular impingement. American Journal of Roentgenology, 204(6), W695.
# Fit a subset of the cartilage data, assuming a Laplace marginal distribution. Compute # confidence intervals in the usual ML way (observed information matrix). data(cartilage) data.cart = as.matrix(cartilage)[1:100, ] colnames(data.cart) = c("c.1.1", "c.2.1") fit.lap = sklars.omega(data.cart, level = "balance", confint = "asymptotic", control = list(dist = "laplace")) summary(fit.lap) # Now assume a noncentral t marginal distribution. fit.t = sklars.omega(data.cart, level = "balance", confint = "asymptotic", control = list(dist = "t")) summary(fit.t)# Fit a subset of the cartilage data, assuming a Laplace marginal distribution. Compute # confidence intervals in the usual ML way (observed information matrix). data(cartilage) data.cart = as.matrix(cartilage)[1:100, ] colnames(data.cart) = c("c.1.1", "c.2.1") fit.lap = sklars.omega(data.cart, level = "balance", confint = "asymptotic", control = list(dist = "laplace")) summary(fit.lap) # Now assume a noncentral t marginal distribution. fit.t = sklars.omega(data.cart, level = "balance", confint = "asymptotic", control = list(dist = "t")) summary(fit.t)
Do Bayesian inference for Sklar's Omega.
sklars.omega.bayes( data, level = c("amount", "balance", "percentage"), verbose = FALSE, control = list() )sklars.omega.bayes( data, level = c("amount", "balance", "percentage"), verbose = FALSE, control = list() )
data |
a matrix of scores. Each row corresponds to a unit, each column a coder. The columns must be named appropriately so that the correct copula correlation matrix can be constructed. See |
level |
the level of measurement, either |
verbose |
logical; if TRUE, various messages are printed to the console. |
control |
a list of control parameters.
|
This function does MCMC for Bayesian inference for continuous scores.
Control parameter dist must be used to select a marginal distribution from among "gaussian", "laplace", "t", and "gamma" (for balances or amounts), or from among "beta" or "kumaraswamy" (for percentages).
Details regarding prior distributions and sampling are provided in the package vignette.
Function sklars.omega.bayes returns an object of class "sklarsomega", which is a list comprising the following elements.
accept |
a vector of acceptance rates. |
DIC |
the value of DIC for the fit. |
call |
the matched call. |
coefficients |
a named vector of parameter estimates. |
control |
the list of control parameters. |
data |
the matrix of scores, perhaps altered to remove rows (units) containing fewer than two scores. |
iter |
the number of posterior samples that were drawn. |
level |
the level of measurement. |
mcse |
a vector of Monte Carlo standard errors. |
method |
always equal to |
mpar |
the number of marginal parameters. |
npar |
the total number of parameters. |
R |
the initial value of the copula correlation matrix. |
R.hat |
the estimated value of the copula correlation matrix. |
residuals |
the residuals. |
root.R.hat |
a square root of the estimated copula correlation matrix. This is used for simulation and to compute the residuals. |
samples |
the posterior samples. |
verbose |
the value of argument |
y |
the scores as a vector, perhaps altered to remove rows (units) containing fewer than two scores. |
Hughes, J. (2018). Sklar's Omega: A Gaussian copula-based framework for assessing agreement. ArXiv e-prints, March.
Nissi, M. J., Mortazavi, S., Hughes, J., Morgan, P., and Ellermann, J. (2015). T2* relaxation time of acetabular and femoral cartilage with and without intra-articular Gd-DTPA2 in patients with femoroacetabular impingement. American Journal of Roentgenology, 204(6), W695.
# Fit a subset of the cartilage data, assuming a Laplace marginal distribution. Compute # 95% HPD intervals. Show the acceptance rates for the three parameters. data(cartilage) data = as.matrix(cartilage)[1:100, ] colnames(data) = c("c.1.1", "c.2.1") set.seed(111111) fit1 = sklars.omega.bayes(data, level = "balance", verbose = FALSE, control = list(dist = "laplace", minit = 1000, maxit = 5000, tol = 0.01, sigma.1 = 1, sigma.2 = 0.1, sigma.omega = 0.2)) summary(fit1) fit1$accept # Now assume a noncentral t marginal distribution. set.seed(4565) fit2 = sklars.omega.bayes(data, level = "balance", verbose = FALSE, control = list(dist = "t", minit = 1000, maxit = 5000, tol = 0.01, sigma.1 = 0.2, sigma.2 = 2, sigma.omega = 0.2)) summary(fit2) fit2$accept# Fit a subset of the cartilage data, assuming a Laplace marginal distribution. Compute # 95% HPD intervals. Show the acceptance rates for the three parameters. data(cartilage) data = as.matrix(cartilage)[1:100, ] colnames(data) = c("c.1.1", "c.2.1") set.seed(111111) fit1 = sklars.omega.bayes(data, level = "balance", verbose = FALSE, control = list(dist = "laplace", minit = 1000, maxit = 5000, tol = 0.01, sigma.1 = 1, sigma.2 = 0.1, sigma.omega = 0.2)) summary(fit1) fit1$accept # Now assume a noncentral t marginal distribution. set.seed(4565) fit2 = sklars.omega.bayes(data, level = "balance", verbose = FALSE, control = list(dist = "t", minit = 1000, maxit = 5000, tol = 0.01, sigma.1 = 0.2, sigma.2 = 2, sigma.omega = 0.2)) summary(fit2) fit2$accept
Print a summary of a Sklar's Omega fit.
## S3 method for class 'sklarsomega' summary(object, alpha = 0.05, digits = 4, ...)## S3 method for class 'sklarsomega' summary(object, alpha = 0.05, digits = 4, ...)
object |
an object of class |
alpha |
the significance level for the confidence intervals. The default is 0.05. |
digits |
the number of significant digits to display. The default is 4. |
... |
additional arguments. |
Unless optimization of the objective function failed, this function prints a summary of the fit. First, the value of the objective function at its maximum is displayed, along with the number of iterations required to find the maximum. Then the values of the control parameters (defaults and/or values supplied in the call) are printed. Then a table of estimates is shown. If applicable, the table includes confidence intervals. Finally, the values of AIC and BIC are displayed (if the scores are continuous and inference is parametric).
Nissi, M. J., Mortazavi, S., Hughes, J., Morgan, P., and Ellermann, J. (2015). T2* relaxation time of acetabular and femoral cartilage with and without intra-articular Gd-DTPA2 in patients with femoroacetabular impingement. American Journal of Roentgenology, 204(6), W695.
# Fit a subset of the cartilage data, assuming a Laplace marginal distribution. Compute # confidence intervals in the usual ML way (observed information matrix). Note that # using confint = bootstrap leads to bootstrap sampling and bootstrap intervals. data(cartilage) data.cart = as.matrix(cartilage)[1:100, ] colnames(data.cart) = c("c.1.1", "c.2.1") fit.lap = sklars.omega(data.cart, level = "balance", confint = "asymptotic", control = list(dist = "laplace")) summary(fit.lap)# Fit a subset of the cartilage data, assuming a Laplace marginal distribution. Compute # confidence intervals in the usual ML way (observed information matrix). Note that # using confint = bootstrap leads to bootstrap sampling and bootstrap intervals. data(cartilage) data.cart = as.matrix(cartilage)[1:100, ] colnames(data.cart) = c("c.1.1", "c.2.1") fit.lap = sklars.omega(data.cart, level = "balance", confint = "asymptotic", control = list(dist = "laplace")) summary(fit.lap)
Compute an estimated covariance matrix for a Sklar's Omega fit.
## S3 method for class 'sklarsomega' vcov(object, ...)## S3 method for class 'sklarsomega' vcov(object, ...)
object |
a fitted model object. |
... |
additional arguments. |
See the package vignette for detailed information regarding covariance estimation for Sklar's Omega.
A matrix of estimated variances and covariances for the parameter estimator. This should have row and column names corresponding to the parameter names given by the coef method. Note that a call to this function will result in an error if sklars.omega was called with argument confint equal to "none", or if optimization failed.
Nissi, M. J., Mortazavi, S., Hughes, J., Morgan, P., and Ellermann, J. (2015). T2* relaxation time of acetabular and femoral cartilage with and without intra-articular Gd-DTPA2 in patients with femoroacetabular impingement. American Journal of Roentgenology, 204(6), W695.
# Fit a subset of the cartilage data, assuming a Laplace marginal distribution. Compute # confidence intervals in the usual ML way (observed information matrix). Also display # the observed information matrix. Note that using confint = bootstrap leads to bootstrap # sampling, in which case vcov returns the sample covariance matrix for the bootstrap # sample. data(cartilage) data.cart = as.matrix(cartilage)[1:100, ] colnames(data.cart) = c("c.1.1", "c.2.1") fit.lap = sklars.omega(data.cart, level = "balance", confint = "asymptotic", control = list(dist = "laplace")) summary(fit.lap) vcov(fit.lap)# Fit a subset of the cartilage data, assuming a Laplace marginal distribution. Compute # confidence intervals in the usual ML way (observed information matrix). Also display # the observed information matrix. Note that using confint = bootstrap leads to bootstrap # sampling, in which case vcov returns the sample covariance matrix for the bootstrap # sample. data(cartilage) data.cart = as.matrix(cartilage)[1:100, ] colnames(data.cart) = c("c.1.1", "c.2.1") fit.lap = sklars.omega(data.cart, level = "balance", confint = "asymptotic", control = list(dist = "laplace")) summary(fit.lap) vcov(fit.lap)