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Type:

Package

Title:

Model Based Clustering of Binary Dissimilarity Measurements

Version:

1.0.3

Date:

2024-09-24

Description:

Functions for fitting a Bayesian model for grouping binary dissimilarity matrices in homogeneous clusters. Currently, it includes methods only for binary data (<doi:10.18637/jss.v100.i16>).

Author:

Sergio Venturini [aut, cre], Raffaella Piccarreta [ctb]

Maintainer:

Sergio Venturini <sergio.venturini@unicatt.it>

License:

GPL-2 |GPL-3 [expanded from: GPL (≥ 2)]

NeedsCompilation:

yes

Repository:

CRAN

LazyData:

TRUE

Imports:

abind, bayesplot (≥ 1.7.0), coda (≥ 0.19-3), ggplot2 (≥3.2.1), ggrepel (≥ 0.8.1), graphics, modeltools (≥ 0.2-22),parallel (≥ 3.6.1), robustbase (≥ 0.93-5), robustX (≥1.2-5), stats4 (≥ 3.6.0), tools

Suggests:

knitr, mcmcplots, testthat

Depends:

methods, R (≥ 3.6.0), stats, utils

LinkingTo:

Rcpp, RcppArmadillo, RcppProgress

BugReports:

https://github.com/sergioventurini/dmbc/issues

Encoding:

UTF-8

RoxygenNote:

7.3.2

Packaged:

2024-09-24 09:22:09 UTC; Sergio

Date/Publication:

2024-09-24 09:40:02 UTC

Model-Based Clustering of Several Dissimilarity Matrices.

Description

Thedmbc package implements a Bayesian algorithm for clustering a setof dissimilarity matrices within a model-based framework. In particular,we consider the case whereS matrices are available, eachdescribing the dissimilarities amongn objects, possibly expressed byS subjects (judges), or measured under different experimental conditions,or with reference to different characteristics of the objects them- selves.Specifically, we focus on binary dissimilarities, taking values 0 or 1depending on whether or not two objects are deemed as similar, with the goalof analyzing such data using multidimensional scaling (MDS). Differentlyfrom the standard MDS algorithms, we are interested in partitioning thedissimilarity matrices into clusters and, simultaneously, to extract aspecific MDS configuration for each cluster. The parameter estimatesare derived using a hybrid Metropolis-Gibbs Markov Chain Monte Carloalgorithm. We also include a BIC-like criterion for jointly selecting theoptimal number of clusters and latent space dimensions.

For efficiency reasons, the core computations in the package are implementedusing theC programming language and theRcppArmadillopackage.

Thedmbc package also supports the simulation of multiple chainsthrough the support of theparallel package.

Plotting functionalities are imported from the nicebayesplotpackage. Currently, the package includes methods for binary data only. Infuture releases routines will be added specifically for continuous(i.e. normal), multinomial and count data.

dmbc classes

Thedmbc package defines the following new classes:

dmbc_data:: defines the data to use in a DMBC model.
dmbc_model:: defines a DMBC model.
dmbc_fit:: defines the results of a DMBC analysisfor a single MCMC chain.
dmbc_fit_list:: defines the results of a DMBC analysisfor multiple MCMC chains.
dmbc_ic:: defines the results of the computation ofthe information criterion for a DMBC analysis.
dmbc_config:: defines the estimate of the latentconfiguration for a DMBC analysis.

The package includesprint,summary andplot methodsfor each one of these classes.

Resources

Bug reports:

If you have noticed a bug that needs to be fixed, please let us know at thedmbc issue tracker on GitHub:

https://github.com/sergioventurini/dmbc/issues/.

General questions and help:

To ask a question aboutdmbc send and email to:

sergio.venturini@unicatt.it.

References

Venturini, S., Piccarreta, R. (2021), "A Bayesian Approach for Model-BasedClustering of Several Binary Dissimilarity Matrices: thedmbcPackage inR", Journal of Statistical Software, 100, 16, 1–35, <10.18637/jss.v100.i16>.

Adjustment of the center and orientation of a latent configuration.

Description

adjust_x adjusts the center and orientation of a latent configurationin Bayesian (metric) multidimensional scaling (BMDS).

Usage

adjust_x(x)

Arguments

x

Numeric matrix containing the latent configuration.

Value

A list with elements:

x: A real matrix containing the adjusted latentconfiguration.
Sig_x: The variance and covariance matrix of the adjustedlatent configuration.

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

Examples

n <- 100nr <- 20nc <- floor(n/nr)x <- matrix(rnorm(1:n), nrow = nr, ncol = nc)adj_x <- adjust_x(x)adj_x$xadj_x$Sig_x

List of binary dissimilarity matrices among 18 animals.

Description

To illustrate the MDS analysis of sorting data, Takane et al. (2009) referto judgments on the similarity betweenn = 18 animals expressed byS = 20 subjects. Each subject was asked to divide the animals intoas many groups as needed, based on their similarity. We converted thesevalues to 0 or 1 depending on whether a pair of animals is placed or notin the same group by a subject.

Usage

data(animals)

Format

Admbc_data object whosediss element is a list of 20binary dissimilarity matrices. Each matrix is defined as adistobject measuring whether each pair of the 18 animals has is placed in thesame group (1) or not (0).

Thedist objects have rows and columns that are named as follows:

be: bear
cm: camel
ct: cat
cw: cow
dg: dog
el: elephant
gf: giraffe
fx: fox
hs: horse
li: lion
mk: monkey
ms: mouse
pg: pig
rb: rabbit
sh: sheep
sq: squirrel
tg: tiger
wf: wolf

References

Takane, Y., Jung, S., Takane, Y. O. (2009). "Multidimensional Scaling". InMillsap, R. E., Maydeu-Olivares, A. (eds.), The SAGE Handbook ofQuantitative Methods in Psychology, chapter 10, pp. 217–242,.

Examples

data(animals)library(bayesplot)cols <- color_scheme_set("teal")plot(animals, colors = unlist(cols)[c(1, 6)], font = 1, cex.font = 0.75)

Bayesian multidimensional scaling (BMDS) using Markov Chain Monte Carlo(MCMC).

Description

bmds computes the Bayesian multidimensional scaling (BMDS) solutionsusing Markov Chain Monte Carlo for a range of specified latent spacedimensions.

Usage

bmds(  D,  min_p = 1,  max_pm1 = 6,  burnin = 0,  nsim = 13000,  ic = TRUE,  verbose = TRUE)

Arguments

D

Observed dissimilarities (provided as a distance matrix).

min_p

A length-one numeric vector providing the minimum valueof the latent space dimension to use.

max_pm1

A length-one numeric vector providing the maximumvalue of the latent space dimension to use (minus 1).

burnin

A length-one numeric vector providing the number ofiterations to use for burnin.

nsim

A length-one numeric vector providing the number ofiterations to use in the MCMC simulation after burnin.

ic

Logical scalar. IfTRUE computes the MDSinformation criterion (MDSIC) for all solution requested.

verbose

Logical scalar. IfTRUE prints informationregarding the evolution of the simulation.

Value

A list with the following elements:

x.chain: MCMC chain of the latent configurationcoordinates.
sigma.chain: MCMC chain of the random error.
lambda.chain: MCMC chain of the latent configurationvariances.
stress: Numeric vector of the stress function values.
mdsIC: List with two elements, the MDSIC and BIC valuesfor the required solutions.
accept: Numeric matrix of acceptance rates.

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

References

Oh, M.-S., Raftery, A. E. (2001), "Bayesian Multidimensional Scaling andChoice of Dimension", Journal of the American Statistical Association,96, 1031-1044.

Examples

## Not run: # Airline Distances Between Citiesairline <- read.csv(file = system.file("extdata", "airline.csv",  package = "dmbc"))airline.nm <- airline[, 1]airline <- airline[, 2:31]colnames(airline) <- airline.nmairline <- as.dist(airline)min_p <- 1max_p <- 4burnin <- 200nsim <- 1000totiter <- burnin + nsimairline.mds <- cmdscale(airline, max_p)airline.bmds <- bmds(airline, min_p, max_p, burnin, nsim)opar <- par(mfrow = c(1, 2))plot(min_p:max_p, airline.bmds$mdsIC$mdsic, type = "b",  main = "MDS Information Criterion", xlab = "p", ylab = "MDSIC")MDSICmin <- which.min(airline.bmds$mdsIC$mdsic)points((min_p:max_p)[MDSICmin], airline.bmds$mdsIC$mdsic[MDSICmin],  col = "red", pch = 10, cex = 1.75, lwd = 1.5)airline.bmds.x.mode <- bmds_get_x_mode(airline, airline.bmds, MDSICmin,  min_p, max_p, start = (burnin + 1), end = totiter)airline.bmds.d <- dist(airline.bmds.x.mode)airline.mds.d <- dist(airline.mds[, 1:((min_p:max_p)[MDSICmin])])plot(airline, airline.bmds.d, type = "n", xlab = "observed",  ylab = "estimated", main = "Airline Distances \n Between Cities",  xlim = c(0, max(airline, airline.bmds.d)),  ylim = c(0, max(airline, airline.bmds.d)))abline(0, 1, lty = 2, col = "gray")points(airline, airline.mds.d, pch = 19, col = "cyan", cex = .5)points(airline, airline.bmds.d, pch = 19, col = "magenta", cex = .5)legend(x = "bottomright", legend = c("Classical MDS", "Bayesian MDS"),  pch = c(19, 19), col = c("cyan", "magenta"))par(opar)# Careers of Lloyds Bank Employeeslloyds <- read.csv(file = system.file("extdata", "lloyds.csv",  package = "dmbc"))lloyds.nm <- lloyds[, 1]lloyds <- lloyds[, 2:81]colnames(lloyds) <- lloyds.nmlloyds <- as.dist(lloyds)min_p <- 1max_p <- 12burnin <- 200nsim <- 1000totiter <- burnin + nsimlloyds.mds <- cmdscale(lloyds, max_p)lloyds.bmds <- bmds(lloyds, min_p, max_p, burnin, nsim)opar <- par(mfrow = c(1, 2))plot((min_p:max_p), lloyds.bmds$mdsIC$mdsic, type = "b",  main = "MDS Information Criterion", xlab = "p", ylab = "MDSIC")MDSICmin <- which.min(lloyds.bmds$mdsIC$mdsic)points((min_p:max_p)[MDSICmin], lloyds.bmds$mdsIC$mdsic[MDSICmin],  col = "red", pch = 10, cex = 1.75, lwd = 1.5)lloyds.bmds.x.mode <- bmds_get_x_mode(lloyds, lloyds.bmds, MDSICmin,  min_p, max_p, start = (burnin + 1), end = totiter)lloyds.bmds.d <- dist(lloyds.bmds.x.mode)lloyds.mds.d <- dist(lloyds.mds[, 1:((min_p:max_p)[MDSICmin])])plot(lloyds, lloyds.bmds.d, type = "n", xlab = "observed",  ylab = "estimated", main = "Careers of Lloyds \n Bank Employees, 1905-1950",  xlim = c(0, max(lloyds, lloyds.bmds.d)),  ylim = c(0, max(lloyds, lloyds.bmds.d)))abline(0, 1, lty = 2, col = "gray")points(lloyds, lloyds.mds.d, pch = 19, col = "cyan", cex = .5)points(lloyds, lloyds.bmds.d, pch = 19, col = "magenta", cex = .5)legend(x = "topleft", legend = c("Classical MDS", "Bayesian MDS"),  pch = c(19, 19), col = c("cyan", "magenta"))par(opar)# Road distances (in km) between 21 cities in Europedata(eurodist, package = "datasets")min_p <- 1max_p <- 10burnin <- 200nsim <- 1000totiter <- burnin + nsimeurodist.mds <- cmdscale(eurodist, max_p)eurodist.bmds <- bmds(eurodist, min_p, max_p, burnin, nsim)opar <- par(mfrow = c(1, 2))plot((min_p:max_p), eurodist.bmds$mdsIC$mdsic, type = "b",  main = "MDS Information Criterion", xlab = "p", ylab = "MDSIC")MDSICmin <- which.min(eurodist.bmds$mdsIC$mdsic)points((min_p:max_p)[MDSICmin], eurodist.bmds$mdsIC$mdsic[MDSICmin],  col = "red", pch = 10, cex = 1.75, lwd = 1.5)eurodist.bmds.x.mode <- bmds_get_x_mode(eurodist, eurodist.bmds,  MDSICmin, min_p, max_p, start = (burnin + 1), end = totiter)eurodist.bmds.d <- dist(eurodist.bmds.x.mode)eurodist.mds.d <- dist(eurodist.mds[, 1:((min_p:max_p)[MDSICmin])])plot(eurodist, eurodist.bmds.d, type = "n", xlab = "observed",  ylab = "estimated", main = "Road distances (in km) \n between 21 cities in Europe",  xlim = c(0, max(eurodist, eurodist.bmds.d)),  ylim = c(0, max(eurodist, eurodist.bmds.d)))abline(0, 1, lty = 2, col = "gray")points(eurodist, eurodist.mds.d, pch = 19, col = "cyan", cex = .5)points(eurodist, eurodist.bmds.d, pch = 19, col = "magenta", cex = .5)legend(x = "topleft", legend = c("Classical MDS", "Bayesian MDS"),  pch = c(19, 19), col = c("cyan", "magenta"))par(opar)## End(Not run)

Posterior mode latent configuration in Bayesian multidimensional scaling (BMDS).

Description

bmds_get_x_mode returns the latent configuration that produced thelargest posterior value during the MCMC.

Usage

bmds_get_x_mode(D, res, p.i, min_p, max_p, start, end)

Arguments

D

Observed dissimilarities (provided as a distance matrix).

res

Results of a BMDS analysis as obtained with thebmds function.

p.i

A length-one numeric vector providing the index of the solution touse.

min_p

A length-one numeric vector providing the minimum value of thelatent space dimension to use.

max_p

A length-one numeric vector providing the maximum valueof the latent space dimension to use.

start

A length-one numeric vector providing the iterationnumber to start from.

end

A length-one numeric vector providing the iterationnumber where to end.

Value

A real matrix containing the posterior mode latent configuration.

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

Examples

## Not run: # Airline Distances Between Citiesairline <- read.csv(file = system.file("extdata", "airline.csv",  package = "dmbc"))airline.nm <- airline[, 1]airline <- airline[, 2:31]colnames(airline) <- airline.nmairline <- as.dist(airline)min_p <- 1max_p <- 4burnin <- 200nsim <- 1000totiter <- burnin + nsimairline.mds <- cmdscale(airline, max_p)airline.bmds <- bmds(airline, min_p, max_p, burnin, nsim)opar <- par(mfrow = c(1, 2))plot(min_p:max_p, airline.bmds$mdsIC$mdsic, type = "b",  main = "MDS Information Criterion", xlab = "p", ylab = "MDSIC")MDSICmin <- which.min(airline.bmds$mdsIC$mdsic)points((min_p:max_p)[MDSICmin], airline.bmds$mdsIC$mdsic[MDSICmin],  col = "red", pch = 10, cex = 1.75, lwd = 1.5)airline.bmds.x.mode <- bmds_get_x_mode(airline, airline.bmds, MDSICmin,  min_p, max_p, start = (burnin + 1), end = totiter)airline.bmds.d <- dist(airline.bmds.x.mode)airline.mds.d <- dist(airline.mds[, 1:((min_p:max_p)[MDSICmin])])plot(airline, airline.bmds.d, type = "n", xlab = "observed",  ylab = "estimated", main = "Airline Distances \n Between Cities",  xlim = c(0, max(airline, airline.bmds.d)),  ylim = c(0, max(airline, airline.bmds.d)))abline(0, 1, lty = 2, col = "gray")points(airline, airline.mds.d, pch = 19, col = "cyan", cex = .5)points(airline, airline.bmds.d, pch = 19, col = "magenta", cex = .5)legend(x = "bottomright", legend = c("Classical MDS", "Bayesian MDS"),  pch = c(19, 19), col = c("cyan", "magenta"))par(opar)## End(Not run)

Auxiliary function to recursively check NAs in a list.

Description

check_list_na() compares two lists and fills in the missingelements in the first with those included in the second. Thecomparison is recursive in the sense that the process is repeated forall lists included in those given.

Usage

check_list_na(orig, des)

Arguments

orig

A list whose content must be checked.

des

A list to use as a reference with which compare the first one.

Value

A list with all elements added.

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

Examples

G <- 5prior <- list(eta = list(a = rep(1, G), b = rep(2, G)))check_list_na(prior, dmbc_prior())

Extract the final cluster memberships from a`dmbc_config` class instance.

Description

Extract the final cluster memberships from admbc_config class instance.

Usage

## S4 method for signature 'dmbc_config'clusters(object, newdata = NULL, ...)

Arguments

object

An object of classdmbc_config.

newdata

An object of no explicit specification (currently ignored).

...

Further arguments to pass on (currently ignored).

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

Sum of squared residuals (SSR) from the observed distances and the givenlatent configuration.

Description

comp_ssr computes the sum of squared residuals (SSR) from theobserved distances (diss) and the given latent coordinates(x).

Usage

comp_ssr(x, diss)

Arguments

x

Real matrix containing the latent configuration.

diss

Observed dissimilarities (provided as a distance matrix).

Value

A length-one numeric vector providing the SSR for its arguments.

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

Examples

n <- 10000nr <- 200nc <- floor(n/nr)x <- matrix(rnorm(1:n), nrow = nr, ncol = nc)obsdiss <- dist(x)ssr <- numeric(ncol(x))for (i in 1:ncol(x)) {  ssr[i] <- comp_ssr(x[, 1:i], obsdiss)}plot(ssr, xlab = "number of dimensions", ylab = "SSR", type = "b")

Estimation of a DMBC model.

Description

dmbc(), the main function of the package, estimates a DMBC modelfor a given set ofS dissimilarity matrices.

Usage

dmbc(  data,  p = 2,  G = 3,  control = dmbc_control(),  prior = NULL,  cl = NULL,  post_all = FALSE)

Arguments

data

An object of classdmbc_data containing the datato analyze.

p

A length-one numeric vector indicating the number of dimensions of thelatent space.

G

A length-one numeric vector indicating the number of cluster topartition theS subjects.

control

A list of control parameters that affect the samplingbut do not affect the posterior distribution. Seedmbc_control() for more details.

prior

A list containing the prior hyperparameters. Seedmbc_prior() for more details.

cl

An optionalparallel orsnowcluster for use ifparallel = "snow". If not supplied, a clusteron the local machine is created for the duration of thedmbc() call.

post_all

A length-one logical vector, which if TRUE applies a furtherpost-processing to the simulated chains (in case these are more than one).

Value

Admbc_fit_list object.

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

References

Examples

## Not run: data(simdiss, package = "dmbc")G <- 3p <- 2prm.prop <- list(z = 1.5, alpha = .75)burnin <- 20000nsim <- 10000seed <- 2301set.seed(seed)control <- list(burnin = burnin, nsim = nsim, z.prop = prm.prop[["z"]],  alpha.prop = prm.prop[["alpha"]], random.start = TRUE, verbose = TRUE,  nchains = 2, thin = 10, store.burnin = TRUE, threads = 2,  parallel = "snow")sim.dmbc <- dmbc(simdiss, p, G, control)summary(sim.dmbc, include.burnin = FALSE)library(bayesplot)library(ggplot2)color_scheme_set("teal")plot(sim.dmbc, what = "trace", regex_pars = "eta")z <- dmbc_get_configuration(sim.dmbc, chain = 1, est = "mean",  labels = 1:16)summary(z)color_scheme_set("mix-pink-blue")graph <- plot(z, size = 2, size_lbl = 3)graph + panel_bg(fill = "gray90", color = NA)## End(Not run)

Model selection of DMBC models.

Description

dmbc_IC() is the main function for simultaneously selecting theoptimal latent space dimension (p) and number of clusters(G) for a DMBC analysis.

Usage

dmbc_IC(  data,  pmax = 3,  Gmax = 5,  control = dmbc_control(),  prior = NULL,  est = "mean")

Arguments

data

An object of classdmbc_data containing the datato analyze.

pmax

A length-one numeric vector indicating the maximum number ofdimensions of the latent space to consider.

Gmax

A length-one numeric vector indicating the maximum number ofcluster to consider.

control

A list of control parameters that affect the samplingbut do not affect the posterior distribution Seedmbc_control() for more details.

prior

A list containing the prior hyperparameters. Seedmbc_prior() for more details.

est

A length-one character vector indicating the estimate type touse. Possible values aremean,median,ml andmap.

Value

Admbc_ic object.

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

References

Examples

## Not run: data(simdiss, package = "dmbc")pmax <- 2Gmax <- 2prm.prop <- list(z = 1.5, alpha = .75)burnin <- 2000nsim <- 1000seed <- 1809set.seed(seed)control <- list(burnin = burnin, nsim = nsim, z.prop = prm.prop[["z"]],  alpha.prop = prm.prop[["alpha"]], random.start = TRUE, verbose = TRUE,  thin = 10, store.burnin = TRUE)sim.ic <- dmbc_IC(data = simdiss, pmax = pmax, Gmax = Gmax, control = control,  est = "mean")pmax <- pmax + 1Gmax <- Gmax + 2new.ic <- update(sim.ic, pmax = pmax, Gmax = Gmax)new.ic# plot the resultslibrary(bayesplot)library(ggplot2)color_scheme_set("mix-yellow-blue")p <- plot(new.ic, size = c(4, 1.5))p + panel_bg(fill = "gray90", color = NA)## End(Not run)

Auxiliary function for checking the grouping results of a fitted DMBC model.

Description

dmbc_check_groups() is an auxiliary function for checking whetherthe cluster membership estimates provided by the individual chains of thefitted model provided agree or not.

Usage

dmbc_check_groups(res, est = "mean")

Arguments

res

An object of classdmbc_fit_list.

est

A length-one character vector indicating the estimate type to use.

Value

A length-one logical vector, which is equal to TRUE if all simulated chainsprovide the same cluster membership estimates, and FALSE otherwise.

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

References

Examples

## Not run: data(simdiss, package = "dmbc")G <- 3p <- 2prm.prop <- list(z = 1.5, alpha = .75)burnin <- 2000nsim <- 1000seed <- 2301set.seed(seed)control <- list(burnin = burnin, nsim = nsim, z.prop = prm.prop[["z"]],  alpha.prop = prm.prop[["alpha"]], random.start = TRUE, verbose = TRUE,  nchains = 2, thin = 10, store.burnin = TRUE, threads = 2,  parallel = "snow")sim.dmbc <- dmbc(simdiss, p, G, control)dmbc_check_groups(sim.dmbc)## End(Not run)

An S4 class to represent the latent configuration estimate for a DMBC model.

Description

An S4 class to represent the the latent configuration estimate for a DMBCmodel.

Slots

Z.est: An array containing the estimate of the latentconfiguration for a DMBC model.
Z.sd: An array containing the standard deviation of the latentconfiguration for a DMBC model.
cluster: A numeric vector providing the estimated groupmembership for theS subjects in the data.
est: A length-one character vector providing the estimate typereturned inZ.est. Possible values aremean (posteriormean),median (posterior median),ml (maximum likelihood)andmap (maximum-a-posteriori).
n: A length-one numeric vector providing the number of objects.
p: A length-one numeric vector providing the number of latentdimensions.
S: A length-one numeric vector providing the number of subjects.
G: A length-one numeric vector providing the number of clusters.
family: An object of classlist; named list withelements representing the parameter estimates corresponding to differentvalues ofp andG.
chain: A length-one numeric vector representing the ID ofthe MCMC chain used to compute the estimates.
labels: A character vector for the (optional) strings to usein the plots for labeling the objects.

References

Examples

showClass("dmbc_config")

Auxiliary Function for Controlling DMBC Model Fitting

Description

dmbc_control() is an auxiliary function as user interface fordmbc() fitting. Typically only used when calling thedmbc()function. It is used to set parameters that affect the sampling but donot affect the posterior distribution.

control_dmbc() is an alias fordmbc_control().

check_control() is an auxiliary function that verifies thecorrectness of the controls provided before a DMBC is fitted withdmbc().

Usage

dmbc_control(  nsim = 5000,  burnin = 10000,  thin = 1,  nchains = 1,  threads = 1,  seed = NULL,  parallel = "no",  z.prop = 1.5,  alpha.prop = 0.75,  random.start = TRUE,  partition = NULL,  method = "manhattan",  procrustes = TRUE,  relabel = TRUE,  store.burnin = TRUE,  verbose = FALSE)control_dmbc(  nsim = 5000,  burnin = 10000,  thin = 1,  nchains = 1,  threads = 1,  seed = NULL,  parallel = "no",  z.prop = 1.5,  alpha.prop = 0.75,  random.start = TRUE,  partition = NULL,  method = "manhattan",  procrustes = TRUE,  relabel = TRUE,  store.burnin = TRUE,  verbose = FALSE)check_control(control)

Arguments

nsim

A length-one numeric vector for the number of draws to be takenfrom the posterior distribution.

burnin

A length-one numeric vector for the number of initial MCMCiterations (usually to be discarded).

thin

A length-one numeric vector for the number of iterations betweenconsecutive draws.

nchains

A length-one numeric vector for the number of parallel chains to run.

threads

A length-one numeric vector for the number of chains to run.If greater than 1, packageparallel is used to take advantage of anymultiprocessing or distributed computing capabilities that may be available.

seed

An integer scalar. If supplied, provides the random number seed.

parallel

A length-one character vector indicating the type of paralleloperation to be used (if any). Possible values aremulticore(which works only on Unix/mcOS),snow andno (i.e. serialinstead of parallel computing).

z.prop

A length-one numeric vector providing the standard deviation of theproposal distribution for the jump in the individual latent spaceposition.

alpha.prop

A length-one numeric vector providing the standard deviationof the proposal distribution for the jump in the individual random effect value.

random.start

A length-one logical vector. IfTRUE the startingvalues are drawn randomly, otherwise a user-defined starting partition mustbe provided through thepartition argument.

partition

A length-one numeric vector providing the user-definedstarting partition.

method

A length-one character vector that specifies the distancemeasure to use in determining the initial partition. Allowed values arethose from thedist() function.

procrustes

A length-one logical vector. IfTRUE the simulatedMCMC chains are post-processed through a Procrustes transformation.

relabel

A length-one logical vector. IfTRUE the simulatedMCMC chains are relabelled to address the label-switching problem.

store.burnin

A logical scalar. IfTRUE, the samples from theburnin are also stored and returned.

verbose

A logical scalar. IfTRUE, causes information to beprinted out about the progress of the fitting.

control

A list of control options.

Value

A named list with the control options as components.

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

Examples

## Not run: data(simdiss, package = "dmbc")# Shorter run than default.sim.fit <- dmbc(simdiss,  control = dmbc_control(burnin = 1000, nsim = 2000, thin = 5, verbose = TRUE))## End(Not run)

An S4 class to represent the data to use in a DMBC model.

Description

An S4 class to represent the data to use in a DMBC model.

Slots

diss: A list whose elements are the dissimilarity matrices correspondingto the judgments expressed by theS subjects/raters. These matricesmust be defined as adist object.
n: A length-one character vector representing the number of objectscompared by each subject.
S: A length-one numeric vector representing the number of subjects.
family: A length-one character vector representing the type of data toanalyze. Currently, it accepts only the 'binomial' value, but futuredevelopments will include the possibility to analyze continuous,multinomial and count data.

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

References

Examples

showClass("dmbc_data")

Fitter function for DMBC models.

Description

dmbc_fit() is the main function that estimates a DMBC model.

Usage

dmbc_fit(D, p, G, family, control, prior, start)

Arguments

D

A list whose elements are the dissimilarity matrices correspondingto the judgments expressed by theS subjects/raters. These matricesmust be defined as adist object.

p

A length-one numeric vector indicating the number of dimensions of thelatent space.

G

A length-one numeric vector indicating the number of cluster topartition theS subjects.

family

A length-one character vector representing the type of data toanalyze. Currently, it accepts only the 'binomial' value, but futuredevelopments will include the possibility to analyze continuous,multinomial and count data.

control

A list of control parameters that affect the samplingbut do not affect the posterior distribution Seedmbc_control() for more details.

prior

A list containing the prior hyperparameters. Seedmbc_prior() for more details.

start

A named list of starting values for the MCMC algorithm (seedmbc_init).

Value

Admbc_fit_list object.

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

References

Examples

## Not run: data(simdiss, package = "dmbc")G <- 3p <- 2prm.prop <- list(z = 1.5, alpha = .75)burnin <- 20000nsim <- 10000seed <- 2301set.seed(seed)control <- list(burnin = burnin, nsim = nsim, z.prop = prm.prop[["z"]],  alpha.prop = prm.prop[["alpha"]], random.start = TRUE, verbose = TRUE,  nchains = 2, thin = 10, store.burnin = TRUE, threads = 2,  parallel = "snow")sim.dmbc <- dmbc(simdiss, p, G, control)summary(sim.dmbc, include.burnin = FALSE)library(bayesplot)library(ggplot2)color_scheme_set("teal")plot(sim.dmbc, what = "trace", regex_pars = "eta")z <- dmbc_get_configuration(sim.dmbc, chain = 1, est = "mean",  labels = 1:16)summary(z)color_scheme_set("mix-pink-blue")graph <- plot(z, size = 2, size_lbl = 3)graph + panel_bg(fill = "gray90", color = NA)## End(Not run)

An S4 class to represent the results of fitting DMBC model.

Description

An S4 class to represent the results of fitting DMBC model using a singleMarkov Chain Monte Carlo chain.

Slots

z.chain: An object of classarray; posterior draws fromthe MCMC algorithm for the (untransformed) latent configurationZ.
z.chain.p: An object of classarray; posterior draws fromthe MCMC algorithm for the (Procrustes-transformed) latent configurationZ.
alpha.chain: An object of classmatrix; posterior drawsfrom the MCMC algorithm for the\alpha parameters.
eta.chain: An object of classmatrix; posterior drawsfrom the MCMC algorithm for the\eta parameters.
sigma2.chain: An object of classmatrix; posterior drawsfrom the MCMC algorithm for the\sigma^2 parameters.
lambda.chain: An object of classmatrix; posterior drawsfrom the MCMC algorithm for the\lambda parameters.
prob.chain: An object of classarray; posterior drawsfrom the MCMC algorithm for the cluster membership probabilities.
x.ind.chain: An object of classarray; posterior drawsfrom the MCMC algorithm for the cluster membership indicators.
x.chain: An object of classmatrix; posterior draws fromthe MCMC algorithm for the cluster membership labels.
accept: An object of classmatrix; final acceptance ratesfor the MCMC algorithm.
diss: An object of classlist; list of observeddissimilarity matrices.
dens: An object of classlist; list of log-likelihood,log-prior and log-posterior values at each iteration of the MCMC simulation.
control: An object of classlist; list of the controlparameters (number of burnin and sample iterations, number of MCMC chains,etc.). Seedmbc_control() for more information.
prior: An object of classlist; list of the priorhyperparameters. Seedmbc_prior() for more information.
dim: An object of classlist; list of dimensions forthe estimated model, i.e. number of objects (n), number of latentdimensions (p), number of clusters (G), and number ofsubjects (S).
model: An object of classdmbc_model.

References

Examples

showClass("dmbc_fit")

An S4 class to represent the results of fitting DMBC model.

Description

An S4 class to represent the results of fitting DMBC model using multipleMarkov Chain Monte Carlo chains.

Slots

results: An object of classlist; list ofdmbc_fitobjects corresponding to the parallel MCMC chains simulated during theestimation.

References

Examples

showClass("dmbc_fit_list")

Conversion of an`dmbc_fit_list` object to a`list`.

Description

dmbc_fit_list_to_list converts an object of classdmbc_fit_list to a list of arrays including all the parameter.chains. It is intended for internal use mainly.

Usage

dmbc_fit_list_to_list(res, include.burnin = FALSE, verbose = TRUE)

Arguments

res

An object of typedmbc_fit_list.

include.burnin

A logical scalar. IfTRUE the burniniterations (if available) are not removed.

verbose

A logical scalar. IfTRUE prints additionalwarnings during the conversion.

Value

An object of typemcmc.list.

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

Examples

## Not run: data(simdiss, package = "dmbc")G <- 3p <- 2prm.prop <- list(z = 1.5, alpha = .75)burnin <- 2000nsim <- 1000seed <- 2301set.seed(seed)control <- list(burnin = burnin, nsim = nsim, z.prop = prm.prop[["z"]],  alpha.prop = prm.prop[["alpha"]], nchains = 2, verbose = TRUE)sim.dmbc <- dmbc(simdiss, p, G, control)sim.list <- dmbc_fit_list_to_list(sim.dmbc, TRUE)library(bayesplot)mcmc_trace(sim.list, regex_pars = "lambda")## End(Not run)

Conversion of an`dmbc_fit_list` object to an object of class`mcmc.list`.

Description

dmbc_fit_list_to_mcmc.list converts an object of classdmbc_fit_list to an object with classmcmc.list.

Usage

dmbc_fit_list_to_mcmc.list(res, include.burnin = FALSE, verbose = TRUE)

Arguments

res

An object of typedmbc_fit_list.

include.burnin

A logical scalar. IfTRUE the burniniterations (if available) are not removed.

verbose

A logical scalar. IfTRUE prints additionalwarnings during the conversion.

Value

An object of typemcmc.list.

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

Examples

## Not run: data(simdiss, package = "dmbc")G <- 3p <- 2prm.prop <- list(z = 1.5, alpha = .75)burnin <- 2000nsim <- 1000seed <- 2301set.seed(seed)control <- list(burnin = burnin, nsim = nsim, z.prop = prm.prop[["z"]],  alpha.prop = prm.prop[["alpha"]], nchains = 2, verbose = TRUE)sim.dmbc <- dmbc(simdiss, p, G, control)sim.mcmc <- dmbc_fit_list_to_mcmc.list(sim.dmbc, TRUE)plot(sim.mcmc)## End(Not run)

Conversion of an`dmbc_fit` object to an object of class`mcmc`.

Description

dmbc_fit_to_mcmc converts an object of classdmbc_fitto an object with classmcmc.

Usage

dmbc_fit_to_mcmc(res, include.burnin = FALSE, verbose = TRUE)

Arguments

res

An object of typedmbc_fit.

include.burnin

A logical scalar. IfTRUE the burniniterations (if available) are not removed.

verbose

A logical scalar. IfTRUE prints additionalwarnings during the conversion.

Value

An object of typemcmc.

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

Examples

## Not run: data(simdiss, package = "dmbc")G <- 3p <- 2prm.prop <- list(z = 1.5, alpha = .75)burnin <- 2000nsim <- 1000seed <- 2301set.seed(seed)control <- list(burnin = burnin, nsim = nsim, z.prop = prm.prop[["z"]],  alpha.prop = prm.prop[["alpha"]], verbose = TRUE)sim.dmbc <- dmbc(simdiss, p, G, control)sim.mcmc <- dmbc_fit_to_mcmc(sim.dmbc@results[[1]], TRUE)plot(sim.mcmc)## End(Not run)

Extractor function for a fitted DMBC model.

Description

dmbc_get_configuration() is an extractor function for extracting thelatent configuration estimates of a fitted DMBC model.

Usage

dmbc_get_configuration(res, chain = 1, est = "mean", labels = character(0))

Arguments

res

An object of classdmbc_fit_list.

chain

A length-one numeric vector indicating the MCMC chain numberto use.

est

A length-one character vector indicating the estimate type to use.

labels

An optional character vector with the object labels.

Value

Admbc_config object.

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

References

Examples

## Not run: data(simdiss, package = "dmbc")G <- 3p <- 2prm.prop <- list(z = 1.5, alpha = .75)burnin <- 2000nsim <- 1000seed <- 2301set.seed(seed)control <- list(burnin = burnin, nsim = nsim, z.prop = prm.prop[["z"]],  alpha.prop = prm.prop[["alpha"]], random.start = TRUE, verbose = TRUE,  nchains = 2, thin = 10, store.burnin = TRUE, threads = 2,  parallel = "snow")sim.dmbc <- dmbc(simdiss, p, G, control)z <- dmbc_get_configuration(sim.dmbc, chain = 1, est = "mean")summary(z)library(bayesplot)library(ggplot2)color_scheme_set("mix-pink-blue")graph <- plot(z, size = 2, size_lbl = 3)graph + panel_bg(fill = "gray90", color = NA)## End(Not run)

Extractor function for a fitted DMBC model.

Description

dmbc_get_map() is an extractor function for extracting themaximum-a-posterior estimates of the parameters for a fitted DMBC model.

Usage

dmbc_get_map(res, chain = 1)

Arguments

res

An object of classdmbc_fit_list.

chain

A length-one numeric vector indicating the MCMC chain numberto use.

Value

A namedlist with the following elements:

z:: array of latent coordinates posterior mean estimates
alpha:: numeric vector of alpha posterior mean estimates
eta:: numeric vector of eta posterior mean estimates
sigma2:: numeric vector of sigma2 posterior mean estimates
lambda:: numeric vector of lambda posterior mean estimates
prob:: numeric matrix of probability posterior mean estimates
cluster:: numeric vector of cluster membership posteriormean estimates
logpost:: length-one numeric vector of the maximumlog-posterior value
chain:: length-one numeric vector of the MCMC chain numberused

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

References

Examples

## Not run: data(simdiss, package = "dmbc")G <- 3p <- 2prm.prop <- list(z = 1.5, alpha = .75)burnin <- 2000nsim <- 1000seed <- 2301set.seed(seed)control <- list(burnin = burnin, nsim = nsim, z.prop = prm.prop[["z"]],  alpha.prop = prm.prop[["alpha"]], random.start = TRUE, verbose = TRUE,  nchains = 2, thin = 10, store.burnin = TRUE, threads = 2,  parallel = "snow")sim.dmbc <- dmbc(simdiss, p, G, control)dmbc_get_map(sim.dmbc, chain = 1)## End(Not run)

Extractor function for a fitted DMBC model.

Description

dmbc_get_ml() is an extractor function for extracting themaximum likelihood estimates of the parameters for a fitted DMBC model.

Usage

dmbc_get_ml(res, chain = 1)

Arguments

res

An object of classdmbc_fit_list.

chain

A length-one numeric vector indicating the MCMC chain numberto use.

Value

A namedlist with the following elements:

z:: array of latent coordinates posterior mean estimates
alpha:: numeric vector of alpha posterior mean estimates
eta:: numeric vector of eta posterior mean estimates
sigma2:: numeric vector of sigma2 posterior mean estimates
lambda:: numeric vector of lambda posterior mean estimates
prob:: numeric matrix of probability posterior mean estimates
cluster:: numeric vector of cluster membership posteriormean estimates
loglik:: length-one numeric vector of the maximumlog-likelihood value
chain:: length-one numeric vector of the MCMC chain numberused

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

References

Examples

## Not run: data(simdiss, package = "dmbc")G <- 3p <- 2prm.prop <- list(z = 1.5, alpha = .75)burnin <- 2000nsim <- 1000seed <- 2301set.seed(seed)control <- list(burnin = burnin, nsim = nsim, z.prop = prm.prop[["z"]],  alpha.prop = prm.prop[["alpha"]], random.start = TRUE, verbose = TRUE,  nchains = 2, thin = 10, store.burnin = TRUE, threads = 2,  parallel = "snow")sim.dmbc <- dmbc(simdiss, p, G, control)dmbc_get_ml(sim.dmbc, chain = 1)## End(Not run)

Extractor function for a fitted DMBC model.

Description

dmbc_get_postmean() is an extractor function for extracting theposterior mean estimates of the parameters for a fitted DMBC model.

Usage

dmbc_get_postmean(res, chain = 1)

Arguments

res

An object of classdmbc_fit_list.

chain

A length-one numeric vector indicating the MCMC chain numberto use.

Value

A namedlist with the following elements:

z:: array of latent coordinates posterior mean estimates
alpha:: numeric vector of alpha posterior mean estimates
eta:: numeric vector of eta posterior mean estimates
sigma2:: numeric vector of sigma2 posterior mean estimates
lambda:: numeric vector of lambda posterior mean estimates
prob:: numeric matrix of probability posterior mean estimates
cluster:: numeric vector of cluster membership posteriormean estimates
chain:: length-one numeric vector of the MCMC chain numberused

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

References

Examples

## Not run: data(simdiss, package = "dmbc")G <- 3p <- 2prm.prop <- list(z = 1.5, alpha = .75)burnin <- 2000nsim <- 1000seed <- 2301set.seed(seed)control <- list(burnin = burnin, nsim = nsim, z.prop = prm.prop[["z"]],  alpha.prop = prm.prop[["alpha"]], random.start = TRUE, verbose = TRUE,  nchains = 2, thin = 10, store.burnin = TRUE, threads = 2,  parallel = "snow")sim.dmbc <- dmbc(simdiss, p, G, control)dmbc_get_postmean(sim.dmbc, chain = 1)## End(Not run)

Extractor function for a fitted DMBC model.

Description

dmbc_get_postmedian() is an extractor function for extracting theposterior median estimates of the parameters for a fitted DMBC model.

Usage

dmbc_get_postmedian(res, chain = 1)

Arguments

res

An object of classdmbc_fit_list.

chain

A length-one numeric vector indicating the MCMC chain numberto use.

Value

A namedlist with the following elements:

z:: array of latent coordinates posterior median estimates
alpha:: numeric vector of alpha posterior median estimates
eta:: numeric vector of eta posterior median estimates
sigma2:: numeric vector of sigma2 posterior median estimates
lambda:: numeric vector of lambda posterior median estimates
prob:: numeric matrix of probability posterior median estimates
cluster:: numeric vector of cluster membership posteriormedian estimates
chain:: length-one numeric vector of the MCMC chain numberused

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

References

Examples

## Not run: data(simdiss, package = "dmbc")G <- 3p <- 2prm.prop <- list(z = 1.5, alpha = .75)burnin <- 2000nsim <- 1000seed <- 2301set.seed(seed)control <- list(burnin = burnin, nsim = nsim, z.prop = prm.prop[["z"]],  alpha.prop = prm.prop[["alpha"]], random.start = TRUE, verbose = TRUE,  nchains = 2, thin = 10, store.burnin = TRUE, threads = 2,  parallel = "snow")sim.dmbc <- dmbc(simdiss, p, G, control)dmbc_get_postmedian(sim.dmbc, chain = 1)## End(Not run)

An S4 class to represent the comparison of a set of DMBC models.

Description

An S4 class to represent the comparison of a set of DMBC models throughthe dissimilarity model-based clustering information criterion (DCIC).

Slots

logprior: An object of classmatrix providing thelog-prior values corresponding to different values ofp andG.
logmlik: An object of classmatrix providing themarginal log-likelihood values corresponding to different values ofp andG.
logcorrfact: An object of classmatrix providing thelogarithm of the correction factors corresponding to different values ofp andG.
DCIC: An object of classmatrix providing the valuesof the DCIC index corresponding to different values ofp andG.
post.est: An object of classlist; named list withelements representing the parameter estimates corresponding to differentvalues ofp andG.
est: A length-one character vector representing the estimatetype used in computing the DCIC index. Possible values aremean,median,ml andmap. Seedmbc_ic() formore details about these values.
res_last_p: An object of classlist; list ofdmbc_fit_list objects with the results of fitting the DMBCmodels corresponding to the last value ofp. This is needed in caseof an update of the DCIC calculations using additionalp and/orG values.

References

Examples

showClass("dmbc_ic")

Function to compute the starting values before fitting a DMBC models.

Description

dmbc_init() is the main function that estimates a DMBC model.

Usage

dmbc_init(D, p, G, family, random.start, method, partition)

Arguments

D

A list whose elements are the dissimilarity matrices correspondingto the judgments expressed by theS subjects/raters. These matricesmust be defined as adist object.

p

A length-one numeric vector indicating the number of dimensions of thelatent space.

G

A length-one numeric vector indicating the number of cluster topartition theS subjects.

family

random.start

A length-one logical vector. IfTRUE the startingvalues are drawn randomly, otherwise.

method

A length-one character vector specifying the distancemeasure to use in determining the initial partition. Allowed values arethose from thedist() function.

partition

A length-one numeric vector providing the user-definedstarting partition.

Value

A namedlist with the following items:

z:: array of latent coordinates starting values
x:: numeric vector of initial cluster memberships
ng:: numeric vector of initial cluster sizes
alpha:: numeric vector of alpha starting values
eta:: numeric vector of eta starting values
sigma2:: numeric vector of sigma2 starting values
lambda:: numeric vector of lambda starting values

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

References

Examples

data(simdiss, package = "dmbc")dmbc_init(simdiss@diss, p = 2, G = 3, family = "binomial", random.start = TRUE)

Log-likelihood for DMBC models.

Description

dmbc_logLik() computes the log-likelihood value for a DMBC model.

Usage

dmbc_logLik(D, Z, alpha, lambda, x)

Arguments

D

A list whose elements are the dissimilarity matrices correspondingto the judgments expressed by theS subjects/raters. These matricesmust be defined as adist object.

Z

A numeric matrix containing the latent configuration.

alpha

A numeric vector containing the alpha values.

lambda

A numeric vector containing the alpha lambda.

x

A numeric vector containing the cluster indicator values.

Value

A length-one numeric vector of the log-likelihood value.

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

References

Log-likelihood for DMBC models.

Description

dmbc_logLik_rbmds() computes the log-likelihood value for a DMBC model.

Usage

dmbc_logLik_rbmds(D, Z, alpha)

Arguments

D

A list whose elements are the dissimilarity matrices correspondingto the judgments expressed by theS subjects/raters. These matricesmust be defined as adist object.

Z

A numeric matrix containing the latent configuration.

alpha

A numeric vector containing the alpha values.

Value

A length-one numeric vector of the log-likelihood value.

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

References

Auxiliary function for realigning the grouping of a fitted DMBC model.

Description

dmbc_match_groups() is an auxiliary function for realigning thecluster membership estimates provided by the individual chains of thefitted model if they do not agree.

Usage

dmbc_match_groups(res, est = "mean", ref = 1)

Arguments

res

An object of classdmbc_fit_list.

est

A length-one character vector indicating the estimate type to use.

ref

A length-one numeric vector indicating the chain number to use asthe reference.

Value

An object of classdmbc_fit_list.

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

References

Examples

## Not run: data(simdiss, package = "dmbc")G <- 5p <- 3prm.prop <- list(z = 4, alpha = 2)burnin <- 2000nsim <- 1000seed <- 2301set.seed(seed)control <- list(burnin = burnin, nsim = nsim, z.prop = prm.prop[["z"]],  alpha.prop = prm.prop[["alpha"]], random.start = TRUE, verbose = TRUE,  nchains = 6, store.burnin = TRUE, threads = 2, parallel = "snow")sim.dmbc <- dmbc(simdiss, p, G, control)sim.dmbc_new <- dmbc_match_groups(sim.dmbc)## End(Not run)

An S4 class to represent a DMBC model.

Description

An S4 class to represent a DMBC model.

Slots

p: A length-one character vector representing the number of dimensionsof the latent space to use in the MDS analysis.
G: A length-one numeric vector representing the number of clusters topartition the subjects into.
family: A length-one character vector representing the type of data toanalyze. Currently, it accepts only the 'binomial' value, but futuredevelopments will include the possibility to analyze continuous,multinomial and count data.

References

Examples

showClass("dmbc_model")

Auxiliary Function for Setting DMBC Model Priors

Description

dmbc_prior() is an auxiliary function as user interface fordmbc() fitting. Typically only used when calling thedmbc()function. It is used to set prior hyperparameters.

prior_dmbc() is an alias fordmbc_prior().

check_prior() is an auxiliary function that verifies thecorrectness of the prior hyperparameters provided before a DMBC is fittedwithdmbc().

update_prior() is an auxiliary function to modify a set of priorchoices using a new value ofp andG. It is intended forinternal use mainly in thedmbc_ic() function.

Usage

dmbc_prior(  eta = list(a = rep(1.5, .dmbcEnv$current_G), b = rep(0.5, .dmbcEnv$current_G)),  sigma2 = list(a = 0.1, b = 0.1),  lambda = rep(1, .dmbcEnv$current_G))prior_dmbc(  eta = list(a = rep(1.5, .dmbcEnv$current_G), b = rep(0.5, .dmbcEnv$current_G)),  sigma2 = list(a = 0.1, b = 0.1),  lambda = rep(1, .dmbcEnv$current_G))check_prior(prior)update_prior(prior, p, G)

Arguments

eta

A named list containing the hyperparameters for the priordistribution of the\eta_1,\ldots,\eta_G parameters. It shouldcontain two numeric vectors, namelya andb.

sigma2

A named list containing the hyperparameters for the priordistributions of the\sigma^2_1,\ldots,\sigma^2_G parameters. Itshould contain two numeric scalars, namelya andb.

lambda

A list containing the hyperparameters for the priordistribution of the\lambda_1,\ldots,\lambda_G parameters. It shouldcontain a single numeric vector.

prior

A named list of prior hyperparameters.

p

A length-one numeric vector indicating the number of dimensions of thelatent space.

G

A length-one numeric vector indicating the number of cluster topartition theS subjects.

Value

A list with the prior hyperparameters as components.

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

Examples

## Not run: data(simdiss, package = "dmbc")# Shorter run than default.sim.fit <- dmbc(simdiss,  control = dmbc_control(burnin = 1000, nsim = 2000, thin = 1, verbose = TRUE),  prior = dmbc_prior(sigma2 = list(a = 1, b = 4)))## End(Not run)

Create an instance of the`dmbc_config` class using new/initialize.

Description

Create an instance of thedmbc_config class using new/initialize.

Usage

## S4 method for signature 'dmbc_config'initialize(  .Object,  Z.est = array(),  Z.sd = array(),  cluster = numeric(),  est = character(),  n = numeric(),  S = numeric(),  p = numeric(),  G = numeric(),  family = character(),  chain = numeric(),  labels = character())

Arguments

.Object

Prototype object from the classdmbc_config.

Z.est

An array containing the estimate of the latentconfiguration for a DMBC model.

Z.sd

An array containing the standard deviation of the latentconfiguration for a DMBC model.

cluster

A numeric vector providing the estimated groupmembership for theS subjects in the data.

est

A length-one character vector providing the estimate typereturned inZ.est. Possible values aremean (posteriormean),median (posterior median),ml (maximum likelihood)andmap (maximum-a-posteriori).

n

A length-one numeric vector providing the number of objects.

S

A length-one numeric vector providing the number of subjects.

p

A length-one numeric vector providing the number of latentdimensions.

G

A length-one numeric vector providing the number of clusters.

family

An object of classlist; named list withelements representing the parameter estimates corresponding to differentvalues ofp andG.

chain

A length-one numeric vector representing the ID ofthe MCMC chain used to compute the estimates.

labels

A character vector for the (optional) strings to usein the plots for labeling the objects.

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

Create an instance of the`dmbc_data` class using new/initialize.

Description

Create an instance of thedmbc_data class using new/initialize.

Usage

## S4 method for signature 'dmbc_data'initialize(  .Object,  diss = list(),  n = numeric(),  S = numeric(),  family = character())

Arguments

.Object

Prototype object from the classdmbc_data.

diss

A list whose elements are the dissimilarity matrices correspondingto the judgments expressed by theS subjects/raters. These matricesmust be defined as adist object.

n

A length-one character vector representing the number of objectscompared by each subject.

S

A length-one numeric vector representing the number of subjects.

family

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

Create an instance of the`dmbc_fit` class using new/initialize.

Description

Create an instance of thedmbc_fit class using new/initialize.

Usage

## S4 method for signature 'dmbc_fit'initialize(  .Object,  z.chain = array(),  z.chain.p = array(),  alpha.chain = matrix(),  eta.chain = matrix(),  sigma2.chain = matrix(),  lambda.chain = matrix(),  prob.chain = array(),  x.ind.chain = array(),  x.chain = matrix(),  accept = matrix(),  diss = list(),  dens = list(),  control = list(),  prior = list(),  dim = list(),  model = NA)

Arguments

.Object

Prototype object from the classdmbc_fit.

z.chain

An object of classarray; posterior draws fromthe MCMC algorithm for the (untransformed) latent configurationZ.

z.chain.p

An object of classarray; posterior draws fromthe MCMC algorithm for the (Procrustes-transformed) latent configurationZ.

alpha.chain

An object of classmatrix; posterior drawsfrom the MCMC algorithm for the\alpha parameters.

eta.chain

An object of classmatrix; posterior drawsfrom the MCMC algorithm for the\eta parameters.

sigma2.chain

An object of classmatrix; posterior drawsfrom the MCMC algorithm for the\sigma^2 parameters.

lambda.chain

An object of classmatrix; posterior drawsfrom the MCMC algorithm for the\lambda parameters.

prob.chain

An object of classarray; posterior drawsfrom the MCMC algorithm for the cluster membership probabilities.

x.ind.chain

An object of classarray; posterior drawsfrom the MCMC algorithm for the cluster membership indicators.

x.chain

An object of classmatrix; posterior draws fromthe MCMC algorithm for the cluster membership labels.

accept

An object of classmatrix; final acceptance ratesfor the MCMC algorithm.

diss

An object of classlist; list of observeddissimilarity matrices.

dens

An object of classlist; list of log-likelihood,log-prior and log-posterior values at each iteration of the MCMC simulation.

control

An object of classlist; list of the controlparameters (number of burnin and sample iterations, number of MCMC chains,etc.). Seedmbc_control() for more information.

prior

An object of classlist; list of the priorhyperparameters. Seedmbc_prior() for more information.

dim

An object of classlist; list of dimensions forthe estimated model, i.e. number of objects (n), number of latentdimensions (p), number of clusters (G), and number ofsubjects (S).

model

An object of classdmbc_model.

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

Create an instance of the`dmbc_fit_list` class using new/initialize.

Description

Create an instance of thedmbc_fit_list class using new/initialize.

Usage

## S4 method for signature 'dmbc_fit_list'initialize(.Object, results = list())

Arguments

.Object

Prototype object from the classdmbc_fit_list.

results

A list whose elements are thedmbc_fit objects foreach simulated chain.

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

Create an instance of the`dmbc_ic` class using new/initialize.

Description

Create an instance of thedmbc_ic class using new/initialize.

Usage

## S4 method for signature 'dmbc_ic'initialize(  .Object,  logprior = matrix(),  logmlik = matrix(),  logcorrfact = matrix(),  DCIC = matrix(),  post.est = list(),  est = character(),  res_last_p = list())

Arguments

.Object

Prototype object from the classdmbc_ic.

logprior

An object of classmatrix providing thelog-prior values corresponding to different values ofp andG.

logmlik

An object of classmatrix providing themarginal log-likelihood values corresponding to different values ofp andG.

logcorrfact

An object of classmatrix providing thelogarithm of the correction factors corresponding to different values ofp andG.

DCIC

An object of classmatrix providing the valuesof the DCIC index corresponding to different values ofp andG.

post.est

An object of classlist; named list withelements representing the parameter estimates corresponding to differentvalues ofp andG.

est

A length-one character vector representing the estimatetype used in computing the DCIC index. Possible values aremean,median,ml andmap. Seedmbc_ic() formore details about these values.

res_last_p

An object of classlist; list ofdmbc_fit_list objects with the results of fitting the DMBCmodels corresponding to the last value ofp. This is needed in caseof an update of the DCIC calculations using additionalp and/orG values.

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

Create an instance of the`dmbc_model` class using new/initialize.

Description

Create an instance of thedmbc_model class using new/initialize.

Usage

## S4 method for signature 'dmbc_model'initialize(.Object, p = numeric(), G = numeric(), family = character())

Arguments

.Object

Prototype object from the classdmbc_model.

p

A length-one character vector representing the number of dimensionsof the latent space to use in the MDS analysis.

G

A length-one numeric vector representing the number of clusters topartition the subjects into.

family

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

List of binary dissimilarity matrices among 15 kinship terms.

Description

Rosenberg and Kim (1975) designed an experiment to analyze the perceivedsimilarities of 15 kinship terms.

Here, we consider the data relative to 85 females made available inRosenberg (1982). Each subject was asked to group the kinship termsaccording to the perceived similarity. Thus,S = 85 binarydissimilarity matrices are available whose elements (0 or 1) indicatewhether or not two kinship terms were grouped together by each individual.

Usage

data(kinship)

Format

Admbc_data object whosediss element is a list of 85binary dissimilarity matrices. Each matrix is defined as adistobject measuring whether each pair of the 15 kinship terms is judged assimilar (1) or not (0).

Thedist objects have rows and columns that are named as follows:

GrF: grandfather
GrM: grandmother
GrD: granddaughter
GrS: grandson
Bro: brother
Sis: sister
Fat: father
Mot: mother
Dau: daughter
Son: son
Nep: nephew
Nie: niece
Cou: cousin
Aun: aunt
Unc: uncle

References

Rosenberg, S. (1982). The method of sorting in multivariate research withapplications selected from cognitive psychology and person perception. InN Hirschberg, LG Humphreys (eds.), Multivariate Applications in the SocialSciences, pp. 117–142. Erlbaum., Hillsdale, NJ.

Rosenberg, S., Kim, M. P. (1975). The method of sorting as a data-gatheringprocedure in multivariate research. Multivariate Behavioral Research, 10.

Examples

data(kinship)library(bayesplot)cols <- color_scheme_set("mix-red-blue")plot(kinship, colors = unlist(cols)[c(1, 6)], font = 1, cex.font = 0.75)

Information criterion for Bayesian multidimensional scaling (BMDS).

Description

mdsic computes the information criterion for a set of Bayesianmultidimensional scaling (BMDS) solutions using the approach inOh & Raftery (2001).

Usage

mdsic(x_star, rmin_ssr, n, min_p = 1, max_p = 6)

Arguments

x_star

An array containing the latent configurationsestimated usingbmds.

rmin_ssr

A numeric vector providing the ratios of SSRfor the latent dimensions requested.

n

A length-one numeric vector providing the number of objects.

min_p

A length-one numeric vector providing the minimum valueof the latent space dimension to use.

max_p

A length-one numeric vector providing the maximumvalue of the latent space dimension to use.

Value

A list with the following elements:

mdsic: A numeric vector with the values of MDSIC index.
bic: A numeric vector with the values of the BIC index.

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

References

Oh, M.-S., Raftery, A. E. (2001), "Bayesian Multidimensional Scaling andChoice of Dimension", Journal of the American Statistical Association,96, 1031-1044.

Examples

## Not run: # Road distances (in km) between 21 cities in Europedata(eurodist, package = "datasets")min_p <- 1max_p <- 10burnin <- 200nsim <- 1000totiter <- burnin + nsimeurodist.mds <- cmdscale(eurodist, max_p)eurodist.bmds <- bmds(eurodist, min_p, max_p, burnin, nsim)plot((min_p:max_p), eurodist.bmds$mdsIC$mdsic, type = "b",  main = "MDS Information Criterion", xlab = "p", ylab = "MDSIC")MDSICmin <- which.min(eurodist.bmds$mdsIC$mdsic)points((min_p:max_p)[MDSICmin], eurodist.bmds$mdsIC$mdsic[MDSICmin],  col = "red", pch = 10, cex = 1.75, lwd = 1.5)## End(Not run)

Provide a graphical summary of a`dmbc_config` class instance.

Description

Provide a graphical summary of admbc_config class instance.

Usage

## S4 method for signature 'dmbc_config,ANY'plot(  x,  size = NULL,  size_lbl = NULL,  nudge_x = 0,  nudge_y = 0,  label_objects = TRUE,  ...)

Arguments

x

An object of classdmbc_config.

size

A length-two numeric vector providing the optional sizes ofpoints and lines in the plot.

size_lbl

A length-one numeric vector providing the size of labels.

nudge_x

A length-one numeric vector providing the optional horizontaladjustment to nudge labels by.

nudge_y

A length-one numeric vector providing the optional verticaladjustment to nudge labels by.

label_objects

A length-one logical vector. IfTRUE, labels areadded to the plot.

...

Further arguments to pass on (currently ignored).

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

Provide a graphical summary of a`dmbc_data` class instance.

Description

Provide a graphical summary of admbc_data class instance.

Usage

## S4 method for signature 'dmbc_data,ANY'plot(x, colors = c("white", "black"), font = NA, cex.font = NA, ...)

Arguments

x

An object of classdmbc_data.

colors

A character vector providing the colors to use in the plot.

font

A length-one numeric vector for the font to use for text.Can be a vector.NA values (the default) mean usepar("font").

cex.font

A length-one numeric vector for the character expansionfactor.NULL andNA are equivalent to1.0. This is anabsolute measure, not scaled bypar("cex") or by setting'par("mfrow") orpar("mfcol"). Can be a vector.

...

Further arguments to pass on (currently ignored).

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

Examples

data(simdiss)library(bayesplot)cols <- color_scheme_set("brightblue")plot(simdiss, colors = unlist(cols)[c(1, 6)], font = 1, cex.font = 0.75)

Provide a graphical summary of a`dmbc_fit` class instance.

Description

Provide a graphical summary of admbc_fit class instance.

Usage

## S4 method for signature 'dmbc_fit,ANY'plot(  x,  what = "trace",  pars = character(),  regex_pars = "lambda",  include.burnin = FALSE,  combo = NULL,  ...)

Arguments

x

An object of classdmbc_fit.

what

A length-one character vector providing the plot type to produce.Admissible values are those provided by thebayesplot package,that is:acf,areas,dens,hex,hist,intervals,neff,pairs,parcoord,recover,rhat,scatter,trace,violin orcombo.In particular,combo allows to mix different plot types. For moredetails see the documentation of thebayesplot package.

pars

An optional character vector of parameter names. If neitherpars norregex_pars is specified, the default is to use all parameters.

regex_pars

An optionalregular expression to use forparameter selection. Can be specified instead ofpars or in addition topars.

include.burnin

A length-one logical vector. IfTRUE theburnin iterations (if available) are included in the summary.

combo

A character vector providing the plot types to combine (seemcmc_combo).

...

Further arguments to pass on.

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

Provide a graphical summary of a`dmbc_fit_list` class instance.

Description

Provide a graphical summary of admbc_fit_list class instance.

Usage

## S4 method for signature 'dmbc_fit_list,ANY'plot(  x,  what = "trace",  pars = character(),  regex_pars = "lambda",  include.burnin = FALSE,  combo = NULL,  ...)

Arguments

x

An object of classdmbc_fit_list.

what

pars

An optional character vector of parameter names. If neitherpars norregex_pars is specified, the default is to use all parameters.

regex_pars

An optionalregular expression to use forparameter selection. Can be specified instead ofpars or in addition topars.

include.burnin

A length-one logical vector. IfTRUE theburnin iterations (if available) are included in the summary.

combo

A character vector providing the plot types to combine (seemcmc_combo).

...

Further arguments to pass on.

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

Provide a graphical summary of a`dmbc_ic` class instance.

Description

Provide a graphical summary of admbc_ic class instance.

Usage

## S4 method for signature 'dmbc_ic,ANY'plot(x, size = NULL, ...)

Arguments

x

An object of classdmbc_ic.

size

A length-two numeric vector providing the optional sizes ofpoints and lines in the plot.

...

Further arguments to pass on (currently ignored).

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

Show an instance of the`dmbc_config` class.

Description

Show an instance of thedmbc_config class.

Usage

## S4 method for signature 'dmbc_config'show(object)

Arguments

object

An object of classdmbc_config.

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

Show an instance of the`dmbc_data` class.

Description

Show an instance of thedmbc_data class.

Usage

## S4 method for signature 'dmbc_data'show(object)

Arguments

object

An object of classdmbc_data.

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

Show an instance of the`dmbc_fit` class.

Description

Show an instance of thedmbc_fit class.

Usage

## S4 method for signature 'dmbc_fit'show(object)

Arguments

object

An object of classdmbc_fit.

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

Show an instance of the`dmbc_fit_list` class.

Description

Show an instance of thedmbc_fit_list class.

Usage

## S4 method for signature 'dmbc_fit_list'show(object)

Arguments

object

An object of classdmbc_fit_list.

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

Show an instance of the`dmbc_ic` class.

Description

Show an instance of thedmbc_ic class.

Usage

## S4 method for signature 'dmbc_ic'show(object)

Arguments

object

An object of classdmbc_ic.

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

Show an instance of the`dmbc_model` class.

Description

Show an instance of thedmbc_model class.

Usage

## S4 method for signature 'dmbc_model'show(object)

Arguments

object

An object of classdmbc_model.

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

Simulated binary dissimilarity matrices.

Description

A dataset containing a list of simulated binary dissimilarity matrices.

Usage

data(simdiss)

Format

Admbc_data object whosediss element is a listof 10 binary dissimilarity matrices. Each matrix is defined as adistobject measuring the agreement among 16 different units.

Examples

data(simdiss)library(bayesplot)cols <- color_scheme_set("brightblue")plot(simdiss, colors = unlist(cols)[c(1, 6)], font = 1, cex.font = 0.75)

Subsetting a`dmbc_fit` object.

Description

Subsetting admbc_fit object.

Usage

## S4 method for signature 'dmbc_fit'subset(x, pars = character(), regex_pars = character(), ...)

Arguments

x

An object of classdmbc_fit.

pars

An optional character vector of parameter names. If neitherpars norregex_pars is specified, the default is to use allparameters.

regex_pars

An optionalregular expression to usefor parameter selection. Can be specified instead ofpars or in additiontopars.

...

Further arguments to pass on (currently ignored).

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

Subsetting a`dmbc_fit_list` object.

Description

Subsetting admbc_fit_list object.

Usage

## S4 method for signature 'dmbc_fit_list'subset(x, pars = character(), regex_pars = character(), ...)

Arguments

x

An object of classdmbc_fit_list.

pars

An optional character vector of parameter names. If neitherpars norregex_pars is specified, the default is to use allparameters.

regex_pars

An optionalregular expression to usefor parameter selection. Can be specified instead ofpars or in additiontopars.

...

Further arguments to pass on (currently ignored).

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

Provide a summary of a`dmbc_config` class instance.

Description

Provide a summary of admbc_config class instance.

Usage

## S4 method for signature 'dmbc_config'summary(object)

Arguments

object

An object of classdmbc_config.

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

Provide a summary of a`dmbc_data` class instance.

Description

Provide a summary of admbc_data class instance.

Usage

## S4 method for signature 'dmbc_data'summary(object)

Arguments

object

An object of classdmbc_data.

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

Provide a summary of a`dmbc_fit` class instance.

Description

Provide a summary of admbc_fit class instance.

Usage

## S4 method for signature 'dmbc_fit'summary(object, include.burnin = FALSE, summary.Z = FALSE, ...)

Arguments

object

An object of classdmbc_fit.

include.burnin

A length-one logical vector. IfTRUE theburnin iterations (if available) are included in the summary.

summary.Z

A length-one logical vector. IfTRUE the summaryalso includes the latent configuration coordinates.

...

Further arguments to pass on (currently ignored).

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

Provide a summary of a`dmbc_fit_list` class instance.

Description

Provide a summary of admbc_fit_list class instance.

Usage

## S4 method for signature 'dmbc_fit_list'summary(object, include.burnin = FALSE, summary.Z = FALSE, ...)

Arguments

object

An object of classdmbc_fit_list.

include.burnin

A length-one logical vector. IfTRUE theburnin iterations (if available) are included in the summary.

summary.Z

A length-one logical vector. IfTRUE the summaryalso includes the latent configuration coordinates.

...

Further arguments to pass on (currently ignored).

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

Provide a summary of a`dmbc_ic` class instance.

Description

Provide a summary of admbc_ic class instance.

Usage

## S4 method for signature 'dmbc_ic'summary(object, p = NULL, G = NULL)

Arguments

object

An object of classdmbc_ic.

p

An optional length-one numeric vector providing the number oflatent space dimension to use in the summary.

G

An optional length-one numeric vector providing the number ofclusters to use in the summary.

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

Provide an update of a`dmbc_ic` class instance.

Description

Provide an update of admbc_ic class instance.

Usage

## S4 method for signature 'dmbc_ic'update(object, pmax = NULL, Gmax = NULL, ...)

Arguments

object

An object of classdmbc_ic.

pmax

A length-one numeric vector indicating the maximum number ofdimensions of the latent space to consider.

Gmax

A length-one numeric vector indicating the maximum number ofcluster to consider.

...

Further arguments to pass on (currently ignored).

Value

Admbc_ic object.

Author(s)

Sergio Venturinisergio.venturini@unicatt.it

References

Examples

## Not run: data(simdiss, package = "dmbc")pmax <- 2Gmax <- 2prm.prop <- list(z = 1.5, alpha = .75)burnin <- 2000nsim <- 1000seed <- 1809set.seed(seed)control <- list(burnin = burnin, nsim = nsim, z.prop = prm.prop[["z"]],  alpha.prop = prm.prop[["alpha"]], random.start = TRUE, verbose = TRUE,  thin = 10, store.burnin = TRUE)sim.ic <- dmbc_IC(data = simdiss, pmax = pmax, Gmax = Gmax, control = control,  est = "mean")pmax <- pmax + 1Gmax <- Gmax + 2new.ic <- update(sim.ic, pmax = pmax, Gmax = Gmax)new.ic# plot the resultslibrary(bayesplot)library(ggplot2)color_scheme_set("mix-yellow-blue")p <- plot(new.ic, size = c(4, 1.5))p + panel_bg(fill = "gray90", color = NA)## End(Not run)

Movatterモバイル変換

Model-Based Clustering of Several Dissimilarity Matrices.

Description

dmbc classes

Resources

References

See Also

Adjustment of the center and orientation of a latent configuration.

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

List of binary dissimilarity matrices among 18 animals.

Description

Usage

Format

References

Examples

Bayesian multidimensional scaling (BMDS) using Markov Chain Monte Carlo(MCMC).

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Posterior mode latent configuration in Bayesian multidimensional scaling (BMDS).

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Auxiliary function to recursively check NAs in a list.

Description

Usage

Arguments

Value

Author(s)

Examples

Extract the final cluster memberships from admbc_config class instance.

Description

Usage

Arguments

Author(s)

Sum of squared residuals (SSR) from the observed distances and the givenlatent configuration.

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Estimation of a DMBC model.

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Model selection of DMBC models.

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Auxiliary function for checking the grouping results of a fitted DMBC model.

Description

Usage

Arguments

Extract the final cluster memberships from a`dmbc_config` class instance.

Conversion of an`dmbc_fit_list` object to a`list`.

Conversion of an`dmbc_fit_list` object to an object of class`mcmc.list`.

Conversion of an`dmbc_fit` object to an object of class`mcmc`.