Type:	Package
Title:	Latent Class Analysis with Dirichlet Diffusion Tree Process Prior
Version:	0.2.1
Date:	2024-03-26
Maintainer:	Mengbing Li <mengbing@umich.edu>
Description:	Implements a Bayesian algorithm for overcoming weak separation in Bayesian latent class analysis. Reference: Li et al. (2023) <doi:10.48550/arXiv.2306.04700>.
Depends:	R(≥ 4.3)
Imports:	ape (≥ 5.6-2), data.table (≥ 1.14.4), extraDistr (≥ 1.9.1), ggplot2 (≥ 3.4.0), ggpubr (≥ 0.6.0), ggtext (≥ 0.1.2), ggtree (≥ 3.4.0), label.switching (≥ 1.8), matrixStats (≥ 0.62.0), methods (≥ 4.2.3), phylobase (≥ 0.8.10), poLCA (≥ 1.6.0.1), testthat (≥ 3.1.7), truncnorm (≥ 1.0-8), BayesLogit (≥ 2.1), Matrix (≥ 1.5-1), Rdpack (≥ 2.5), R.utils (≥ 2.12.2)
Suggests:	knitr, parallel, rmarkdown, xfun
License:	MIT + file LICENSE
Encoding:	UTF-8
LazyData:	true
VignetteBuilder:	knitr
RoxygenNote:	7.3.1
URL:	https://github.com/limengbinggz/ddtlcm
BugReports:	https://github.com/limengbinggz/ddtlcm/issues
Config/testthat/edition:	3
NeedsCompilation:	no
Packaged:	2024-04-04 00:58:26 UTC; mengbing
Author:	Mengbing Li [cre, aut], Briana Stephenson [ctb], Zhenke Wu [ctb]
Repository:	CRAN
Date/Publication:	2024-04-04 02:32:57 UTC

ddtlcm: Latent Class Analysis with Dirichlet Diffusion Tree Process Prior

Description

Implements a Bayesian algorithm for overcoming weak separation in Bayesian latent class analysis. Reference: Li et al. (2023) arXiv:2306.04700.

Author(s)

Maintainer: Mengbing Li mengbing@umich.edu (ORCID)

Other contributors:

• Briana Stephenson bstephenson@hsph.harvard.edu [contributor]

• Zhenke Wu zhenkewu@umich.edu (ORCID) [contributor]

See Also

Useful links:

• https://github.com/limengbinggz/ddtlcm

• Report bugs at https://github.com/limengbinggz/ddtlcm/issues

Harmonic series

Description

Harmonic series

Usage

H_n(k)

Arguments

Compute factor in the exponent of the divergence time distribution

Description

Compute factor in the exponent of the divergence time distribution

Usage

J_n(l, r)

Arguments

Compute WAIC

Description

Compute the Widely Applicable Information Criterion (WAIC), also known as the Widely Available Information Criterion or the Watanable-Akaike, of Watanabe (2010).

Usage

WAIC(llk_matrix)

Arguments

Value

a named list

Compute divergence function

Description

Compute value, cumulative hazard, and inverse for divergence function a(t) = c / (1-t)

Usage

a_t_one(c, t)

a_t_one_cum(c, t)

A_t_inv_one(c, y)

Arguments

Value

The value and cumulative hazard return a positive number. The inverse function returns a number in the interval (0, 1).

Functions

• a_t_one(): value of the divergence function

• a_t_one_cum(): cumulative hazard function

• A_t_inv_one(): inverse function

See Also

Other divergence functions: a_t_two()

Examples

a_t_one(1, 0.5)
a_t_one_cum(1, 0.5)
A_t_inv_one(1, 2)

Compute divergence function

Description

Compute value, cumulative hazard, and inverse for divergence function a(t) = c / (1-t)^2

Usage

a_t_two(c, t)

a_t_two_cum(c, t)

A_t_inv_two(c, y)

Arguments

Value

The value and cumulative hazard return a positive number. The inverse function returns a number in the interval (0, 1).

Functions

• a_t_two(): value of the divergence function

• a_t_two_cum(): cumulative hazard function

• A_t_inv_two(): inverse function

See Also

Other divergence functions: a_t_one()

Examples

a_t_two(1, 0.5)
a_t_two_cum(1, 0.5)
A_t_inv_two(1, 2)

Add a leaf branch to an existing tree tree_old

Description

Add a leaf branch to an existing tree tree_old

Usage

add_leaf_branch(tree_old, div_t, new_leaf_label, where, position)

Arguments

Value

a "phylo" tree with K+1 leaves

Add a leaf branch to an existing tree tree_old to make a multichotomus branch

Description

Add a leaf branch to an existing tree tree_old to make a multichotomus branch

Usage

add_multichotomous_tip(tree_old, div_t, new_leaf_label, where)

Arguments

Value

a "phylo" tree with K+1 leaves that could possibly be multichotomus

Functions to simulate trees and node parameters from a DDT process. Add a branch to an existing tree according to the branching process of DDT

Description

Functions to simulate trees and node parameters from a DDT process. Add a branch to an existing tree according to the branching process of DDT

Usage

add_one_sample(tree_old, c, c_order, theta, alpha)

Arguments

Value

a "phylo" object. A tree with K+1 leaves. if t2 > t1, then select which path to take, with probability proportional to the number of data points that already traversed the path

Add a singular root node to an existing nonsingular tree

Description

Add a singular root node to an existing nonsingular tree

Usage

add_root(tree_old, root_edge_length, root_label, leaf_label)

Arguments

Value

a singular "phylo" tree

Attach a subtree to a given DDT at a randomly selected location

Description

Attach a subtree to a given DDT at a randomly selected location

Usage

attach_subtree(
  subtree,
  tree_kept,
  detach_div_time,
  pa_detach_node_label,
  c,
  c_order = 1,
  theta = 0,
  alpha = 0
)

Arguments

See Also

Other sample trees: random_detach_subtree(), reattach_point()

Compute information criteria for the DDT-LCM model

Description

Compute information criteria for the DDT-LCM model, including the Widely Applicable Information Criterion (WAIC), and Deviance Information Criterion (DIC). WAIC and DIC are computed using two different methods described in Gelman, Hwang, and Vehtari (2013), one based on (1) posterior means and the other based on (2) posterior variances.

Usage

compute_IC(result, burnin = 5000, ncores = 1L)

Arguments

Value

a named list of the following elements

WAIC_result

a list of WAIC-related results computed using the two methods

DIC1

DIC computed using method 1.

DIC2

DIC computed using method 2.

Examples

data(result_diet_1000iters)
IC_result <- compute_IC(result = result_diet_1000iters, burnin = 800, ncores = 1L)

Create a tree-structured covariance matrix from a given tree

Description

Retrieve the covariance matrix of leaf nodes of a DDT tree

Usage

create_leaf_cor_matrix(tree_phylo4d)

Arguments

Value

a K by K covariance matrix

Examples

# load the MAP tree structure obtained from the real HCHS/SOL data
data(data_synthetic)
# extract elements into the global environment
list2env(setNames(data_synthetic, names(data_synthetic)), envir = globalenv())
create_leaf_cor_matrix(tree_with_parameter)

Synthetic data example

Description

This list contains one synthetic data with K = 3 latent classes. The elements are as follows:

Usage

data(data_synthetic)

Format

A list with 8 elements

Details

• tree_phylo. A "phylo" tree with K = 3 leaves.

• class_probability. A K-vector with entries between 0 and 1.

• item_membership_list. A list of G = 7 elements, where the g-th element contains the indices of items belonging to major food group g.

• item_name_list. A list of G = 7 elements, where the g-th element contains the item labels of items in major food group g, and the name of the g-th element is the major food group label.

• Sigma_by_group. A G-vector greater than 0. The group-specific diffusion variances.

• response_matrix. A binary matrix with N = 100 rows and J = 80 columns. Each row contains a multivariate binary response vector of a synthetic individual.

• response_prob. A K by J probability matrix. The k-th row contains the item response probabilities of class k.

• tree_with_parameter. A phylobase::phylo4d object. Basically the tree_phylo embedded with additional logit(response_prob) at the leaf nodes.

MH-within-Gibbs sampler to sample from the full posterior distribution of DDT-LCM

Description

Use DDT-LCM to estimate latent class and tree on class profiles for multivariate binary outcomes.

Usage

ddtlcm_fit(
  K,
  data,
  item_membership_list,
  total_iters = 5000,
  initials = list(),
  priors = list(),
  controls = list(),
  initialize_args = list(method_lcm = "random", method_dist = "euclidean", method_hclust
    = "ward.D", method_add_root = "min_cor", alpha = 0, theta = 0)
)

Arguments

Value

an object of class "ddt_lcm"; a list containing the following elements:

tree_samples

a list of information of the tree collected from the sampling algorithm, including: accept: a binary vector where 1 indicates acceptance of the proposal tree and 0 indicates rejection. tree_list: a list of posterior samples of the tree. dist_mat_list: a list of tree-structured covariance matrices representing the marginal covariances among the leaf parameters, integrating out the internal node parameters and all intermediate stochastic paths in the DDT branching process.

response_probs_samples

a total_iters x K x J array of posterior samples of item response probabilities

class_probs_samples

a K x total_iters matrix of posterior samples of class probabilities

Z_samples

a N x total_iters integer matrix of posterior samples of individual class assignments

Sigma_by_group_samples

a G x total_iters matrix of posterior samples of diffusion variances

c_samples

a total_iters vector of posterior samples of divergence function hyperparameter

loglikelihood

a total_iters vector of log-likelihoods of the full model

loglikelihood_lcm

a total_iters vector of log-likelihoods of the LCM model only

setting

a list of model setup information, including: K, item_membership_list, and G

controls

a list of model controls, including: fix_tree: FALSE to perform MH sampling of the tree, TRUE to fix the tree at the initial input. c_order: a numeric value of 1 or 2 (see Arguments))

data

the input data matrix

Examples

# load the MAP tree structure obtained from the real HCHS/SOL data
data(data_synthetic)
# extract elements into the global environment
list2env(setNames(data_synthetic, names(data_synthetic)), envir = globalenv()) 
# run DDT-LCM
result <- ddtlcm_fit(K = 3, data = response_matrix, item_membership_list, total_iters = 50)

Sample divergence time on an edge uv previously traversed by m(v) data points

Description

Sample divergence time on an edge uv previously traversed by m(v) data points

Usage

div_time(t_u, m_v, c, c_order = 1, alpha = 0, theta = 0)

Arguments

Value

a number in the interval (0, 1)

Efficiently sample multivariate normal using precision matrix from x ~ N(Q^{-1}a, Q^{-1}), where Q^{-1} is the precision matrix

Description

Efficiently sample multivariate normal using precision matrix from x ~ N(Q^{-1}a, Q^{-1}), where Q^{-1} is the precision matrix

Usage

draw_mnorm(precision_mat, precision_a_vec)

Arguments

Compute normalized probabilities: exp(x_i) / sum_j exp(x_j)

Description

Compute normalized probabilities: exp(x_i) / sum_j exp(x_j)

Usage

exp_normalize(x)

Arguments

Value

a number or real-valued vector

The expit function

Description

The expit function: f(x) = exp(x) / (1+exp(x)), computed in a way to avoid numerical underflow.

Usage

expit(x)

Arguments

Value

a number or real-valued vector

Examples

expit(0.2)
expit(c(-1, -0.3, 0.6))

Initialize the MH-within-Gibbs algorithm for DDT-LCM

Description

Initialize the MH-within-Gibbs algorithm for DDT-LCM

Usage

initialize(
  K,
  data,
  item_membership_list,
  c = 1,
  c_order = 1,
  method_lcm = "random",
  method_dist = "euclidean",
  method_hclust = "ward.D",
  method_add_root = "min_cor",
  fixed_initials = list(),
  fixed_priors = list(),
  alpha = 0,
  theta = 0,
  ...
)

Arguments

Value

phylo4d object of tree topology

See Also

ddtlcm_fit()

Other initialization functions: initialize_hclust(), initialize_poLCA()

Examples

# load the MAP tree structure obtained from the real HCHS/SOL data
data(data_synthetic)
# extract elements into the global environment
list2env(setNames(data_synthetic, names(data_synthetic)), envir = globalenv())
K <- 3
G <- length(item_membership_list)
fixed_initials <- list("c" = 5)
fixed_priors <- list("rate_sigma" = rep(3, G), "shape_c" = 2, "rate_c" = 2)
initials <- initialize(K, data = response_matrix, item_membership_list,
  c=1, c_order=1, fixed_initials = fixed_initials, fixed_priors = fixed_priors)

Estimate an initial binary tree on latent classes using hclust()

Description

Estimate an initial binary tree on latent classes using hclust()

Usage

initialize_hclust(
  leaf_data,
  c,
  c_order = 1,
  method_dist = "euclidean",
  method_hclust = "ward.D",
  method_add_root = "min_cor",
  alpha = 0,
  theta = 0,
  ...
)

Arguments

Value

phylo4d object of tree topology

See Also

Other initialization functions: initialize(), initialize_poLCA()

Estimate an initial response profile from latent class model using poLCA()

Description

Estimate an initial response profile from latent class model using poLCA()

Usage

initialize_poLCA(K, data, ...)

Arguments

Value

a K by J probability matrix, the k,j-th entry being the response probability to item j of an individual in class k

See Also

Other initialization functions: initialize(), initialize_hclust()

Provide a random initial response profile based on latent class mode

Description

Provide a random initial response profile based on latent class mode

Usage

initialize_randomLCM(K, data)

Arguments

Value

a K by J probability matrix, the k,j-th entry being the response probability to item j of an individual in class k

Numerically accurately compute f(x) = log(x / (1/x)).

Description

Numerically accurately compute f(x) = log(x / (1/x)).

Usage

log_expit(x)

Arguments

Value

a number or real-valued vector

The logistic function

Description

The logit function: f(x) = log(x / (1/x)). Large absolute values of x will be truncated to +/- 5 after logit transformation according to its sign.

Usage

logit(x)

Arguments

Value

a number or real-valued vector

Examples

logit(0.2)
logit(c(0.2, 0.6, 0.95))

Calculate loglikelihood of a DDT, including the tree structure and node parameters

Description

Calculate loglikelihood of a DDT, including the tree structure and node parameters

Usage

logllk_ddt(
  c,
  c_order,
  Sigma_by_group,
  tree_phylo4d,
  item_membership_list,
  tree_structure_old = NULL,
  dist_mat_old = NULL
)

Arguments

Value

a numeric of loglikelihood

See Also

Other likelihood functions: logllk_ddt_lcm(), logllk_div_time_one(), logllk_div_time_two(), logllk_lcm(), logllk_location(), logllk_tree_topology()

Calculate loglikelihood of the DDT-LCM

Description

Calculate loglikelihood of the DDT-LCM

Usage

logllk_ddt_lcm(
  c,
  Sigma_by_group,
  tree_phylo4d,
  item_membership_list,
  tree_structure_old = NULL,
  dist_mat_old = NULL,
  response_matrix,
  leaf_data,
  prior_class_probability,
  prior_dirichlet,
  ClassItem,
  Class_count
)

Arguments

Value

a numeric of loglikelihood

See Also

Other likelihood functions: logllk_ddt(), logllk_div_time_one(), logllk_div_time_two(), logllk_lcm(), logllk_location(), logllk_tree_topology()

Compute loglikelihood of divergence times for a(t) = c/(1-t)

Description

Compute loglikelihood of divergence times for a(t) = c/(1-t)

Usage

logllk_div_time_one(c, l, r, t)

Arguments

See Also

Other likelihood functions: logllk_ddt(), logllk_ddt_lcm(), logllk_div_time_two(), logllk_lcm(), logllk_location(), logllk_tree_topology()

Compute loglikelihood of divergence times for a(t) = c/(1-t)^2

Description

Compute loglikelihood of divergence times for a(t) = c/(1-t)^2

Usage

logllk_div_time_two(c, l, r, t)

Arguments

See Also

Other likelihood functions: logllk_ddt(), logllk_ddt_lcm(), logllk_div_time_one(), logllk_lcm(), logllk_location(), logllk_tree_topology()

Calculate loglikelihood of the latent class model, conditional on tree structure

Description

Calculate loglikelihood of the latent class model, conditional on tree structure

Usage

logllk_lcm(
  response_matrix,
  leaf_data,
  prior_class_probability,
  prior_dirichlet,
  ClassItem,
  Class_count
)

Arguments

Value

a numeric of loglikelihood

See Also

Other likelihood functions: logllk_ddt(), logllk_ddt_lcm(), logllk_div_time_one(), logllk_div_time_two(), logllk_location(), logllk_tree_topology()

Compute log likelihood of parameters

Description

Compute the marginal log likelihood of the parameters on the leaves of a tree

Usage

logllk_location(
  tree_phylo4d,
  Sigma_by_group,
  item_membership_list,
  dist_mat = NULL,
  tol = 1e-07
)

Arguments

Value

A list of two elements: a numeric loglikelihood, a covariance matrix of the input tree

See Also

Other likelihood functions: logllk_ddt(), logllk_ddt_lcm(), logllk_div_time_one(), logllk_div_time_two(), logllk_lcm(), logllk_tree_topology()

Compute loglikelihood of the tree topology

Description

Compute loglikelihood of the tree topology

Usage

logllk_tree_topology(l, r)

Arguments

See Also

Other likelihood functions: logllk_ddt(), logllk_ddt_lcm(), logllk_div_time_one(), logllk_div_time_two(), logllk_lcm(), logllk_location()

Parameters for the HCHS dietary recall data example

Description

A list of five variables containing the food items and parameter estimates obtained from MCMC chains. The real multivariate binary dataset is not included for privacy. The variables are as follows:

Usage

data(parameter_diet)

Format

An object of class list of length 5.

Details

• item_membership_list. A list of G = 7 elements, where the g-th element contains the indices of items belonging to major food group g.

• item_name_list. A list of G = 7 elements, where the g-th element contains the item labels of items in major food group g, and the name of the g-th element is the major food group label.

• tree_phylo. The maximum a posterior tree estimate with K = 6 leaves obtained from the real HCHS data. Class "phylo".

• class_probability. A K-vector with entries between 0 and 1. The posterior mean estimate for class probabilities obtained from the real HCHS data.

• Sigma_by_group. A G-vector greater than 0. The posterior mean estimate for group-specific diffusion variances obtained from the real HCHS data.

References

https://arxiv.org/abs/2306.04700

Create trace plots of DDT-LCM parameters

Description

Create trace plots of DDT-LCM parameters

Usage

## S3 method for class 'ddt_lcm'
plot(
  x,
  parameter_names = c("responseprob_1,1,1", "classprob_1", "c", "diffusionvar_1"),
  burnin = 50,
  ...
)

Arguments

Value

NULLs

Examples

data(result_diet_1000iters)
# Plot "c" for the divergence function parameter; "diffusionvar_1" for diffusion variance of group 1
plot(x = result_diet_1000iters, parameter_names = c("c", "diffusionvar_1"), burnin = 500)
# Plot "responseprob_1,1,1" for the class 1 response probability of item 3 in major group 2
plot(x = result_diet_1000iters, parameter_names = "responseprob_1,1,1", burnin = 500)
# Plot "classprob_1" for the probability of being assigned to class 1
plot(x = result_diet_1000iters, parameter_names = "classprob_1", burnin = 500)
# plot all class probabilities
plot(x = result_diet_1000iters, parameter_names = "classprob", burnin = 500)
# plot all diffusion variances
plot(x = result_diet_1000iters, "diffusionvar", burnin = 500)

Plot the MAP tree and class profiles of summarized DDT-LCM results

Description

Plot the MAP tree and class profiles of summarized DDT-LCM results

Usage

## S3 method for class 'summary.ddt_lcm'
plot(
  x,
  log = TRUE,
  plot_option = c("all", "profile", "tree"),
  item_name_list = NULL,
  color_palette = c("#E69F00", "#56B4E9", "#009E73", "#000000", "#0072B2", "#D55E00",
    "#CC79A7", "#F0E442", "#999999"),
  ...
)

Arguments

Value

a ggplot2 object. If plot_option is "all", then a plot with maximum a posterior tree structure on the left and a bar plot of item response probabilities (with 95% credible intervals and class probabilities) on the right. If plot_option is "profile", then only a bar plot of item response probabilities. If plot_option is "tree", then only a plot of the tree structure.

Examples

data(result_diet_1000iters)
burnin <- 500
summarized_result <- summary(result_diet_1000iters, burnin, relabel = TRUE, be_quiet = TRUE)
plot(x = summarized_result, item_name_list = NULL, plot_option = "all")

Plot the MAP tree and class profiles (bar plot) of summarized DDT-LCM results

Description

Plot the MAP tree and class profiles (bar plot) of summarized DDT-LCM results

Usage

plot_tree_with_barplot(
  tree_with_parameter,
  response_prob,
  item_membership_list,
  item_name_list = NULL,
  class_probability = NULL,
  class_probability_lower = NULL,
  class_probability_higher = NULL,
  color_palette = c("#E69F00", "#56B4E9", "#009E73", "#000000", "#0072B2", "#D55E00",
    "#CC79A7", "#F0E442", "#999999"),
  return_separate_plots = FALSE
)

Arguments

Value

a ggplot2 object. A bar plot of item response probabilities.

Examples

# load the MAP tree structure obtained from the real HCHS/SOL data
data(data_synthetic)
# extract elements into the global environment
list2env(setNames(data_synthetic, names(data_synthetic)), envir = globalenv())
plot_tree_with_barplot(tree_with_parameter, response_prob, item_membership_list)

Plot the MAP tree and class profiles (heatmap) of summarized DDT-LCM results

Description

Plot the MAP tree and class profiles (heatmap) of summarized DDT-LCM results

Usage

plot_tree_with_heatmap(
  tree_with_parameter,
  response_prob,
  item_membership_list
)

Arguments

Value

a ggplot2 object. A plot with the tree structure on the left and a heatmap of item response probabilities on the right, with indication of item group memberships beneath the heatmap.

Examples

# load the MAP tree structure obtained from the real HCHS/SOL data
data(data_synthetic)
# extract elements into the global environment
list2env(setNames(data_synthetic, names(data_synthetic)), envir = globalenv())
plot_tree_with_heatmap(tree_with_parameter, response_prob, item_membership_list)

Prediction of class memberships from posterior predictive distributions

Description

Predict individual class memberships based on posterior predictive distributions. For each posterior sample, let the class memberships be modal assignments. Then aggregate over all posterior samples to obtain the most likely assigned classes.

Usage

## S3 method for class 'ddt_lcm'
predict(object, data, burnin = 3000, ...)

Arguments

Value

a list of the following named elements:

class_assignments

an integer vector of individual predicted class memberships taking values in 1, ..., K

predictive_probs

a N x K matrix of probabilities, where the (i,k)-th element is the probability that the i-th individual is predicted to belong to class k.

Examples

data(result_diet_1000iters)
burnin <- 500
predicted <- predict(result_diet_1000iters, result_diet_1000iters$data, burnin)

Prediction of class memberships from posterior summaries

Description

Predict individual class memberships based on posterior summary (point estimates of model parameters). The predicted class memberships are modal assignments.

Usage

## S3 method for class 'summary.ddt_lcm'
predict(object, data, ...)

Arguments

Value

a list of the following named elements:

class_assignments

an integer vector of individual predicted class memberships taking values in 1, ..., K

predictive_probs

a N x K matrix of probabilities, where the (i,k)-th element is the probability that the i-th individual is predicted to belong to class k.

Examples

data(result_diet_1000iters)
burnin <- 500
summarized_result <- summary(result_diet_1000iters, burnin, relabel = TRUE, be_quiet = TRUE)
predicted <- predict(summarized_result, result_diet_1000iters$data)

Print out setup of a ddt_lcm model

Description

Print out setup of a ddt_lcm model

Usage

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

Arguments

See Also

Other ddt_lcm results: print.summary.ddt_lcm(), summary.ddt_lcm()

Examples

data(result_diet_1000iters)
print(result_diet_1000iters)

Print out summary of a ddt_lcm model

Description

Print out summary of a ddt_lcm model

Usage

## S3 method for class 'summary.ddt_lcm'
print(x, digits = 3L, ...)

Arguments

See Also

Other ddt_lcm results: print.ddt_lcm(), summary.ddt_lcm()

Examples

data(result_diet_1000iters)
burnin <- 500
summarized_result <- summary(result_diet_1000iters, burnin, relabel = TRUE, be_quiet = TRUE)
print(summarized_result)

Calculate proposal likelihood

Description

Given an old tree, propose a new tree and calculate the original and proposal tree likelihood in the DDT process

Usage

proposal_log_prob(
  old_tree_phylo4,
  tree_kept,
  old_detach_pa_div_time,
  old_pa_detach_node_label,
  old_detach_node_label,
  new_div_time,
  new_attach_root,
  new_attach_to,
  c,
  c_order = 1
)

Arguments

Value

a list containing the following elements:

q_new

a "phylo" tree detached from the input tree

q_old

the remaining "phylo" tree after detachment

Suppress print from cat()

Description

Suppress print from cat()

Usage

quiet(x, be_quiet = TRUE)

Arguments

Metropolis-Hasting algorithm for sampling tree topology and branch lengths from the DDT branching process.

Description

Randomly detach a subtree from a given tree

Usage

random_detach_subtree(tree_phylo4)

Arguments

Value

a list containing the following elements:

tree_detached

a "phylo" tree detached from the input tree

tree_kept

the remaining "phylo" tree after detachment

pa_detach_node_label

a character label of the parent of the node from which the detachment happens

pa_div_time

a number in (0, 1) indicating the divergence time of the parent of the detached node

detach_div_time

a number in (0, 1) indicating the divergence time of the detached node

detach_node_label

a character label of the parent of the detached node

See Also

Other sample trees: attach_subtree(), reattach_point()

Examples

library(phylobase)
# load the MAP tree structure obtained from the real HCHS/SOL data
data(data_synthetic)
# extract elements into the global environment
list2env(setNames(data_synthetic, names(data_synthetic)), envir = globalenv()) 
detachment <- random_detach_subtree(extractTree(tree_with_parameter)) 

Attach a subtree to a given DDT at a randomly selected location

Description

Attach a subtree to a given DDT at a randomly selected location

Usage

reattach_point(tree_kept, c, c_order = 1, theta = 0, alpha = 0)

Arguments

Value

a list of the following objects:

div_time

a numeric value of newly sampled divergence time. Between 0 and 1.

root_node

a character. Label of the root node of tree_kept.

root_child

a character. Label of the child node of the root of tree_kept.

div_dist_to_root_child

a N-vector with integer entries from 1, ..., K. The initial values for individual class assignments.

See Also

Other sample trees: attach_subtree(), random_detach_subtree()

Result of fitting DDT-LCM to a semi-synthetic data example

Description

This is a "ddtlcm" object obtained from running ddtlcm_fit to a semi-synthetic dataset with 1000 posterior samples (for the sake of time). See ddtlcm_fit for description of the object.

Usage

data(result_diet_1000iters)

Format

A list with 8 elements

Sample divergence function parameter c for a(t) = c / (1-t) through Gibbs sampler

Description

Sample divergence function parameter c for a(t) = c / (1-t) through Gibbs sampler

Usage

sample_c_one(shape0, rate0, tree_structure)

Arguments

Value

a numeric value of the newly sampled c

Sample divergence function parameter c for a(t) = c / (1-t)^2 through Gibbs sampler

Description

Sample divergence function parameter c for a(t) = c / (1-t)^2 through Gibbs sampler

Usage

sample_c_two(shape0, rate0, tree_structure)

Arguments

Value

a numeric value of the newly sampled c

Sample individual class assignments Z_i, i = 1, ..., N

Description

Sample individual class assignments Z_i, i = 1, ..., N

Usage

sample_class_assignment(
  data,
  leaf_data,
  a_pg,
  auxiliary_mat,
  class_probability
)

Arguments

Value

a vector of length N, where the i-th element is the class assignment of individual i

Sample the leaf locations and Polya-Gamma auxilliary variables

Description

Sample the leaf locations and Polya-Gamma auxilliary variables

Usage

sample_leaf_locations_pg(
  item_membership_list,
  dist_mat_old,
  Sigma_by_group,
  pg_mat,
  a_pg,
  auxiliary_mat,
  auxiliary_mat_range,
  class_assignments
)

Arguments

Value

a named list of three matrices: the newly sampled leaf parameters, the Polya-gamma random variables, and the auxiliary truncated normal variables

Sample item group-specific variances through Gibbs sampler

Description

Sample item group-specific variances through Gibbs sampler

Usage

sample_sigmasq(shape0, rate0, dist_mat, item_membership_list, locations)

Arguments

Value

a numeric vector of G elements, each being the newly sampled variance of the latent location of this group

Sample a new tree topology using Metropolis-Hastings through randomly detaching and re-attaching subtrees

Description

Sample a new tree topology using Metropolis-Hastings through randomly detaching and re-attaching subtrees

Usage

sample_tree_topology(
  tree_phylo4d_old,
  Sigma_by_group,
  item_membership_list,
  c,
  c_order = 1,
  tree_structure_old = NULL,
  dist_mat_old = NULL
)

Arguments

Value

a numeric vector of G elements, each being the newly sampled variance of the latent location of this group

Simulate a tree from a DDT process. Only the tree topology and branch lengths are simulated, without node parameters.

Description

Simulate a tree from a DDT process. Only the tree topology and branch lengths are simulated, without node parameters.

Usage

simulate_DDT_tree(K, c, c_order = 1, alpha = 0, theta = 0)

Arguments

Value

A class "phylo" tree with K leaves. The leaf nodes are labeled "v1", ..., "vK", root node "u1", and internal nodes "u2", ..., "uK". Note that this tree does not contain any node parameters.

References

Knowles, D. A., & Ghahramani, Z. (2014). Pitman yor diffusion trees for bayesian hierarchical clustering. IEEE transactions on pattern analysis and machine intelligence, 37(2), 271-289.

See Also

Other simulate DDT-LCM data: simulate_lcm_given_tree(), simulate_lcm_response(), simulate_parameter_on_tree()

Examples

K <- 6
c <- 5
c_order <- 1
tree1 <- simulate_DDT_tree(K, c, c_order)
tree2 <- simulate_DDT_tree(K, c, c_order, alpha = 0.4, theta = 0.1)
tree3 <- simulate_DDT_tree(K, c, c_order, alpha = 0.8, theta = 0.1)

Simulate multivariate binary responses from a latent class model given a tree

Description

Generate multivariate binary responses from the following process: For individual i = 1, ..., N, Z_i ~ Categorical_K(prior_class_probability) For item j = 1, ..., J, Y_{ij} | Z_i = k ~ Binomial(class_item_probability_{kj})

Usage

simulate_lcm_given_tree(
  tree_phylo,
  N,
  class_probability = 1,
  item_membership_list,
  Sigma_by_group = NULL,
  root_node_location = 0,
  seed_parameter = 1,
  seed_response = 1
)

Arguments

Value

a named list of the following elements:

tree_with_parameter

a "phylo4d" tree with K leaves.

response_prob

a K by J matrix, where the k,j-th element is the response probability of item j for individuals in class k

response_matrix

a K by J matrix with entries between 0 and 1 for the item response probabilities.

class_probability

a K-vector with entries between 0 and 1 for the class probabilities. Entries should be nonzero and sum up to 1, or otherwise will be normalized

class_assignments

a N-vector with integer entries from 1, ..., K. The initial values for individual class assignments.

Sigma_by_group

a G-vector greater than 0. The initial values for the group-specific diffusion variances.

c

a value greater than 0. The initial values for the group-specific diffusion variances.

item_membership_list

same as input

See Also

Other simulate DDT-LCM data: simulate_DDT_tree(), simulate_lcm_response(), simulate_parameter_on_tree()

Examples

# load the MAP tree structure obtained from the real HCHS/SOL data
data(parameter_diet)
# unlist the elements into variables in the global environment
list2env(setNames(parameter_diet, names(parameter_diet)), envir = globalenv()) 
# number of individuals
N <- 496
# set random seed to generate node parameters given the tree
seed_parameter = 1
# set random seed to generate multivariate binary observations from LCM
seed_response = 1
# simulate data given the parameters
sim_data <- simulate_lcm_given_tree(tree_phylo, N, 
                                    class_probability, item_membership_list, Sigma_by_group, 
                                    root_node_location = 0, seed_parameter = 1, seed_response = 1)

Simulate multivariate binary responses from a latent class model

Description

Generate multivariate binary responses from the following process: For individual i = 1, ..., N, draw Z_i from Categorical distribution with prior class probability (length K). For item j = 1, ..., J, given Z_i = k, draw Y_{ij} from Binomial with class-item probability

Usage

simulate_lcm_response(N, response_prob, class_probability)

Arguments

Value

a named list of the following elements:

response_matrix

a K by J matrix with entries between 0 and 1 for the item response probabilities.

class_probability

a K-vector with entries between 0 and 1 for the class probabilities. Entries should be nonzero and sum up to 1, or otherwise will be normalized

See Also

Other simulate DDT-LCM data: simulate_DDT_tree(), simulate_lcm_given_tree(), simulate_parameter_on_tree()

Examples

# number of latent classes
K <- 6
# number of items
J <- 78
response_prob <- matrix(runif(K*J), nrow = K)
class_probability <- rep(1/K, K)
# number of individuals
N <- 100
response_matrix <- simulate_lcm_response(N, response_prob, class_probability)

Simulate node parameters along a given tree.

Description

Simulate node parameters along a given tree.

Usage

simulate_parameter_on_tree(
  tree_phylo,
  Sigma_by_group,
  item_membership_list,
  root_node_location = 0
)

Arguments

Value

A class "phylo4d" tree with K leaves with node parameters. The leaf nodes are labeled "v1", ..., "vK", root node "u1", and internal nodes "u2", ..., "uK".

See Also

Other simulate DDT-LCM data: simulate_DDT_tree(), simulate_lcm_given_tree(), simulate_lcm_response()

Examples

library(ape)
tr_txt <- "(((v1:0.25, v2:0.25):0.65, v3:0.9):0.1);"
tree <- read.tree(text = tr_txt)
tree$node.label <- paste0("u", 1:Nnode(tree))
plot(tree, show.node.label = TRUE)
# create a list of item membership indices of 7 major groups
item_membership_list <- list()
num_items_per_group <- c(rep(10, 5), 15, 15)
G <- length(num_items_per_group)
j <- 0
for (g in 1:G) {
  item_membership_list[[g]] <- (j+1):(j+num_items_per_group[g])
  j <- j+num_items_per_group[g]
}
# variance of logit response probabilities of items in each group
Sigma_by_group <- c(rep(0.6**2, 5), rep(2**2, 2)) #rep(1**2, G)
set.seed(50)
tree_with_parameter <- simulate_parameter_on_tree(tree, Sigma_by_group, item_membership_list)

Summarize the output of a ddt_lcm model

Description

Summarize the output of a ddt_lcm model

Usage

## S3 method for class 'ddt_lcm'
summary(object, burnin = 3000, relabel = TRUE, be_quiet = FALSE, ...)

Arguments

Value

an object of class "summary.ddt_lcm"; a list containing the following elements:

tree_map

the MAP tree of "phylo4d" class

tree_Sigma

the tree-structured covariance matrix associated with tree_map

response_probs_summary, class_probs_summary, Sigma_summary, c_summary

each is a matrix with 7 columns of summary statistics of posterior chains, including means, standard deviation, and five quantiles. In particular, for the summary of item response probabilities, each row name theta_k,g,j represents the response probability of a person in class k to consume item j in group g

max_llk_full

a numeric value of the maximum log-likelihood of the full model (tree and LCM)

max_llk_lcm

a numeric value of the maximum log-likelihood of the LCM only

Z_samples

a N x total_iters integer matrix of posterior samples of individual class assignments

Sigma_by_group_samples

a G x total_iters matrix of posterior samples of diffusion variances

c_samples

a total_iters vector of posterior samples of divergence function hyperparameter

loglikelihood

a total_iters vector of log-likelihoods of the full model

loglikelihood_lcm

a total_iters vector of log-likelihoods of the LCM model only

setting

a list of model setup information. See ddtlcm_fit

controls

a list of model controls. See ddtlcm_fit

data

the input data matrix

See Also

Other ddt_lcm results: print.ddt_lcm(), print.summary.ddt_lcm()

Examples

# load the result of fitting semi-synthetic data with 1000 (for the sake of time) posterior samples
data(result_diet_1000iters)
summarized_result <- summary(result_diet_1000iters, burnin = 500, relabel = TRUE, be_quiet = TRUE)