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  "Title": "Latent Class Analysis with Dirichlet Diffusion Tree Process\nPrior",
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    "compute_IC",
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    "initialize",
    "logit",
    "plot_tree_with_barplot",
    "plot_tree_with_heatmap",
    "random_detach_subtree",
    "simulate_DDT_tree",
    "simulate_lcm_given_tree",
    "simulate_lcm_response",
    "simulate_parameter_on_tree"
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      "title": "Synthetic data example",
      "object": "data_synthetic",
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        "list"
      ],
      "fields": [],
      "table": false,
      "tojson": false
    },
    {
      "name": "parameter_diet",
      "title": "Parameters for the HCHS dietary recall data example",
      "object": "parameter_diet",
      "class": [
        "list"
      ],
      "fields": [],
      "table": false,
      "tojson": false
    },
    {
      "name": "result_diet_1000iters",
      "title": "Result of fitting DDT-LCM to a semi-synthetic data example",
      "object": "result_diet_1000iters",
      "class": [
        "ddt_lcm"
      ],
      "fields": [],
      "table": false,
      "tojson": false
    }
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    {
      "page": "a_t_one",
      "title": "Compute divergence function",
      "concept": [
        "divergence functions"
      ],
      "topics": [
        "A_t_inv_one",
        "a_t_one",
        "a_t_one_cum"
      ]
    },
    {
      "page": "a_t_two",
      "title": "Compute divergence function",
      "concept": [
        "divergence functions"
      ],
      "topics": [
        "A_t_inv_two",
        "a_t_two",
        "a_t_two_cum"
      ]
    },
    {
      "page": "add_leaf_branch",
      "title": "Add a leaf branch to an existing tree tree_old",
      "topics": [
        "add_leaf_branch"
      ]
    },
    {
      "page": "add_multichotomous_tip",
      "title": "Add a leaf branch to an existing tree tree_old to make a multichotomus branch",
      "topics": [
        "add_multichotomous_tip"
      ]
    },
    {
      "page": "add_one_sample",
      "title": "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",
      "topics": [
        "add_one_sample"
      ]
    },
    {
      "page": "add_root",
      "title": "Add a singular root node to an existing nonsingular tree",
      "topics": [
        "add_root"
      ]
    },
    {
      "page": "attach_subtree",
      "title": "Attach a subtree to a given DDT at a randomly selected location",
      "concept": [
        "sample trees"
      ],
      "topics": [
        "attach_subtree"
      ]
    },
    {
      "page": "compute_IC",
      "title": "Compute information criteria for the DDT-LCM model",
      "topics": [
        "compute_IC"
      ]
    },
    {
      "page": "create_leaf_cor_matrix",
      "title": "Create a tree-structured covariance matrix from a given tree",
      "topics": [
        "create_leaf_cor_matrix"
      ]
    },
    {
      "page": "data_synthetic",
      "title": "Synthetic data example",
      "topics": [
        "data_synthetic"
      ]
    },
    {
      "page": "ddtlcm_fit",
      "title": "MH-within-Gibbs sampler to sample from the full posterior distribution of DDT-LCM",
      "topics": [
        "ddtlcm_fit"
      ]
    },
    {
      "page": "div_time",
      "title": "Sample divergence time on an edge uv previously traversed by m(v) data points",
      "topics": [
        "div_time"
      ]
    },
    {
      "page": "draw_mnorm",
      "title": "Efficiently sample multivariate normal using precision matrix from x ~ N(Q^{-1}a, Q^{-1}), where Q^{-1} is the precision matrix",
      "topics": [
        "draw_mnorm"
      ]
    },
    {
      "page": "exp_normalize",
      "title": "Compute normalized probabilities: exp(x_i) / sum_j exp(x_j)",
      "topics": [
        "exp_normalize"
      ]
    },
    {
      "page": "expit",
      "title": "The expit function",
      "topics": [
        "expit"
      ]
    },
    {
      "page": "H_n",
      "title": "Harmonic series",
      "topics": [
        "H_n"
      ]
    },
    {
      "page": "initialize",
      "title": "Initialize the MH-within-Gibbs algorithm for DDT-LCM",
      "concept": [
        "initialization functions"
      ],
      "topics": [
        "initialize"
      ]
    },
    {
      "page": "initialize_hclust",
      "title": "Estimate an initial binary tree on latent classes using hclust()",
      "concept": [
        "initialization functions"
      ],
      "topics": [
        "initialize_hclust"
      ]
    },
    {
      "page": "initialize_poLCA",
      "title": "Estimate an initial response profile from latent class model using poLCA()",
      "concept": [
        "initialization functions"
      ],
      "topics": [
        "initialize_poLCA"
      ]
    },
    {
      "page": "initialize_randomLCM",
      "title": "Provide a random initial response profile based on latent class mode",
      "topics": [
        "initialize_randomLCM"
      ]
    },
    {
      "page": "J_n",
      "title": "Compute factor in the exponent of the divergence time distribution",
      "topics": [
        "J_n"
      ]
    },
    {
      "page": "log_expit",
      "title": "Numerically accurately compute f(x) = log(x / (1/x)).",
      "topics": [
        "log_expit"
      ]
    },
    {
      "page": "logit",
      "title": "The logistic function",
      "topics": [
        "logit"
      ]
    },
    {
      "page": "logllk_ddt",
      "title": "Calculate loglikelihood of a DDT, including the tree structure and node parameters",
      "concept": [
        "likelihood functions"
      ],
      "topics": [
        "logllk_ddt"
      ]
    },
    {
      "page": "logllk_ddt_lcm",
      "title": "Calculate loglikelihood of the DDT-LCM",
      "concept": [
        "likelihood functions"
      ],
      "topics": [
        "logllk_ddt_lcm"
      ]
    },
    {
      "page": "logllk_div_time_one",
      "title": "Compute loglikelihood of divergence times for a(t) = c/(1-t)",
      "concept": [
        "likelihood functions"
      ],
      "topics": [
        "logllk_div_time_one"
      ]
    },
    {
      "page": "logllk_div_time_two",
      "title": "Compute loglikelihood of divergence times for a(t) = c/(1-t)^2",
      "concept": [
        "likelihood functions"
      ],
      "topics": [
        "logllk_div_time_two"
      ]
    },
    {
      "page": "logllk_lcm",
      "title": "Calculate loglikelihood of the latent class model, conditional on tree structure",
      "concept": [
        "likelihood functions"
      ],
      "topics": [
        "logllk_lcm"
      ]
    },
    {
      "page": "logllk_location",
      "title": "Compute log likelihood of parameters",
      "concept": [
        "likelihood functions"
      ],
      "topics": [
        "logllk_location"
      ]
    },
    {
      "page": "logllk_tree_topology",
      "title": "Compute loglikelihood of the tree topology",
      "concept": [
        "likelihood functions"
      ],
      "topics": [
        "logllk_tree_topology"
      ]
    },
    {
      "page": "parameter_diet",
      "title": "Parameters for the HCHS dietary recall data example",
      "topics": [
        "parameter_diet"
      ]
    },
    {
      "page": "plot_tree_with_barplot",
      "title": "Plot the MAP tree and class profiles (bar plot) of summarized DDT-LCM results",
      "topics": [
        "plot_tree_with_barplot"
      ]
    },
    {
      "page": "plot_tree_with_heatmap",
      "title": "Plot the MAP tree and class profiles (heatmap) of summarized DDT-LCM results",
      "topics": [
        "plot_tree_with_heatmap"
      ]
    },
    {
      "page": "plot.ddt_lcm",
      "title": "Create trace plots of DDT-LCM parameters",
      "topics": [
        "plot.ddt_lcm"
      ]
    },
    {
      "page": "plot.summary.ddt_lcm",
      "title": "Plot the MAP tree and class profiles of summarized DDT-LCM results",
      "topics": [
        "plot.summary.ddt_lcm"
      ]
    },
    {
      "page": "predict.ddt_lcm",
      "title": "Prediction of class memberships from posterior predictive distributions",
      "topics": [
        "predict.ddt_lcm"
      ]
    },
    {
      "page": "predict.summary.ddt_lcm",
      "title": "Prediction of class memberships from posterior summaries",
      "topics": [
        "predict.summary.ddt_lcm"
      ]
    },
    {
      "page": "print.ddt_lcm",
      "title": "Print out setup of a ddt_lcm model",
      "concept": [
        "ddt_lcm results"
      ],
      "topics": [
        "print.ddt_lcm"
      ]
    },
    {
      "page": "print.summary.ddt_lcm",
      "title": "Print out summary of a ddt_lcm model",
      "concept": [
        "ddt_lcm results"
      ],
      "topics": [
        "print.summary.ddt_lcm"
      ]
    },
    {
      "page": "proposal_log_prob",
      "title": "Calculate proposal likelihood",
      "topics": [
        "proposal_log_prob"
      ]
    },
    {
      "page": "quiet",
      "title": "Suppress print from cat()",
      "topics": [
        "quiet"
      ]
    },
    {
      "page": "random_detach_subtree",
      "title": "Metropolis-Hasting algorithm for sampling tree topology and branch lengths from the DDT branching process.",
      "concept": [
        "sample trees"
      ],
      "topics": [
        "random_detach_subtree"
      ]
    },
    {
      "page": "reattach_point",
      "title": "Attach a subtree to a given DDT at a randomly selected location",
      "concept": [
        "sample trees"
      ],
      "topics": [
        "reattach_point"
      ]
    },
    {
      "page": "result_diet_1000iters",
      "title": "Result of fitting DDT-LCM to a semi-synthetic data example",
      "topics": [
        "result_diet_1000iters"
      ]
    },
    {
      "page": "sample_c_one",
      "title": "Sample divergence function parameter c for a(t) = c / (1-t) through Gibbs sampler",
      "topics": [
        "sample_c_one"
      ]
    },
    {
      "page": "sample_c_two",
      "title": "Sample divergence function parameter c for a(t) = c / (1-t)^2 through Gibbs sampler",
      "topics": [
        "sample_c_two"
      ]
    },
    {
      "page": "sample_class_assignment",
      "title": "Sample individual class assignments Z_i, i = 1, ..., N",
      "topics": [
        "sample_class_assignment"
      ]
    },
    {
      "page": "sample_leaf_locations_pg",
      "title": "Sample the leaf locations and Polya-Gamma auxilliary variables",
      "topics": [
        "sample_leaf_locations_pg"
      ]
    },
    {
      "page": "sample_sigmasq",
      "title": "Sample item group-specific variances through Gibbs sampler",
      "topics": [
        "sample_sigmasq"
      ]
    },
    {
      "page": "sample_tree_topology",
      "title": "Sample a new tree topology using Metropolis-Hastings through randomly detaching and re-attaching subtrees",
      "topics": [
        "sample_tree_topology"
      ]
    },
    {
      "page": "simulate_DDT_tree",
      "title": "Simulate a tree from a DDT process. Only the tree topology and branch lengths are simulated, without node parameters.",
      "concept": [
        "simulate DDT-LCM data"
      ],
      "topics": [
        "simulate_DDT_tree"
      ]
    },
    {
      "page": "simulate_lcm_given_tree",
      "title": "Simulate multivariate binary responses from a latent class model given a tree",
      "concept": [
        "simulate DDT-LCM data"
      ],
      "topics": [
        "simulate_lcm_given_tree"
      ]
    },
    {
      "page": "simulate_lcm_response",
      "title": "Simulate multivariate binary responses from a latent class model",
      "concept": [
        "simulate DDT-LCM data"
      ],
      "topics": [
        "simulate_lcm_response"
      ]
    },
    {
      "page": "simulate_parameter_on_tree",
      "title": "Simulate node parameters along a given tree.",
      "concept": [
        "simulate DDT-LCM data"
      ],
      "topics": [
        "simulate_parameter_on_tree"
      ]
    },
    {
      "page": "summary.ddt_lcm",
      "title": "Summarize the output of a ddt_lcm model",
      "concept": [
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