An emc object of an LNR model of the Forstmann dataset using the first three subjects

An emc object with a limited number of samples and subjects of the Forstmann dataset. The object is a nested list of lenght three, each list containing the MCMC samples of the respective chain. The MCMC samples are stored in the samples element.

Usage

samples_LNR

Format

An emc object. An emc object is a list with a specific structure and elements, as outlined below.

data

A list of dataframes, one for each subject included

par_names

A character vector containing the model parameter names

n_pars

The number of parameters in the model

n_subjects

The number of unique subject ID's in the data

subjects

A vector containing the unique subject ID's

prior

A list that holds the prior for theta_mu (the model parameters). Contains the mean (theta_mu_mean), covariance matrix (theta_mu_var), degrees of freedom (v), and scale (A) and inverse covariance matrix (theta_mu_invar)

ll_func

The log likelihood function used by pmwg for model estimation

samples

A list with defined structure containing the samples, see the Samples Element section for more detail

grouped

Which parameters are grouped across subjects, in this case none

sampler_nuis

A sampler list for nuisance parameters (in this case there are none), similarly structured to the overall samples list of one of the MCMC chains.

Source

https://www.pnas.org/doi/10.1073/pnas.0805903105

Samples Element

The samples element of a emc object contains the different types of samples estimated by EMC2. These include the three main types of samples theta_mu, theta_var and alpha as well as a number of other items which are detailed here.

theta_mu

samples used for estimating the model parameters (group level), an array of size (n_pars x n_samples)

theta_var

samples used for estimating the parameter covariance matrix, an array of size (n_pars x n_pars x n_samples)

alpha

samples used for estimating the subject random effects, an array of size (n_pars x n_subjects x n_samples)

stage

A vector containing what PMwG stage each sample was drawn in

subj_ll

The winning particles log-likelihood for each subject and sample

a_half

Mixing weights used during the Gibbs step when creating a new sample for the covariance matrix

last_theta_var_inv

The inverse of the last samples covariance matrix

idx

The index of the last sample drawn

epsilon

The scaling parameter of the proposal distributions for each subject array of size (n_subjects x n_samples)

origin

From which propoosal distribution the accepted samples in the MCMC chain came, an array of size (n_subjects x n_samples)