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a single symbolic description of the linear model of themixture GLM components to be fitted. The syntax is the sameas used in thelm function.

eihter NULL (default) or a single symbolic description of thelinear model of the hierarchical component of the model.It specifies how the average parameter of the base measureof the Dirichlet Process Prior varies linearly as a functionof group level covariates. IfNULL, it will usea single base measure to the DPP mixture model.

a data.frame with all the variables specified informula1 andformula2. Note: it is advisable to scale the variables before the estimation

a named list with the following elements

-burn.in (required): an integer greater or equal to 0indicating the number iterations used in theburn-in period of the MCMC.

-n.iter (required): an integer greater or equal to 1indicating the number of iterations to recordafter the burn-in period for the MCMC.

-epsilon (optional): a positive number. Default is 0.01.Used whenfamily='binomial' orfamily='multinomial'. It is used in theStormer-Verlet Integrator (a.k.a leapfrogintegrator) to solve the Hamiltonian MonteCarlo in the estimation of the model.

-leapFrog (optional) an integer. Default is 40. Used whenfamily='binomial' orfamily='multinomial'.It indicates the number of steps taken at eachiteration of the Hamiltonian Monte Carlo forthe Stormer-Verlet Integrator.

-hmc_iter (optional) an integer. Default is 1. Used whenfamily='binomial' orfamily='multinomial'.It indicates the number of HMC iteration(s)for each Gibbs iteration.

a character with either 'gaussian', 'binomial', or 'multinomial'.It indicates the family of the GLM components of the mixture model.

an integer indicating the maximum number of clusters to truncate theDirichlet Process Prior in order to use the blocked Gibbs sampler.

string with the name of the column in the data that uniquely identifies the contexts. IfNULL (default) contexts will be identified by numerical indexes and unique context-level variables. The user is advised to pre-process the data to provide meaningful labels for the contexts to facilitate later visualization and analysis of the results.

either NULL or a list with the constants of the model. If not NULL,it must contain a vector namedmu_beta, whose size must beequal to the number of covariates specified informula1plus one for the constant term;Sigma_beta, which must be a squaredmatrix, and each dimension must be equal to the size of the vectormu_beta; andalpha, which must be a single number. If @param family is 'gaussian',then it must also contains2_sigma anddf_sigma, bothsingle numbers. If NULL, the defaults aremu_beta=0,Sigma_beta=diag(10),alpha=1,df_sigma=10,s2_sigma=10 (all with the dimension automatically set to thecorrect values).

numeric vector with the same size as the number of rows of the data. It must contain the weights of the observations in the data set. NOTE: FEATURE NOT IMPLEMENTED YET

an integer indicating the number of iterations to wait before printing informationabout the estimation process. If zero, it does not display any information.Note: displaying informaiton at every iteration (n.display=1) may increasethe time to estimate the model slightly.

string with action to be taken for theNA values. (currently, onlyexclude is available)

string, either "R" or "Cpp" indicating the language of the implementation of the binomial model.

a data frame with the data set used to estimate thehdpGLM model

the output ofhdpGLM

adpGLM object returned by the functionhdpGLM

The additional parameters accepted are:

adpGLM object returned by the functionhdpGLM

The additional parameters accepted are:

a data frame with the data set used to estimate thehdpGLM model

the output ofhdpGLM

integer, the number of clusters. If there are multiple contexts, K is the average number of clusters across contexts, and each context gets a number of clusters sampled from a Poisson distribution, except ifsame.K isTRUE.

integer, the number of covariates of theGLM components

an integer indicating the number of covariates determining the average parameter of the base measure of the Dirichlet process prior

an integer representing the number of contexts @param parameters either NULL or a list with the parameters to generate the model. If not NULL, it must contain a sublist name beta, a vector named tau, and a vector named pi. The sublist beta must be a list of vectors, each one with size nCov+1 to be the coefficients of the GLM mixtures components that will generate the data. For the vector tau, if nCovj=0 (single-context case) then it must be a 1x1 matrix containing 1. If ncovj>0, it must be a (nCov+1)x(nCovj+1) matrix. The vector pi must add up to 1 and have length K.

either NULL or a vector with length K that add up to 1. If not NULL, it determines the mixture probabilities

boolean, used when data is sampled from more than one context. IfTRUE all contexts get the same number of clusters. IfFALSE, each context gets a number of clusters sampled from a Poisson distribution with expectation equals toK (current not implemented)

a seed forset.seed

eitherNULL or a two dimensional integer vector. If it isNULL, all the coefficients (beta) of the individual level covariates are functions of context-level features (tau). If it is notNULL, the first component of the vector indicates the index of the lower level covariate (X) whose linear effectbeta depends on context (tau) (0 is the intercept). The second component indicates the index context-level covariate (W) whose linear coefficient (tau) is non-zero.

boolean, ifTRUE all the contexts will have the same number of clusters AND each cluster will have the same coefficientbeta.

integer, indicates which cluster will be context-dependent. Ifzero, all clusters will be context-dependent

integer, the sample size of the data. If there are multiple contexts, each context will have n cases.

integer, the number of clusters. If there are multiple contexts, K is the average number of clusters across contexts, and each context gets a number of clusters sampled from a Poisson distribution, except ifsame.K isTRUE.

integer, the number of covariates of the GLM components.

an integer indicating the number of covariates determining the average parameter of the base measure of the Dirichlet process prior

an integer representing the number of contexts @param parameters either NULL or a list with the parameters to generate the model. If not NULL, it must contain a sublist name beta, a vector named tau, and a vector named pi. The sublist beta must be a list of vectors, each one with size nCov+1 to be the coefficients of the GLM mixtures components that will generate the data. For the vector tau, if nCovj=0 (single-context case) then it must be a 1x1 matrix containing 1. If nCovj>0, it must be a (nCov+1)x(nCovj+1) matrix. The vector pi must add up to 1 and have length K.

a character with either 'gaussian', 'binomial', or 'multinomial'. It indicates the family of the GLM components of the mixture model.

a list with the parameter values of the model. Format should be the same of the output of the function hdpGLM_simulateParameters()

either NULL or a vector with length K that add up to 1. If not NULL, it determines the mixture probabilities

boolean, used when data is sampled from more than one context. IfTRUE all contexts get the same number of clusters. IfFALSE, each context gets a number of clusters sampled from a Poisson distribution with expectation equals toK (current not implemented)

a seed forset.seed

eitherNULL or a two dimensional integer vector. If it isNULL, all the coefficients (beta) of the individual level covariates are functions of context-level features (tau). If it is notNULL, the first component of the vector indicates the index of the lower level covariate (X) whose linear effectbeta depends on context (tau) (0 is the intercept). The second component indicates the index context-level covariate (W) whose linear coefficient (tau) is non-zero.

boolean, ifTRUE all the contexts will have the same number of clusters AND each cluster will have the same coefficientbeta.

integer, indicates which cluster will be context-dependent. Ifzero, all clusters will be context-dependent

adpGLM object returned by the functionhdpGLM

ignore

ahdpGLM object returned by the functionhdpGLM

ignore

adpGLM object returned by the functionhdpGLM

a dpGLM object with the samples from generated byhdpGLM

string vector with the name of covariates to plot. IfNULL (default), all covariates are plotted.

boolean, ifTRUE the linear coefficientsbeta will be displayed in their separate clusters.

boolean, ifTRUE andseparate=T, the 95% HPDI lines will be displayed.

eitherNULL (default) or adata.frame with the true values of the linear coefficientsbeta if they are known. Thedata.frame must contain a column namedk indicating the cluster ofbeta, and a column namedParameter with the name of the linear coefficients (beta1,beta2, ...,beta_dx, wheredx is the number of covariates at the individual level, and beta1 is the coefficient of the intercept term). It must contain a column namedTrue with the true value of thebetas.

string, the title of the plot

string, the subtitle of the plot

the bandwidth used is actuallyadjust*bw.This makes it easy to specify values like ‘half the default’bandwidth.

integer, the number of columns in the plot

boolean, ifTRUE it shows only the densities of the clusters that actually have data points assigned to it with high probability

boolean, ifTRUE and separate is alsoTRUE it will display only the 95% HPDI of the posterior density of the linear coefficientsbeta

one of four options: "bottom" (default), "top", "left", or "right". It indicates the position of the legend

= string with color to fill the density plot

number between 0 and 1 indicating the degree of transparency of the density

boolean, ifTRUE (default), the covariate name is displayed in the plot

boolean, ifTRUE the posterior mean of every cluster is displayed

a string with the value to display in the legend when thetrue.beta is used

ignored

an object of the classhdpGLM generted by the functionhdpGLM

string vector with the name of the individual-level covariates to plot. IfNULL (default), all covariates are plotted.

string vector with the names of the contexts to plot. An alternative is to use the context indexes with the parameterj.idx instead of the context labels. IfNULL (default) and j.idx is alsoNULL, the posterior distribution of all contexts are plotted. Note: if contexts to plot are selected usingj.label, the parametercontext.id must also be provided.

integer vector with the index of the contexts to plot. An alternative is to use the context labels with the parameterj.label instead of the indexes. IfNULL (default) and j.label is alsoNULL, the posterior distribution of all contexts are plotted

string, the title of the plot

string, the subtitle of the plot

adata.frame with the true values of the linear coefficientsbeta if they are known. Thedata.frame must contain a column namedj with the index of the context associated with that particular linear coefficientbeta. It must match the indexes used in the data set for each context. Another column namedk must be provided, indicating the cluster ofbeta, and a column namedParameter with the name of the linear coefficients (beta1,beta2, ...,beta_dx, wheredx is the number of covariates at the individual level, and beta1 is the coefficient of the intercept term). It must contain a column namedTrue with the true value of thebetas. Finally, thedata.frame must contain columns with the context-level covariates as used in the estimation of thehdpGLM function (see Details below).

interger, the number of columns in the plot

one of four options: "bottom" (default), "top", "left", or "right". It indicates the position of the legend

boolean, ifTRUE (default), the covariate name is displayed in the plot

string with the name of the column containing the labels identifying the contexts. This variable should have been specified when the estimation was conducted using the functionhdpGLM.

string, the label of the y-axis

string, the label of the x-axis

numeric, the relative size of the label in the x-axis

numeric, the relative size of the label in the y-axis

numeric, the relative size of the title of the plot

numeric, the relative size of the titles in the panel of the plot

numeric, the relative size of the legend

see ggridges::geom_density_ridges

string with the color of the densities

string with the color of the border of the densities

Additional arguments accepted are:

true.beta: adata.frame with the true values of the linear coefficientsbeta if they are known. Thedata.frame must contain a column namedj with the index of the context associated with that particular linear coefficientbeta. It must match the indexes used in the data set for each context. Another column namedk must be provided, indicating the cluster ofbeta, and a column namedParameter with the name of the linear coefficients (beta1,beta2, ...,beta_dx, wheredx is the number of covariates at the individual level, and beta1 is the coefficient of the intercept term). It must contain a column namedTrue with the true value of thebetas. Finally, thedata.frame must contain columns with the context-level covariates as used in the estimation of thehdpGLM function (see Details below).

true.tau: adata.frame with four columns. The first must be namedw and it indicates the index of each context-level covariate, starting with 0 for the intercept term. The second column namedbeta must contain the indexes of the betas of individual-level covariates, starting with 0 for the intercept term. The third column namedParameter must be namedtau<w><beta>, wherew andbeta must be the actual values displayed in the columnsw andbeta. Finally, it must have a column namedTrue with the true value of the parameter.

an output of the functionhdpGLM

a string vector with the name of the first-level covariates whose associated tau should be displayed

string with the name of the column containing the labels identifying the contexts. This variable should have been specified when the estimation was conducted using the functionhdpGLM.

adata.frame with the true values of the linear coefficientsbeta if they are known. Thedata.frame must contain a column namedj with the index of the context associated with that particular linear coefficientbeta. It must match the indexes used in the data set for each context. Another column namedk must be provided, indicating the cluster ofbeta, and a column namedParameter with the name of the linear coefficients (beta1,beta2, ...,beta_dx, wheredx is the number of covariates at the individual level, and beta1 is the coefficient of the intercept term). It must contain a column namedTrue with the true value of thebetas. Finally, thedata.frame must contain columns with the context-level covariates as used in the estimation of thehdpGLM function (see Details below).

string, title of the plot

string, the subtitle of the plot

boolean, ifTRUE the posterior mean of every cluster is displayed

boolean, ifTRUE a grid is displayed in the background

boolean, ifTRUE a message with the number of estimated clusters by context is displayed

string, color of the densities

numeric, size of the breaks in the x-axis

numeric, size of the breaks in the y-axis

numeric, size of the title

numeric, size of the legend

numeric, distance between x-axis marks and bottom of the figure

numeric, distance between left margin and left side of the figure

numeric, distance between y-axis marks and bottom of the figure

string, color of the border of the densities

the output of the functionhdpGLM_simulateData

integer, the index of the context level covariate the plot

integer, the number of columns in the grid of the plot

an output of the functionhdpGLM

a string vector with the name of the first-level covariates whose associated tau should be displayed

a string vector with the name of the context-level covariate(s) whose linear effect will be displayed. IfNULL, the linear effect tau of all context-level covariates are displayed. Note: the context-level covariate must have been included in the estimation of the model.

integer with the number of columns of the grid containing the posterior distribution of tau

integer with the number of columns of the posterior expectation of betas as function of context-level features

integer with the number of columns to use to display the different context-level covariates

integer with the number of rows to use to display the different context-level covariates

boolean, ifTRUE the plot will display a regression line representing the regression of the posterior expectation of the linear coefficients betas on the context-level covariates. DefaultFALSE

boolean, ifTRUE the plots will display a line with the predicted posterior expectation of betas obtained using the posterior expectation of taus, the linear coefficients of the expectation of beta

string, the title for the posterior distribution of the context effects

adata.frame with four columns. The first must be namedw and it indicates the index of each context-level covariate, starting with 0 for the intercept term. The second column namedbeta must contain the indexes of the betas of individual-level covariates, starting with 0 for the intercept term. The third column namedParameter must be namedtau<w><beta>, wherew andbeta must be the actual values displayed in the columnsw andbeta. Finally, it must have a column namedTrue with the true value of the parameter.

string, the title for the posterior expectation of beta as function of context-level covariate

numeric, relative size of the x-axis of the plot with tau

numeric, relative size of the y-axis of the plot with tau

numeric, relative size of the title of the plot with tau

numeric, relative size of the title of the panels of the plot with tau

numeric, relative size of the legend of the plot with tau

numeric, relative size of the x-axis of the plot with beta

numeric, relative size of the y-axis of the plot with beta

numeric, relative size of the title of the plot with beta

numeric, relative size of the title of the panels of the plot with beta

numeric, relative size of the legend of the plot with beta

string, the label of the x-axis for the plot with tau

an output of the functionhdpGLM

a string vector with the name of the first-level covariates whose associated tau should be displayed

a string vector with the name of the context-level covariate(s) whose linear effect will be displayed. IfNULL, the linear effect tau of all context-level covariates are displayed. Note: the context-level covariate must have been included in the estimation of the model.

boolean, ifTRUE the plots will display a line with the predicted posterior expectation of betas obtained using the posterior expectation of taus, the linear coefficients of the expectation of beta

integer with number of columns of the grid used for each group of context-level covariates

string, the label of the y-axis

integer with the number of rows of the grid

integer with the number of columns of the grid

boolean, ifTRUE the plot will display a regression line representing the regression of the posterior expectation of the linear coefficients betas on the context-level covariates. DefaultFALSE

string, title of the plot

one of four options: "bottom" (default), "top", "left", or "right". It indicates the position of the legend

string with color of fitted line. Only works ifpred.pexp.beta=TRUE

numeric, the relative size of the label in the x-axis

numeric, the relative size of the label in the y-axis

numeric, absolute size of the title

numeric, the relative size of the titles in the panel of the plot

numeric, the relative size of the legend

an output of the functionhdpGLM

a string vector with the name of the first-level covariates whose associated tau should be displayed

a string vector with the name of the context-level covariate(s) whose linear effect will be displayed. IfNULL, the linear effect tau of all context-level covariates are displayed. Note: the context-level covariate must have been included in the estimation of the model.

string, title of the plot

adata.frame with four columns. The first must be namedw and it indicates the index of each context-level covariate, starting with 0 for the intercept term. The second column namedbeta must contain the indexes of the betas of individual-level covariates, starting with 0 for the intercept term. The third column namedParameter must be namedtau<w><beta>, wherew andbeta must be the actual values displayed in the columnsw andbeta. Finally, it must have a column namedTrue with the true value of the parameter.

boolean, ifFALSE (default) the posterior distribution of taus representing the intercept of the expectation of beta are omitted

boolean, ifFALSE (default) the taus affecting only the intercept terms of the outcome variable are omitted

number of columns of the grid. IfNULL, one column is used

one of four options: "bottom" (default), "top", "left", or "right". It indicates the position of the legend

numeric, the relative size of the label in the x-axis

numeric, the relative size of the label in the y-axis

numeric, the relative size of the title of the plot

numeric, the relative size of the titles in the panel of the plot

numeric, the relative size of the legend

string, the label of the x-axis

outcome of the function hdpLGM

data frame with the values of the covariates that are goingto be used to generate the predicted/fitted values. The posterior mean isused to create the predicted values

family : a string with the family of the output variable:gaussian (default),binomial, etc...

outcome of the function hdpLGM

data frame with the values of the covariates that are goingto be used to generate the predicted/fitted values. The posterior mean isused to create the predicted values

family : a string with the family of the output variable:gaussian (default),binomial, etc...

adpGLM object returned by the functionhdpGLM

ignore

adpGLM_data object returned by the functionhdpGLM_simulateData

ignore

ahdpGLM object returned by the functionhdpGLM

ignore

ahdpGLM_data object returned by the functionhdpGLM_simulateData

ignore

adpGLM object returned by the functionhdpGLM

The additional parameters accepted are:

true.beta: (seeplot.dpGLM)

an object of the class dpGLM_data

ignored

an object of the classhdpGLM generted by the functionhdpGLM

Additional arguments accepted are:

true.beta: adata.frame with the true values of the linear coefficientsbeta if they are known. Thedata.frame must contain a column namedj with the index of the context associated with that particular linear coefficientbeta. It must match the indexes used in the data set for each context. Another column namedk must be provided, indicating the cluster ofbeta, and a column namedParameter with the name of the linear coefficients (beta1,beta2, ...,beta_dx, wheredx is the number of covariates at the individual level, and beta1 is the coefficient of the intercept term). It must contain a column namedTrue with the true value of thebetas. Finally, thedata.frame must contain columns with the context-level covariates as used in the estimation of thehdpGLM function (see Details below).

true.tau: adata.frame with four columns. The first must be namedw and it indicates the index of each context-level covariate, starting with 0 for the intercept term. The second column namedbeta must contain the indexes of the betas of individual-level covariates, starting with 0 for the intercept term. The third column namedParameter must be namedtau<w><beta>, wherew andbeta must be the actual values displayed in the columnsw andbeta. Finally, it must have a column namedTrue with the true value of the parameter.

an object of the classhdpGLM_data, which is produced by the functionhdpGLM_simulateData

ignored

adpGLM object returned by the functionhdpGLM

The additional parameters accepted are:

true.beta: (seeplot.dpGLM)