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matrix of standardized fixed effects (seestd function inncvreg documenation). X should not include intercept.

numeric vector of response values. If "survival" family,y are the event indicatorvalues (0 if censored, 1 if event)

a description of the error distribution and link function to be used in the model. Currently, theglmmPen algorithm allows the Binomial ("binomial" or binomial()), Gaussian ("gaussian" or gaussian()), and Poisson ("poisson" or poisson()) familieswith canonical links only. SeephmmPen for variable selection withinproportional hazards mixed models for survival data.

numeric vector that can be used to specify an a priori known component to be included in the linear predictor during fitting. This should beNULL or a numeric vector of length equal to the number of observations

Tuning parameter for the Mnet estimator which controls the relative contributions from the MCP/SCAD/LASSO penalty and the ridge, or L2, penalty.alpha=1 is equivalent to the MCP/SCAD/LASSO penalty, whilealpha=0 is equivalent to ridge regression. However,alpha=0 is not supported;alpha may be arbitrarily small, but not exactly zero

numeric fraction between 0 and 1. The sequence of the lambda penalty parametersranges from the maximum lambda where all fixed and random effects are penalized to 0 and a minimum lambda value, which equals a small fraction of the maximum lambda. The parameterlambda.min specifies this fraction. Default value is set toNULL, whichautomatically selectslambda.min to equal 0.01 when the number of observations isgreater than the number of fixed effects predictors and 0.05 otherwise.Only usedif eitherlambda0_seq orlambda1_seq remain unspecified by the user(one or both of these sequence arguments set toNULL) and, consequently, one or more default sequences needto be calculated.

positive integer specifying number of penalty parameters (lambda) with which to fit a model.

an optional numeric vector equal to thefixef_noPen argumentinglmmPen

positive integer specifying the number of posterior samples to collectbefore the proposal variance is adjusted based on the acceptance rate of the lastbatch_length accepted posterior samples. Default is set to 100. Batch length restrictedto be no less than 50.

non-negative integer specifying an offset value for the increment of the proposalvariance adjustment. Optionally used to ensure the required diminishing adaptation condition. Default set to 0.⁠increment = min(0.01, 1 / sqrt(batch*batch_length + offset))⁠

a two-sided linear formula object describing both the fixed effects and random effects part of the model, with the response on the left of a ~ operator and the terms, separated by + operators, on the right. Random-effects terms are distinguished by vertical bars ("|") separating expression for design matrices from the grouping factor.formula should be of the same format needed forglmer in packagelme4. Only one grouping factor will be recognized. The random effects covariates need to be a subset of the fixed effects covariates.The offset must be specified outside of the formula in the 'offset' argument.

an optional data frame containing the variables named informula. Ifdata is omitted, variables will be taken from the environment offormula.

a description of the error distribution and link function to be used in the model. Currently, theglmmPen algorithm allows the Binomial ("binomial" or binomial()), Gaussian ("gaussian" or gaussian()), and Poisson ("poisson" or poisson()) familieswith canonical links only. SeephmmPen for variable selection withinproportional hazards mixed models for survival data.

character string specifying whether the covariance matrix should be unstructured("unstructured") or diagonal with no covariances between variables ("independent").Default is set toNULL. Ifcovar is set toNULL and the number of random effectspredictors (not including the intercept) is greater than or equal to 10 (i.e. high dimensional), then the algorithm automatically assumes an independent covariance structure andcovar is set to "independent". Otherwise ifcovaris set toNULL and the number of random effects predictors is less than 10, then thealgorithm automatically assumes an unstructured covariance structure andcovar is set to "unstructured".

This can be used to specify ana priori known component to be included in the linear predictor during fitting. Default set toNULL (no offset). If the data argument is notNULL, this should be a numeric vector of length equal to the number of cases (the length of the response vector). If the data argument specifies a data.frame, the offsetargument should specify the name of a column in the data.frame.

a structure of class "optimControl" created from functionoptimControl that specifies several optimization parameters. See the documentation foroptimControl for more details on defaults.

a list of class "adaptControl" from functionadaptControl containing the control parameters for the adaptive random walk Metropolis-within-Gibbs procedure. Ignored ifoptimControl parametersampler is set to "stan" (default) or "independence".

an integer specifying print output to include as function runs. Default value is 0. See Details for more information about output provided when trace = 0, 1, or 2.

a list of class "selectControl" or "lambdaControl" resulting fromselectControl orlambdaControl containing additional control parameters.When functionglmm is used,the algorithm may be run using one specific set ofpenalty parameterslambda0 andlambda1 by specifying such values inlambdaControl(). The default forglmm is to run the model fit with no penalization (lambda0 =lambda1 = 0).When functionglmmPen is run,tuning_options is specified usingselectControl(). See thelambdaControl andselectControl documentation for further details.

a logical value indicating if additional output should be given showing theprogress of the fit procedure. IfTRUE, such output includes iteration-level informationfor the fit procedure (iteration number EM_iter,number of MCMC samples nMC, average Euclidean distance between current coefficients and coefficientsfrom t–defined inoptimControl–iterations back EM_conv, and number of non-zero fixed and random effects covariatesnot including the intercept). Additionally,progress = TRUEgives some other information regarding the progress of the variable selection procedure, including the model selection criteria and log-likelihood estimatesfor each model fit.Default isTRUE.

additional arguments that could be passed intoglmmPen. SeeglmmPenfor further details.

a two-sided linear formula object describing both the fixed effects and random effects part of the model, with the response on the left of a ~ operator and the terms, separated by + operators, on the right. Random-effects terms are distinguished by vertical bars ("|") separating expression for design matrices from the grouping factor.formula should be of the same format needed forglmer in packagelme4. Only one grouping factor will be recognized. The random effects covariates need to be a subset of the fixed effects covariates.The offset must be specified outside of the formula in the 'offset' argument.

an optional data frame containing the variables named informula. Ifdata is omitted, variables will be taken from the environment offormula.

a description of the error distribution and link function to be used in the model. Currently, theglmmPen algorithm allows the Binomial ("binomial" or binomial()), Gaussian ("gaussian" or gaussian()), and Poisson ("poisson" or poisson()) familieswith canonical links only. SeephmmPen for variable selection withinproportional hazards mixed models for survival data.

character string specifying whether the covariance matrix should be unstructured("unstructured") or diagonal with no covariances between variables ("independent").Default is set toNULL. Ifcovar is set toNULL and the number of random effectspredictors (not including the intercept) is greater than or equal to 10 (i.e. high dimensional), then the algorithm automatically assumes an independent covariance structure andcovar is set to "independent". Otherwise ifcovaris set toNULL and the number of random effects predictors is less than 10, then thealgorithm automatically assumes an unstructured covariance structure andcovar is set to "unstructured".

This can be used to specify ana priori known component to be included in the linear predictor during fitting. Default set toNULL (no offset). If the data argument is notNULL, this should be a numeric vector of length equal to the number of cases (the length of the response vector). If the data argument specifies a data.frame, the offsetargument should specify the name of a column in the data.frame.

Optional vector of 0's and 1's of the same length as the number of fixed effects covariatesused in the model. Value 0 indicates the variable should not have its fixed effect coefficientpenalized, 1 indicates that it can be penalized. Order should correspond to the same order of the fixed effects given in the formula.

character describing the type of penalty to use in the variable selection procedure.Options include 'MCP', 'SCAD', and 'lasso'. Default is MCP penalty. If the random effect covariancematrix is "unstructured", then a group MCP, group SCAD, or group LASSO penalty is used on the random effects coefficients. See Breheny and Huang (2011) <doi:10.1214/10-AOAS388> and Breheny and Huang (2015) <doi:10.1007/s11222-013-9424-2> for details of these penalties.

Tuning parameter for the Mnet estimator which controls the relative contributions from the MCP/SCAD/LASSO penalty and the ridge, or L2, penalty.alpha=1 is equivalent to the MCP/SCAD/LASSO penalty, whilealpha=0 is equivalent to ridge regression. However,alpha=0 is not supported;alpha may be arbitrarily small, but not exactly zero

The scaling factor of the MCP and SCAD penalties. Not used by LASSO penalty.Default is 4.0 for SCAD and 3.0 for MCP. See Breheny and Huang (2011) <doi:10.1214/10-AOAS388> and Breheny and Huang (2015) <doi:10.1007/s11222-013-9424-2> for further details.

a structure of class "optimControl" created from functionoptimControl that specifies several optimization parameters. See the documentation foroptimControl for more details on defaults.

a list of class "adaptControl" from functionadaptControl containing the control parameters for the adaptive random walk Metropolis-within-Gibbs procedure. Ignored ifoptimControl parametersampler is set to "stan" (default) or "independence".

an integer specifying print output to include as function runs. Default value is 0. See Details for more information about output provided when trace = 0, 1, or 2.

a list of class "selectControl" or "lambdaControl" resulting fromselectControl orlambdaControl containing additional control parameters.When functionglmm is used,the algorithm may be run using one specific set ofpenalty parameterslambda0 andlambda1 by specifying such values inlambdaControl(). The default forglmm is to run the model fit with no penalization (lambda0 =lambda1 = 0).When functionglmmPen is run,tuning_options is specified usingselectControl(). See thelambdaControl andselectControl documentation for further details.

an optional character string expressing the path and file basename of a file combination that will file-back or currently file-backs abig.matrix of the posterior samples from the minimal penalty model used for the BIC-ICQ calculation used for model selection. T(BIC-ICQ reference: Ibrahim et al (2011)<doi:10.1111/j.1541-0420.2010.01463.x>). If this argument isspecified asNULL (default) and BIC-ICQ calculations are requested (seeselectControl)for details), the posterior sampleswill be saved in the file combination 'BICq_Posterior_Draws.bin' and 'BICq_Posterior_Draws.desc'in the working directory.See 'Details' section for additional details about the required format ofBICq_posteriorand the file-backed big matrix.

a logical value indicating if additional output should be given showing theprogress of the fit procedure. IfTRUE, such output includes iteration-level informationfor the fit procedure (iteration number EM_iter,number of MCMC samples nMC, average Euclidean distance between current coefficients and coefficientsfrom t–defined inoptimControl–iterations back EM_conv, and number of non-zero fixed and random effects covariatesnot including the intercept). Additionally,progress = TRUEgives some other information regarding the progress of the variable selection procedure, including the model selection criteria and log-likelihood estimatesfor each model fit.Default isTRUE.

additional arguments that could be passed intoglmmPen. SeeglmmPen_FAandphmmPen_FA for further details.

a two-sided linear formula object describing both the fixed effects and random effects part of the model, with the response on the left of a ~ operator and the terms, separated by + operators, on the right. Random-effects terms are distinguished by vertical bars ("|") separating expression for design matrices from the grouping factor.formula should be of the same format needed forglmer in packagelme4. Only one grouping factor will be recognized. The random effects covariates need to be a subset of the fixed effects covariates.The offset must be specified outside of the formula in the 'offset' argument.

an optional data frame containing the variables named informula. Ifdata is omitted, variables will be taken from the environment offormula.

a description of the error distribution and link function to be used in the model. Currently, theglmmPen algorithm allows the Binomial ("binomial" or binomial()), Gaussian ("gaussian" or gaussian()), and Poisson ("poisson" or poisson()) familieswith canonical links only. SeephmmPen for variable selection withinproportional hazards mixed models for survival data.

This can be used to specify ana priori known component to be included in the linear predictor during fitting. Default set toNULL (no offset). If the data argument is notNULL, this should be a numeric vector of length equal to the number of cases (the length of the response vector). If the data argument specifies a data.frame, the offsetargument should specify the name of a column in the data.frame.

a list of class "rControl" from functionrControl containing the control parameters for the estimation of the number of latentfactors to use in theglmmPen_FA andglmm_FA estimation procedures.

Optional vector of 0's and 1's of the same length as the number of fixed effects covariatesused in the model. Value 0 indicates the variable should not have its fixed effect coefficientpenalized, 1 indicates that it can be penalized. Order should correspond to the same order of the fixed effects given in the formula.

character describing the type of penalty to use in the variable selection procedure.Options include 'MCP', 'SCAD', and 'lasso'. Default is MCP penalty. If the random effect covariancematrix is "unstructured", then a group MCP, group SCAD, or group LASSO penalty is used on the random effects coefficients. See Breheny and Huang (2011) <doi:10.1214/10-AOAS388> and Breheny and Huang (2015) <doi:10.1007/s11222-013-9424-2> for details of these penalties.

Tuning parameter for the Mnet estimator which controls the relative contributions from the MCP/SCAD/LASSO penalty and the ridge, or L2, penalty.alpha=1 is equivalent to the MCP/SCAD/LASSO penalty, whilealpha=0 is equivalent to ridge regression. However,alpha=0 is not supported;alpha may be arbitrarily small, but not exactly zero

The scaling factor of the MCP and SCAD penalties. Not used by LASSO penalty.Default is 4.0 for SCAD and 3.0 for MCP. See Breheny and Huang (2011) <doi:10.1214/10-AOAS388> and Breheny and Huang (2015) <doi:10.1007/s11222-013-9424-2> for further details.

a structure of class "optimControl" created from functionoptimControl that specifies several optimization parameters. See the documentation foroptimControl for more details on defaults.

a list of class "adaptControl" from functionadaptControl containing the control parameters for the adaptive random walk Metropolis-within-Gibbs procedure. Ignored ifoptimControl parametersampler is set to "stan" (default) or "independence".

an integer specifying print output to include as function runs. Default value is 0. See Details for more information about output provided when trace = 0, 1, or 2.

a list of class "selectControl" or "lambdaControl" resulting fromselectControl orlambdaControl containing additional control parameters.When functionglmm is used,the algorithm may be run using one specific set ofpenalty parameterslambda0 andlambda1 by specifying such values inlambdaControl(). The default forglmm is to run the model fit with no penalization (lambda0 =lambda1 = 0).When functionglmmPen is run,tuning_options is specified usingselectControl(). See thelambdaControl andselectControl documentation for further details.

an optional character string expressing the path and file basename of a file combination that will file-back or currently file-backs abig.matrix of the posterior samples from the minimal penalty model used for the BIC-ICQ calculation used for model selection. T(BIC-ICQ reference: Ibrahim et al (2011)<doi:10.1111/j.1541-0420.2010.01463.x>). If this argument isspecified asNULL (default) and BIC-ICQ calculations are requested (seeselectControl)for details), the posterior sampleswill be saved in the file combination 'BICq_Posterior_Draws.bin' and 'BICq_Posterior_Draws.desc'in the working directory.See 'Details' section for additional details about the required format ofBICq_posteriorand the file-backed big matrix.

a logical value indicating if additional output should be given showing theprogress of the fit procedure. IfTRUE, such output includes iteration-level informationfor the fit procedure (iteration number EM_iter,number of MCMC samples nMC, average Euclidean distance between current coefficients and coefficientsfrom t–defined inoptimControl–iterations back EM_conv, and number of non-zero fixed and random effects covariatesnot including the intercept). Additionally,progress = TRUEgives some other information regarding the progress of the variable selection procedure, including the model selection criteria and log-likelihood estimatesfor each model fit.Default isTRUE.

additional arguments that could be passed intoglmmPen_FA. SeephmmPen_FA for further details (e.g.survival_options argument).

a two-sided linear formula object describing both the fixed effects and random effects part of the model, with the response on the left of a ~ operator and the terms, separated by + operators, on the right. Random-effects terms are distinguished by vertical bars ("|") separating expression for design matrices from the grouping factor.formula should be of the same format needed forglmer in packagelme4. Only one grouping factor will be recognized. The random effects covariates need to be a subset of the fixed effects covariates.The offset must be specified outside of the formula in the 'offset' argument.

an optional data frame containing the variables named informula. Ifdata is omitted, variables will be taken from the environment offormula.

a description of the error distribution and link function to be used in the model. Currently, theglmmPen algorithm allows the Binomial ("binomial" or binomial()), Gaussian ("gaussian" or gaussian()), and Poisson ("poisson" or poisson()) familieswith canonical links only. SeephmmPen for variable selection withinproportional hazards mixed models for survival data.

This can be used to specify ana priori known component to be included in the linear predictor during fitting. Default set toNULL (no offset). If the data argument is notNULL, this should be a numeric vector of length equal to the number of cases (the length of the response vector). If the data argument specifies a data.frame, the offsetargument should specify the name of a column in the data.frame.

a list of class "rControl" from functionrControl containing the control parameters for the estimation of the number of latentfactors to use in theglmmPen_FA andglmm_FA estimation procedures.

a structure of class "optimControl" created from functionoptimControl that specifies several optimization parameters. See the documentation foroptimControl for more details on defaults.

a list of class "adaptControl" from functionadaptControl containing the control parameters for the adaptive random walk Metropolis-within-Gibbs procedure. Ignored ifoptimControl parametersampler is set to "stan" (default) or "independence".

an integer specifying print output to include as function runs. Default value is 0. See Details for more information about output provided when trace = 0, 1, or 2.

a list of class "selectControl" or "lambdaControl" resulting fromselectControl orlambdaControl containing additional control parameters.When functionglmm is used,the algorithm may be run using one specific set ofpenalty parameterslambda0 andlambda1 by specifying such values inlambdaControl(). The default forglmm is to run the model fit with no penalization (lambda0 =lambda1 = 0).When functionglmmPen is run,tuning_options is specified usingselectControl(). See thelambdaControl andselectControl documentation for further details.

a logical value indicating if additional output should be given showing theprogress of the fit procedure. IfTRUE, such output includes iteration-level informationfor the fit procedure (iteration number EM_iter,number of MCMC samples nMC, average Euclidean distance between current coefficients and coefficientsfrom t–defined inoptimControl–iterations back EM_conv, and number of non-zero fixed and random effects covariatesnot including the intercept). Additionally,progress = TRUEgives some other information regarding the progress of the variable selection procedure, including the model selection criteria and log-likelihood estimatesfor each model fit.Default isTRUE.

additional arguments that could be passed intoglmmPen_FA. SeeglmmPen_FA for further details (e.g. arguments related to variable selectionthat could be used to fit a single penalized GLMM model).

a non-negative numeric penalty parameter for the fixed effects coefficients

a non-negative numeric penalty parameter for the (grouped) random effectscovariance coefficients

a sequence of non-negative numeric penalty parameters for the fixed and random effect coefficients (lambda0_seq andlambda1_seq, respectively). IfNULL, then a sequence will be automatically calculated. See 'Details' section for more details on these default calculations.

positive integer specifying number of penalty parametersto use for the fixed and random effects penalty parameters. Default set to 10. Only usedif eitherlambda0_seq orlambda1_seq remain unspecified by the user(one or both of these arguments set toNULL) and, consequently, one or more default sequences needto be calculated.

character string of "abbrev" (default) or "full_grid" indicating if the search of models over the penalty parameter space should be the full grid search (total number of models equals'nlambda'^2 or length('lambda0_seq')*length('lambda1_seq')) or an abbreviated grid search.The abbreviated grid search is described in more detail in the Details section. Te authorshighly recommend the abbreviated grid search.

character string specifying the selection criteria used to select the 'best' model.Default "BICq" option specifies the BIC-ICQ criterion (Ibrahim et al (2011)<doi:10.1111/j.1541-0420.2010.01463.x>),which requires a fit of a 'minimum penalty' model; a small penalty (the minimum of the penalty sequence) is used for the fixed and random effects. See "Details" section for what these small penalties will be.The "BICh" option utilizes the hybrid BIC value described in Delattre, Lavielle, and Poursat (2014) <doi:10.1214/14-EJS890>.The regular "BIC" option penalty term uses (total non-zero coefficients)*(length(y) = total numberobservations). The "BICNgrp" option penalty term uses (total non-zero coefficients)*(nlevels(group) = numbergroups).

logical value specifying if the log likelihood (and log-likelihood based calculations BIC, BICh, and BICNgrp) should be calculated for all of the models in the selection procedure. If BIC-ICQ is used for selection, the log-likelihood is not needed for each model. However, if users are interestedin comparing the best models from BIC-ICQ and other BIC-type selection criteria, settinglogLik_calc toTRUE will calculate these other quantities for all of the models.

numeric fraction between 0 and 1. The sequence of the lambda penalty parametersranges from the maximum lambda where all fixed and random effects are penalized to 0 and a minimum lambda value, which equals a small fraction of the maximum lambda. The parameterlambda.min specifies this fraction. Default value is set toNULL, whichautomatically selectslambda.min to equal 0.01 when the number of observations isgreater than the number of fixed effects predictors and 0.05 otherwise.Only usedif eitherlambda0_seq orlambda1_seq remain unspecified by the user(one or both of these sequence arguments set toNULL) and, consequently, one or more default sequences needto be calculated.

logical value indicating whether pre-screening should be performed beforemodel selection (defaultTRUE). If the number of random effects covariatesconsidered is 4 or less, thenno pre-screening will be performed. Pre-screening removes random effects from considerationduring the model selection process, which can significantly speed up the algorithm.See "Details" section for a further discussion.

numeric fraction between 0 and 1. During pre-screening and the minimal penaltymodel fit for the BIC-ICQ calculation, the small penalty used on the random effect isthe fractionlambda.min.presc multiplied by the maximum penalty parameter that penalizesall fixed and random effects to 0. If left asNULL, the default value is 0.01 when the numberof random effect covariates is 10 or less and 0.05 otherwise.Only used iflambda1_seq remains unspecified by the user(this argument set toNULL so the random effects penalty parameter sequenceneeds to be automatically calculated) AND either the pre-screening procedure is selected by the argumentpre_screen or the BIC-ICQ is selected as the model selection criteria,i.e.,BIC_option = "BICq". See the "Details" section for a further discussion.

character string indicating how the random effect covariancematrix should be initialized at the beginning of the algorithmwhen penalties are applied to the coefficients. If "none" (default), all random effect predictors are initialized to have non-zero variances.If "fixef", the code first examines the initialized fixed effects (initialized using a regularpenalized GLM), and only the random effect predictors that are initialized with non-zero fixed effectsare initialized with non-zero variances.

a non-negative numeric convergence criteria for the convergence of the EM algorithm. Default is 0.0015. EM algorithm is considered to have converge if the average Euclidean distance between the current coefficient estimates and the coefficient estimates fromt EM iterations back is less thanconv_EMmcc times in a row.Seet andmcc for more details.

a non-negative numeric convergence criteria for the convergence of the grouped coordinate descent loop within the M step of the EM algorithm. Default 0.0005.

positive integer specifying the number of posterior samples to use asburn-in for each E step in the EM algorithm. If set toNULL, the algorithm inputsthe following defaults: Default 250 when the number of random effects predictors is less than or equal to 10; default 100 otherwise. Function will not allownMC_burninto be less than 100.

a positive integer for the initial number of Monte Carlo draws. If set toNULL, the algorithm inputs the following defaults: Default 250 when the number of random effects predictors is less than or equal to 10; default 100 otherwise.

a positive integer for the maximum number of allowed Monte Carlo draws usedin each step of the EM algorithm. If set toNULL, the algorithm inputs the following defaults: When the number of random effect covariates is greater than 10,the default is set to 1000; when the number of random effect covariates is10 or less, the default is set to 2500.

a positive integer for the number of posterior samples to save from the finalmodel. These posterior samples can be used for diagnostic purposes, seeplot_mcmc.Default set to 5000.

a positive integer for the maximum number of allowed EM iterations. If set toNULL, then the algorithm inputs the following defaults:Default equals 50 for the Binomial and Poisson families, 65 for the Gaussian family.

a positive integer for the maximum number of allowed iterations for thecoordinate descent algorithms used within the M-step of each EM iteration. Default equals 50.

positive integer specifying the number of posterior samples to use within the Pajor log-likelihood calculation. Default is 10^4; minimum allowed value is 5000.

the convergence criteria is based on the average Euclidean distance between the most recent coefficient estimates and the coefficient estimates fromt EM iterations back.Positive integer, default equals 2.

the number of times the convergence criteria must be met before the algorithm isseen as having converged (mcc for 'meet condition counter'). Default set to 2. Value restricted to be no less than 2.

character string specifying whether the posterior samples of the random effectsshould be drawn using Stan (default, from package rstan) or the Metropolis-within-Gibbs procedure incorporating an adaptive random walk sampler ("random_walk") or anindependence sampler ("independence"). If using the random walk sampler, seeadaptControlfor some additional control structure parameters.

either the character string "recommend" or a positive number specifying the starting values to initialize the variance of the covariance matrix. ForglmmPen,the default "recommend" firstfits a simple model with a fixed and random intercept only using the lme4 R package, seeglmer for details on fitting generalized linear mixed models orlmer for details on fitting linear mixed models. The random intercept variance estimate from this model is then multiplied by 2 and used as the starting variance. ForglmmPen_FA, the default is set to 0.10 (seeB_init_type for further information).

positive numeric value indicating the starting step size to use in the Majorization-Minimization scheme of the M-step. Only relevant when the distributional assumptionused is not Binomial or Gaussian with canonical links (e.g. Poisson with log link)

logical value indicating whether covariates shouldstandardized (TRUE, default) or unstandardized (FALSE) before beingused within the algorithm. Ifstandardization = TRUE, then the standardized covariateswill also be used to create the Z matrix used in the estimation of the random effects.

character string indicating the type of convergence criteria to use within the EM algorithm to determine when a model has converged. The default is "AvgEuclid1",which calculates the average Euclidean distance between the most recent coefficient vector andthe coefficient vectort EM iterations back (Euclidean distance divided by the numberof non-zero coefficientst EM iterations back). Alternative convergence options include"maxdiff", which determines convergence based on the maximum difference between the coefficient vectors; "AvgEuclid2", which is similar to "AvgEuclid1" except it divides the Euclidean distance by the square-rootof the number of non-zero coefficients; and "Qfun", which determines convergence based onthe relative difference in the Q-function estimates calculated with the most recent coefficient vector and the coefficient vectort EM iterations back.

character string indicating how the B matrix within theglmmPen_FAmethod should be initialized. (This argument is not used within theglmmPen function.)The default "deterministic" initializes all non-zero variance and covariance values of the random effect covariance matrix to the value ofvar_start,such that each non-zero element of the B matrix issqrt(var_start / r) (wherer isthe number of latent factors). Option "data" is similar to "deterministic", but thevar_start value is the default data-driven variance estimate used inglmmPen (see argumentvar_start for more details).

pglmmObj object output fromglmm,glmmPen, orglmmPen_FineSearch

potentially further arguments passed from other methods

an R object of classpglmmObj

logical value; defaultTRUE indicates that only the fixed effects should be used in the fitted value/prediction, whileFALSE indicates that both the fixed and random effects posterior modes should be used in the fitted value/prediction

logical value used informula;TRUE indicates that only the formula elements relating to the random effects should be returned

in the case of model.frame, apglmmObj object

See details oftype options for each function under "Functions" section.

optional new data.frame containing the same variables used in the model fit procedure

number of significant digits for printing; default of 4

type of residuals to summarize in output. Seepredict.pglmmObjfor residual options available.

vector of fixed effects coefficients

matrix of random effects coefficients for each explanatory variable for each level of the grouping factor

random effects covariance matrix

if family is Gaussian, returns the residual error variance

Samples from the posterior distribution of the random effects,taken at the end of the model fit (after convergence or after maximum iterations allowed).Can be used for diagnositics purposes. Note: These posterior samples are from a single chain.

character string for type of sampling used to calculate the posterior samplesin the E-step of the algorithm

matrix of results from all model fits during variable selection (if selectionperformed). Output for each model includes: penalty parameters for fixed (lambda0) and random (lambda1) effects, BIC-derived quantities and the log-likelihood (note: the argumentsBIC_option andlogLik_calc inselectControldetermine which of these quantities are calculated for each model), the number of non-zero fixed and random effects (includes intercept),number of EM iterations used for model fit, whether or not the model converged (0 for no vs 1 for yes), and the fixed and random effects coefficients

results from the 'best' model fit; see results_all for details. BICh, BIC, BICNgrp, and LogLik computed for this best model if not previously calculated.

Family

list of penalty information

arguments plugged intoglmm,glmmPen,glmm_FA, orglmmPen_FA

formula

names of fixed effects variables

list of data used in model fit, including the response y, the fixed effects covariates matrix X, the random effects model matrix Z (which is composed of values from the standardized fixed effects model matrix), the grouping factor, offset, model frame,and standarization information used to standardize the fixed effects covariates

Information about the optimization of the 'best' model

optimization parameters used for the model fit

materials that can be used to initialize another E-step, if desired

list of materials to perform diagnositics on the Metropolis-within-Gibbssample chains, including the Gibbs acceptance rates (included for both the independenceand adaptive random walk samplers) and the final proposal standard deviations (included for the adaptive random walk sampler only))

list of output related to estimation of number of latent common factors, r. Only relevant for the output of functionsglmm_FA andglmmPen_FA, which are currently in development and are not yet ready forgeneral use.

a two-sided linear formula object describing both the fixed effects and random effects part of the model, with the response on the left of a ~ operator and the terms, separated by + operators, on the right. The response must be aSurv object (seeSurv from thesurvival package).Random-effects terms are distinguished by vertical bars ("|") separating expression for design matrices from the grouping factor.formula should be of the same format needed forglmer in packagelme4. Only one grouping factor will be recognized. The random effects covariates need to be a subset of the fixed effects covariates.The offset must be specified outside of the formula in the 'offset' argument.

an optional data frame containing the variables named informula. Ifdata is omitted, variables will be taken from the environment offormula.

character string specifying whether the covariance matrix should be unstructured("unstructured") or diagonal with no covariances between variables ("independent").Default is set toNULL. Ifcovar is set toNULL and the number of random effectspredictors (not including the intercept) is greater than or equal to 10 (i.e. high dimensional), then the algorithm automatically assumes an independent covariance structure andcovar is set to "independent". Otherwise ifcovaris set toNULL and the number of random effects predictors is less than 10, then thealgorithm automatically assumes an unstructured covariance structure andcovar is set to "unstructured".

This can be used to specify ana priori known component to be included in the linear predictor during fitting. Default set toNULL (no offset). If the data argument is notNULL, this should be a numeric vector of length equal to the number of cases (the length of the response vector). If the data argument specifies a data.frame, the offsetargument should specify the name of a column in the data.frame.

a structure of class "optimControl" created from functionoptimControl that specifies several optimization parameters. See the documentation foroptimControl for more details on defaults.

a list of class "adaptControl" from functionadaptControl containing the control parameters for the adaptive random walk Metropolis-within-Gibbs procedure. Ignored ifoptimControl parametersampler is set to "stan" (default) or "independence".

an integer specifying print output to include as function runs. Default value is 0. See Details for more information about output provided when trace = 0, 1, or 2.

a list of class "selectControl" or "lambdaControl" resulting fromselectControl orlambdaControl containing additional control parameters.When functionglmm is used,the algorithm may be run using one specific set ofpenalty parameterslambda0 andlambda1 by specifying such values inlambdaControl(). The default forglmm is to run the model fit with no penalization (lambda0 =lambda1 = 0).When functionglmmPen is run,tuning_options is specified usingselectControl(). See thelambdaControl andselectControl documentation for further details.

a structure of class "survivalControl" created from functionsurvivalControl that specifies several parameters needed to properly fit the input survival data using a piecewise constant hazard mixed model. See the documentation forsurvivalControl for more details on defaults.

a logical value indicating if additional output should be given showing theprogress of the fit procedure. IfTRUE, such output includes iteration-level informationfor the fit procedure (iteration number EM_iter,number of MCMC samples nMC, average Euclidean distance between current coefficients and coefficientsfrom t–defined inoptimControl–iterations back EM_conv, and number of non-zero fixed and random effects covariatesnot including the intercept). Additionally,progress = TRUEgives some other information regarding the progress of the variable selection procedure, including the model selection criteria and log-likelihood estimatesfor each model fit.Default isTRUE.

additional arguments that could be passed intophmmPen. SeephmmPenfor further details.

a two-sided linear formula object describing both the fixed effects and random effects part of the model, with the response on the left of a ~ operator and the terms, separated by + operators, on the right. The response must be aSurv object (seeSurv from thesurvival package).Random-effects terms are distinguished by vertical bars ("|") separating expression for design matrices from the grouping factor.formula should be of the same format needed forglmer in packagelme4. Only one grouping factor will be recognized. The random effects covariates need to be a subset of the fixed effects covariates.The offset must be specified outside of the formula in the 'offset' argument.

an optional data frame containing the variables named informula. Ifdata is omitted, variables will be taken from the environment offormula.

character string specifying whether the covariance matrix should be unstructured("unstructured") or diagonal with no covariances between variables ("independent").Default is set toNULL. Ifcovar is set toNULL and the number of random effectspredictors (not including the intercept) is greater than or equal to 10 (i.e. high dimensional), then the algorithm automatically assumes an independent covariance structure andcovar is set to "independent". Otherwise ifcovaris set toNULL and the number of random effects predictors is less than 10, then thealgorithm automatically assumes an unstructured covariance structure andcovar is set to "unstructured".

This can be used to specify ana priori known component to be included in the linear predictor during fitting. Default set toNULL (no offset). If the data argument is notNULL, this should be a numeric vector of length equal to the number of cases (the length of the response vector). If the data argument specifies a data.frame, the offsetargument should specify the name of a column in the data.frame.

Optional vector of 0's and 1's of the same length as the number of fixed effects covariatesused in the model. Value 0 indicates the variable should not have its fixed effect coefficientpenalized, 1 indicates that it can be penalized. Order should correspond to the same order of the fixed effects given in the formula.

character describing the type of penalty to use in the variable selection procedure.Options include 'MCP', 'SCAD', and 'lasso'. Default is MCP penalty. If the random effect covariancematrix is "unstructured", then a group MCP, group SCAD, or group LASSO penalty is used on the random effects coefficients. See Breheny and Huang (2011) <doi:10.1214/10-AOAS388> and Breheny and Huang (2015) <doi:10.1007/s11222-013-9424-2> for details of these penalties.

Tuning parameter for the Mnet estimator which controls the relative contributions from the MCP/SCAD/LASSO penalty and the ridge, or L2, penalty.alpha=1 is equivalent to the MCP/SCAD/LASSO penalty, whilealpha=0 is equivalent to ridge regression. However,alpha=0 is not supported;alpha may be arbitrarily small, but not exactly zero

The scaling factor of the MCP and SCAD penalties. Not used by LASSO penalty.Default is 4.0 for SCAD and 3.0 for MCP. See Breheny and Huang (2011) <doi:10.1214/10-AOAS388> and Breheny and Huang (2015) <doi:10.1007/s11222-013-9424-2> for further details.

a structure of class "optimControl" created from functionoptimControl that specifies several optimization parameters. See the documentation foroptimControl for more details on defaults.

a list of class "adaptControl" from functionadaptControl containing the control parameters for the adaptive random walk Metropolis-within-Gibbs procedure. Ignored ifoptimControl parametersampler is set to "stan" (default) or "independence".

an integer specifying print output to include as function runs. Default value is 0. See Details for more information about output provided when trace = 0, 1, or 2.

a list of class "selectControl" or "lambdaControl" resulting fromselectControl orlambdaControl containing additional control parameters.When functionglmm is used,the algorithm may be run using one specific set ofpenalty parameterslambda0 andlambda1 by specifying such values inlambdaControl(). The default forglmm is to run the model fit with no penalization (lambda0 =lambda1 = 0).When functionglmmPen is run,tuning_options is specified usingselectControl(). See thelambdaControl andselectControl documentation for further details.

a structure of class "survivalControl" created from functionsurvivalControl that specifies several parameters needed to properly fit the input survival data using a piecewise constant hazard mixed model. See the documentation forsurvivalControl for more details on defaults.

an optional character string expressing the path and file basename of a file combination that will file-back or currently file-backs abig.matrix of the posterior samples from the minimal penalty model used for the BIC-ICQ calculation used for model selection. T(BIC-ICQ reference: Ibrahim et al (2011)<doi:10.1111/j.1541-0420.2010.01463.x>). If this argument isspecified asNULL (default) and BIC-ICQ calculations are requested (seeselectControl)for details), the posterior sampleswill be saved in the file combination 'BICq_Posterior_Draws.bin' and 'BICq_Posterior_Draws.desc'in the working directory.See 'Details' section for additional details about the required format ofBICq_posteriorand the file-backed big matrix.

a logical value indicating if additional output should be given showing theprogress of the fit procedure. IfTRUE, such output includes iteration-level informationfor the fit procedure (iteration number EM_iter,number of MCMC samples nMC, average Euclidean distance between current coefficients and coefficientsfrom t–defined inoptimControl–iterations back EM_conv, and number of non-zero fixed and random effects covariatesnot including the intercept). Additionally,progress = TRUEgives some other information regarding the progress of the variable selection procedure, including the model selection criteria and log-likelihood estimatesfor each model fit.Default isTRUE.

a two-sided linear formula object describing both the fixed effects and random effects part of the model, with the response on the left of a ~ operator and the terms, separated by + operators, on the right. The response must be aSurv object (seeSurv from thesurvival package).Random-effects terms are distinguished by vertical bars ("|") separating expression for design matrices from the grouping factor.formula should be of the same format needed forglmer in packagelme4. Only one grouping factor will be recognized. The random effects covariates need to be a subset of the fixed effects covariates.The offset must be specified outside of the formula in the 'offset' argument.

an optional data frame containing the variables named informula. Ifdata is omitted, variables will be taken from the environment offormula.

This can be used to specify ana priori known component to be included in the linear predictor during fitting. Default set toNULL (no offset). If the data argument is notNULL, this should be a numeric vector of length equal to the number of cases (the length of the response vector). If the data argument specifies a data.frame, the offsetargument should specify the name of a column in the data.frame.

a list of class "rControl" from functionrControl containing the control parameters for the estimation of the number of latentfactors to use in theglmmPen_FA andglmm_FA estimation procedures.

Optional vector of 0's and 1's of the same length as the number of fixed effects covariatesused in the model. Value 0 indicates the variable should not have its fixed effect coefficientpenalized, 1 indicates that it can be penalized. Order should correspond to the same order of the fixed effects given in the formula.

character describing the type of penalty to use in the variable selection procedure.Options include 'MCP', 'SCAD', and 'lasso'. Default is MCP penalty. If the random effect covariancematrix is "unstructured", then a group MCP, group SCAD, or group LASSO penalty is used on the random effects coefficients. See Breheny and Huang (2011) <doi:10.1214/10-AOAS388> and Breheny and Huang (2015) <doi:10.1007/s11222-013-9424-2> for details of these penalties.

Tuning parameter for the Mnet estimator which controls the relative contributions from the MCP/SCAD/LASSO penalty and the ridge, or L2, penalty.alpha=1 is equivalent to the MCP/SCAD/LASSO penalty, whilealpha=0 is equivalent to ridge regression. However,alpha=0 is not supported;alpha may be arbitrarily small, but not exactly zero

The scaling factor of the MCP and SCAD penalties. Not used by LASSO penalty.Default is 4.0 for SCAD and 3.0 for MCP. See Breheny and Huang (2011) <doi:10.1214/10-AOAS388> and Breheny and Huang (2015) <doi:10.1007/s11222-013-9424-2> for further details.

a structure of class "optimControl" created from functionoptimControl that specifies several optimization parameters. See the documentation foroptimControl for more details on defaults.

a list of class "adaptControl" from functionadaptControl containing the control parameters for the adaptive random walk Metropolis-within-Gibbs procedure. Ignored ifoptimControl parametersampler is set to "stan" (default) or "independence".

an integer specifying print output to include as function runs. Default value is 0. See Details for more information about output provided when trace = 0, 1, or 2.

a list of class "selectControl" or "lambdaControl" resulting fromselectControl orlambdaControl containing additional control parameters.When functionglmm is used,the algorithm may be run using one specific set ofpenalty parameterslambda0 andlambda1 by specifying such values inlambdaControl(). The default forglmm is to run the model fit with no penalization (lambda0 =lambda1 = 0).When functionglmmPen is run,tuning_options is specified usingselectControl(). See thelambdaControl andselectControl documentation for further details.

a structure of class "survivalControl" created from functionsurvivalControl that specifies several parameters needed to properly fit the input survival data using a piecewise constant hazard mixed model. See the documentation forsurvivalControl for more details on defaults.

an optional character string expressing the path and file basename of a file combination that will file-back or currently file-backs abig.matrix of the posterior samples from the minimal penalty model used for the BIC-ICQ calculation used for model selection. T(BIC-ICQ reference: Ibrahim et al (2011)<doi:10.1111/j.1541-0420.2010.01463.x>). If this argument isspecified asNULL (default) and BIC-ICQ calculations are requested (seeselectControl)for details), the posterior sampleswill be saved in the file combination 'BICq_Posterior_Draws.bin' and 'BICq_Posterior_Draws.desc'in the working directory.See 'Details' section for additional details about the required format ofBICq_posteriorand the file-backed big matrix.

a logical value indicating if additional output should be given showing theprogress of the fit procedure. IfTRUE, such output includes iteration-level informationfor the fit procedure (iteration number EM_iter,number of MCMC samples nMC, average Euclidean distance between current coefficients and coefficientsfrom t–defined inoptimControl–iterations back EM_conv, and number of non-zero fixed and random effects covariatesnot including the intercept). Additionally,progress = TRUEgives some other information regarding the progress of the variable selection procedure, including the model selection criteria and log-likelihood estimatesfor each model fit.Default isTRUE.

a two-sided linear formula object describing both the fixed effects and random effects part of the model, with the response on the left of a ~ operator and the terms, separated by + operators, on the right. The response must be aSurv object (seeSurv from thesurvival package).Random-effects terms are distinguished by vertical bars ("|") separating expression for design matrices from the grouping factor.formula should be of the same format needed forglmer in packagelme4. Only one grouping factor will be recognized. The random effects covariates need to be a subset of the fixed effects covariates.The offset must be specified outside of the formula in the 'offset' argument.

an optional data frame containing the variables named informula. Ifdata is omitted, variables will be taken from the environment offormula.

This can be used to specify ana priori known component to be included in the linear predictor during fitting. Default set toNULL (no offset). If the data argument is notNULL, this should be a numeric vector of length equal to the number of cases (the length of the response vector). If the data argument specifies a data.frame, the offsetargument should specify the name of a column in the data.frame.

a list of class "rControl" from functionrControl containing the control parameters for the estimation of the number of latentfactors to use in theglmmPen_FA andglmm_FA estimation procedures.

a structure of class "optimControl" created from functionoptimControl that specifies several optimization parameters. See the documentation foroptimControl for more details on defaults.

a list of class "adaptControl" from functionadaptControl containing the control parameters for the adaptive random walk Metropolis-within-Gibbs procedure. Ignored ifoptimControl parametersampler is set to "stan" (default) or "independence".

an integer specifying print output to include as function runs. Default value is 0. See Details for more information about output provided when trace = 0, 1, or 2.

a list of class "selectControl" or "lambdaControl" resulting fromselectControl orlambdaControl containing additional control parameters.When functionglmm is used,the algorithm may be run using one specific set ofpenalty parameterslambda0 andlambda1 by specifying such values inlambdaControl(). The default forglmm is to run the model fit with no penalization (lambda0 =lambda1 = 0).When functionglmmPen is run,tuning_options is specified usingselectControl(). See thelambdaControl andselectControl documentation for further details.

a structure of class "survivalControl" created from functionsurvivalControl that specifies several parameters needed to properly fit the input survival data using a piecewise constant hazard mixed model. See the documentation forsurvivalControl for more details on defaults.

a logical value indicating if additional output should be given showing theprogress of the fit procedure. IfTRUE, such output includes iteration-level informationfor the fit procedure (iteration number EM_iter,number of MCMC samples nMC, average Euclidean distance between current coefficients and coefficientsfrom t–defined inoptimControl–iterations back EM_conv, and number of non-zero fixed and random effects covariatesnot including the intercept). Additionally,progress = TRUEgives some other information regarding the progress of the variable selection procedure, including the model selection criteria and log-likelihood estimatesfor each model fit.Default isTRUE.

additional arguments that could be passed intophmmPen_FA. SeephmmPen_FAfor further details.

an object of classpglmmObj

a character string or a vector of character strings specifying which graphicaldiagnostics to provide. Options include a sample path plot (default, "sample.path"), autocorrelation plots ("autocorr"), histograms ("histogram"), cumulative sum plots ("cumsum"),and all four possible plot options ("all"). While the "all" option will produce all fourpossible plots, subsets of the types of plots (e.g. sample path plots and autocorrelation plotsonly) can be specified with a vector of the relevant character strings (e.g. c("sample.path","autocorr"))

a character string or a vector of character strings specifying which groups should have diagnostics provided. The names of the groups match the input group factor levels.Default is set to 'all' for all groups.

a character string or a vector of character strings specifying which variablesshould have diagnostics provided. Default is set to'all', which picks all variables with non-zero random effects.Tip: can find the names of the random effect variables inthe output sigma matrix found in thepglmmObj object, runsigma(object).

if TRUE, specifies that the groups factor should be converted to numeric values. This option could be used to ensure that the organization of the groups is in the proper numeric order (e.g. groups with levels 1-10 are ordered 1-10, not 1, 10, 2-9).

optional binwidth argument forgeom_histogram from theggplot2 package. Default set toNULL, which specifies the defaultgeom_histogram binwidth. This argument only applies if the "histogram" plot type is selected.

positive integer specifying number of latent common factors to assume in the model. IfNULL (default), this value estimated from the data. Seer_est_method for available estimation procedures, and the Detailssection for further details on the general estimation procedure.Ifr is specified, the no estimation procedure is performed and the algorithmuses the input value or r. All other parameters for this function arerelevant for the estimation procedure.

positive integer specifying maximum number of latent factors to consider.IfNULL (default), this value is automatically calculated.

character string indicating method used to estimate numberof latent factorsr. Default "GR" uses the Growth Ratio method ofAhn and Horenstein (2013) (<doi:10.3982/ECTA8968>). Other available options include "ER" forthe Eigenvalue Ratio method of Ahn and Horenstein (2013) (<doi:10.3982/ECTA8968>) and "BN1" or "BN2",the Bai and Ng (2002) method (<dio:10.1111/1468-0262.00273>) using one of two penalties: (1)(d + p) / (d p) log(d p/(d+p)) or(2)(d + p) / (d p) log(min(d,p)) where d is the number of groups inthe data and p is the number of total random effect covariates (including the intercept)

positive integer specifying the total number of pseudo randomeffect estimates to use in the estimation procedure for the number of latent factorsr, which is restricted to be no less than 25. If thissize is greaterthan the number of groups in the data (i.e.~the number of levels of the groupingvariable), then a sampling procedure is used to increase the number of pseudo estimatesto the value ofsize if the value ofsample isTRUE.

logical value indicating if the total number of pseudo random effectestimates to use in the estimation procedure for the number of latent common factors rshould be larger than the number of unique groups in the data, where the number of pseudo estimates are increased to the value ofsize using a sampling procedure. Default isFALSE. IfTRUE, the sampling procedure is onlyperformed if the value ofsize is greater than the number of groups in the data.

integer specifying total number of samples to generate

integer specifying total number of covariates to generate (values randomly generated from the standard normal distribution)

integer specifying how may of the covariates should havenon-zero fixed and random effects

number of studies/groups to have in the data

non-negative value specifying the standard deviation of therandom effects covariance matrix (applied to the non-zero random effects)

character string specifying which family to generate data from.Family options include "binomial" (default), "poisson", and "gaussian".

optional value to specify correlation between covariatesin the model matrix. DefaultNULL, only available withinsim.data.

integer to use for the setting of a random seed

integer of 0 or 1 indicating whether the observations shouldbe equally distributed among the groups (0) or unequally distributed (1).

numeric vector of the fixed effects (including intercept)

non-negative integer specifying the number of covariates with a zero-valued fixed effect but a non-zero random effect.

non-negative value specifying the standard deviation of thesimulated covariates (drawn from a normal distribution with mean 0,standard deviationsd_x)

matrix specifying the factor loadings matrix for the random effects,only used withinsim.data.FA.Dimensions: number of columns is the number of random effects (including the intercept),and number of rows is the number of latent common factors (r).The random effect covariance matrix is specified as Sigma = B x t(B) + diag(sd_raneff)

positive integer specifying number of latent common factors that describe the random effects,only used withinsim.data.FA

vector of cut points to use for the time intervals when simulating piecewise exponential data. Length of cut points must equal length oflhaz_vals, and the value of the first cut point must be 0.

vector of the log baseline hazard values for each time interval (whichcorrespond to the time intervals defined by thecut_points argument) withinpiecewise exponential data. Hazards are assumed to be constant within each time interval.

character specifying type of censoring to implement. Default "unif" specifiesuniform censoring from 0 tocens_max. The option "exp" specifies exponentialcensoring with rateexp_rate

numeric value used to characterize the range of the uniform censoring procedure (from 0 tocens_max)

numeric value used to characterize the exponential censoring rate (where rateis defined as the rate used inrexp)

numeric value that gives the log of the scale parameter for the Weibull distribution (for description of Weibull scale parameter without log transformation, see "lambdas" argument insimsurv and the lambda notation in section "Weibull distribution" in the simsurv vignette https://cran.r-project.org/web/packages/simsurv/vignettes/simsurv_technical.html)

numeric value > 0 that gives the shape parameter for the Weibull distribution (for description of Weibull shape paraemeter,see "gammas" argument insimsurv and the gamma notation in section "Weibulldistribution" in the simsurv vignette https://cran.r-project.org/web/packages/simsurv/vignettes/simsurv_technical.html)

vector of the response

model matrix for the fixed effects

model matrix for the random effects, organized first by variableand then by group

number of non-zero fixed effects

values of the random effects for each variable for each level of the grouping factor

grouping factor

model matrix for just the non-zero fixed effects

positive integer specifying the number of time intervals to include inthe piecewise constant hazard model assumptions for the sampling step. Default is 8.General recommendation: use between 5 and 10 intervals. See the Details section foradditional information.

character specifying how the time intervals are calculated.Options include 'equal' (default), 'manual', or 'group'.If 'equal' (default), time intervalsare calculated such that there are approximately equal numbers of events per time interval.If 'manual', the user needs to inputtheir own cut points (seecut_points for details).If 'group', time intervals are calculated such that there are approximatelyequal numbers of events per time interval AND there are at least 4 events observedby each group within each time interval. The input number of time intervalscut_nummay be modified to a lower number in order to accomplish this goal. This option is generally difficult to perform when there are a large number of groups in the data.

numeric vector specifying the value of the cut points to usein the calculation of the time intervals for the piecewise constant hazard model. Ifinterval_type set to 'equal' or 'group', then this argument is not utilized.Ifinterval_type set to 'manual', then this argument is required.First value must be 0, and all values must be ordered smallest to largest.

positive numeric value (greater than 1) used to scale the time variable in the survival data. In order to calculate the piecewise constant hazard mixed model,the log of the time a subject survived within a particular time intervalis used as an offset in the model fit. Sometimes multiplying the time scaleby a factor greater than 1 improves the stability of the model fit algorithm.

response, which must be aSurv object (seeSurv from thesurvival package)

matrix of fixed effects covariates

matrix of random effects covariates

vector specifying the group assignment for each subject

vector specifying the offset. This can be used to specify ana priori known component to be included in the linear predictor during fitting. Default set toNULL (no offset). If the data argument is notNULL, this should be a numeric vector of length equal to the number of cases (the length of the response vector).

a structure of class "survivalControl" created from functionsurvivalControl that specifies several parameters needed to properly fit the input survival data using a piecewise constant hazard mixed model. See the documentation forsurvivalControl for more details on defaults.