lambdaControl: Control of Penalization Parameters and Selection Criteria

In hheiling/glmmPen: High Dimensional Penalized Generalized Linear Mixed Models (pGLMM)

Control of Penalization Parameters and Selection Criteria

Description

Constructs control structures for penalized mixed model fitting.

Usage

lambdaControl(lambda0 = 0, lambda1 = 0)

selectControl(
  lambda0_seq = NULL,
  lambda1_seq = NULL,
  nlambda = 10,
  search = c("abbrev", "full_grid"),
  BIC_option = c("BICq", "BICh", "BIC", "BICNgrp"),
  logLik_calc = switch(BIC_option[1], BICq = FALSE, TRUE),
  lambda.min = NULL,
  pre_screen = TRUE,
  lambda.min.presc = NULL
)

Arguments

lambda0	a non-negative numeric penalty parameter for the fixed effects coefficients
lambda1	a non-negative numeric penalty parameter for the (grouped) random effects covariance coefficients
lambda0_seq, lambda1_seq	a sequence of non-negative numeric penalty parameters for the fixed and random effect coefficients (lambda0_seq and lambda1_seq, respectively). If NULL, then a sequence will be automatically calculated. See 'Details' section for more details on these default calculations.
nlambda	positive integer specifying number of penalty parameters to use for the fixed and random effects penalty parameters. Default set to 10. Only used if either lambda0_seq or lambda1_seq remain unspecified by the user (one or both of these arguments set to NULL) and, consequently, one or more default sequences need to be calculated.
search	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 authors highly recommend the abbreviated grid search.
BIC_option	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 number observations). The "BICNgrp" option penalty term uses (total non-zero coefficients)*(nlevels(group) = number groups).
logLik_calc	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 interested in comparing the best models from BIC-ICQ and other BIC-type selection criteria, setting logLik_calc to TRUE will calculate these other quantities for all of the models.
lambda.min	numeric fraction between 0 and 1. The sequence of the lambda penalty parameters ranges 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 parameter lambda.min specifies this fraction. Default value is set to NULL, which automatically selects lambda.min to equal 0.01 when the number of observations is greater than the number of fixed effects predictors and 0.05 otherwise. Only used if either lambda0_seq or lambda1_seq remain unspecified by the user (one or both of these sequence arguments set to NULL) and, consequently, one or more default sequences need to be calculated.
pre_screen	logical value indicating whether pre-screening should be performed before model selection (default TRUE). If the number of random effects covariates considered is 4 or less, then no pre-screening will be performed. Pre-screening removes random effects from consideration during the model selection process, which can significantly speed up the algorithm. See "Details" section for a further discussion.
lambda.min.presc	numeric fraction between 0 and 1. During pre-screening and the minimal penalty model fit for the BIC-ICQ calculation, the small penalty used on the random effect is the fraction lambda.min.presc multiplied by the maximum penalty parameter that penalizes all fixed and random effects to 0. If left as NULL, the default value is 0.01 when the number of random effect covariates is 10 or less and 0.05 otherwise. Only used if lambda1_seq remains unspecified by the user (this argument set to NULL so the random effects penalty parameter sequence needs to be automatically calculated) AND either the pre-screening procedure is selected by the argument pre_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.

Details

If left as the default NULL values, the lambda0_seq and lambda1_seq numeric sequences are automatically calculated. The sequence will be calculated in the same manner as ncvreg calculates the range: the max value (let's denote this as lambda_max) penalizes all fixed and random effects to 0, the min value is a small portion of max (lambda.min*lambda_max), and the sequence is composed of nlambda values ranging from these min and max values spread evenly on the log scale. Unlike ncvreg, the order of penalty values used in the algorithm must run from the min lambda to the max lambda (as opposed to running from max lambda to min lambda). The length of the sequence is specified by nlambda. By default, these sequences are calculated using LambdaSeq.

The lambda0 and lambda1 arguments used within the glmm function allow for a user to fit a model with a single non-zero penalty parameter combination. However, this is generally not recommended.

Abbreviated grid search: The abbreviated grid search proceeds in two stages. In stage 1, the algorithm fits the following series of models: the fixed effects penalty parameter remains a fixed value evaluated at the minimum of the fixed effects penalty parameters, and all random effects penalty parameters are examined. The 'best' model from this first stage of models determines the optimum random effect penalty parameter. In stage 2, the algorithm fits the following series of models: the random effects penalty parameter remains fixed at the value of the optimum random effect penalty parameter (from stage 1) and all fixed effects penalty parameters are considered. The best overall model is the best model from stage 2. This reduces the number of models considered to length('lambda0_seq') + length('lambda1_seq'). The authors found that this abbreviated grid search worked well in simulations, and performed considerably faster than the full grid search that examined all possible fixed and random effect penalty parameter combinations.

The arguments nlambda and lambda.min are only used if one or both of the lambda0_seq and lambda1_seq penalty sequences (corresponding to the fixed and random effects penalty sequences, respectively) remain unspecified by the user (one or both of these arguments left as NULL), indicating that the algorithm needs to calculate default penalty sequences.

The argument lambda.min.presc is only used under the following condition: lambda1_seq remains unspecified by the user (this argument set to NULL so the random effects penalty parameter sequence needs to be calculated) AND either the pre-screening procedure is selected by the argument pre_screen or the BIC-ICQ is selected as the model selection criteria, i.e., BIC_option = "BICq". If lambda1_seq is specified by the user, the minimum value in that sequence will be used as the random effect penalty in the pre-screening procedure and/or the minimal penalty model for the BIC-ICQ calculation.

BIC-ICQ calculation: This model selection criteria requires the fitting of a 'minimal penalty' model, which fits a model with a small penalty on the fixed and random effects. For the fixed effects penalty, the minimal penalty is: (a) 0 if the number of fixed effects covariates is 4 or less or (b) the minimum fixed effect penalty from the fixed effects penalty sequence (either from the default sequence or from the sequence specified by the user). For the random effects penalty, the minimal penalty is (a) 0 if the number of random effects covariates is 4 or less; (b) the minimum random effect penalty from the random effects penalty sequence specified by the user, or (c) lambda.min.presc multiplied to the lambda_max maximum penalty specified above when a default random effects penalty sequence is calculated.

Pre-screening: The minimum fixed effects penalty used in the pre-screening stage will be the minimum penalty of the fixed effects penalty sequence, lambda0_seq. The minimum random effects penalty used in the pre-screening stage will be either (a) the minimum random effects penalty in the sequence lambda1_seq if this sequence specified by the user, or (b) lambda.min.pres x lambda_max, where lambda_max was described above.

Value

The *Control functions return a list (inheriting from class "pglmmControl") containing parameter values that determine settings for variable selection.

hheiling/glmmPen documentation built on Jan. 15, 2024, 11:47 p.m.