Estimate step or beta selection model — selection

Estimate step or beta selection model, with standard errors and confidence intervals based on either cluster-robust variance estimators (i.e., sandwich estimators) or cluster-level bootstrapping to handle dependent effect size estimates.

Usage

selection_model(
  data,
  yi,
  vi,
  sei,
  pi,
  ai,
  cluster,
  selection_type = c("step", "beta"),
  steps = NULL,
  mean_mods = NULL,
  var_mods = NULL,
  sel_mods = NULL,
  sel_zero_mods = NULL,
  priors = define_priors(),
  subset = NULL,
  estimator = "CML",
  vcov_type = "robust",
  CI_type = "large-sample",
  conf_level = 0.95,
  theta = NULL,
  optimizer = NULL,
  optimizer_control = list(),
  use_jac = NULL,
  bootstrap = "none",
  R = 1999,
  retry_bootstrap = 0L,
  ...
)

Arguments

data: data.frame or tibble containing the meta-analytic data
yi: vector of effect sizes estimates.
vi: vector of sample variances. If vi is specified, then the sei argument must be omitted.
sei: vector of sampling standard errors. If sei is specified, then the vi argument must be omitted.
pi: optional vector of one-sided p-values. If not specified, p-values will be computed from yi and sei.
ai: optional vector of analytic weights.
cluster: vector indicating which observations belong to the same cluster.
selection_type: character string specifying the type selection model to estimate, with possible options "step" or "beta".
steps: If selection_type = "step", a numeric vector of one or more values specifying the thresholds (or steps) where the selection probability changes, with a default of steps = .025. If selection_type = "beta", then a numeric vector of two values specifying the thresholds beyond which the selection function is truncated, with a default of steps = c(.025, .975).
mean_mods: optional model formula for moderators related to average effect size magnitude.
var_mods: optional model formula for moderators related to effect size heterogeneity.
sel_mods: optional model formula for moderators related to the probability of selection. Only relevant for selection_type = "step".
sel_zero_mods: optional model formula for moderators related to the probability of selection for p-values below the lowest threshold value of steps. Only relevant for selection_type = "step".
priors: a selmodel_prior object that defines priors (i.e., penalty terms) for model parameters, with a default of define_priors(). Set to NULL to obtain unpenalized estimates.
subset: optional logical expression indicating a subset of observations to use for estimation.
estimator: vector indicating whether to use the composite marginal likelihood estimator (option "CML") or the augmented and reweighted Gaussian likelihood estimator (option "ARGL" or "ARGL-full"). If selection_type = "beta", only the composite marginal likelihood estimator, "CML", is available. For step function models, both estimators are available.
vcov_type: character string specifying the type of variance-covariance matrix to calculate, with possible options "robust" for robust or cluster-robust standard errors, "model-based" for model-based standard errors, or "none".
CI_type: character string specifying the type of confidence interval to calculate, with possible options "large-sample" for large-sample normal interval (the default), "percentile" for a percentile interval, "BCa" for a bias-corrected-and-accelerated interval, "bias-corrected" for a bias-corrected percentile interval (without acceleration correction), "normal" for a standard normal interval, "basic" for a basic interval, "student" for a studentized interval, or "none".
conf_level: desired coverage level for confidence intervals, with the default value set to .95.
theta: optional numeric vector of starting values to use in optimization routines.
optimizer: character string indicating the optimizer to use. Ignored if estimator = "ARGL" or "ARGL-full".
optimizer_control: an optional list of control parameters to be used for optimization
use_jac: logical indicating whether to use the Jacobian of the estimating equations for optimization. If NULL (the default), it will be reset to FALSE if estimator = "CML" or to TRUE if estimator = "ARGL"
bootstrap: character string specifying the type of bootstrap to run, with possible options "none" (the default), "exponential" for the fractionally re-weighted cluster bootstrap, "multinomial" for a conventional clustered bootstrap, or , "two-stage" for a two-stage clustered bootstrap.
R: number of bootstrap replications, with a default of 1999.
retry_bootstrap: number of times to re-draw a bootstrap sample in the event of non-convergence, with a default of 0.
...: further arguments passed to simhelpers::bootstrap_CIs.

Value

An object of class "selmodel" containing the following components:

est: A data frame with parameter estimates, standard errors, and confidence intervals. Note that the results do not include p-values so as to focus interpretation on the parameter estimates, rather than on the statistical significance of any given parameter.
vcov: A matrix containing the estimated variance-covariance matrix of the parameter estiamtes
method: Character string indicating the optimization method used to solve for parameter estimates.
info: Further informaton about the optimization results.
ll: Log likelihood of the model evaluated at the reported parameter estimates.
wpll: Weighted partial log likelihood of the random effects model, with weights corresponding to inverse selection probabilities
n_clusters: Number of independent clusters of effect sizes.
n_effects: Number of effect size estimates in the data.
...: Some additional elements containing information about the methods used to estimate the model.

Examples

res_ML <- selection_model(
  data = self_control,
  yi = g,
  sei = se_g,
  cluster = studyid,
  steps = 0.025,
  estimator = "CML",
  bootstrap = "none"
)

res_ML
#>    param    Est     SE  p_value   CI_lo CI_hi
#>     beta 0.2196 0.0525 2.85e-05 0.11677 0.322
#>     tau2 0.0394 0.0286       NA 0.00951 0.163
#>  lambda1 1.0350 0.5058 9.44e-01 0.39711 2.697
summary(res_ML)
#> Step Function Model 
#>  
#> Call: 
#> selection_model(data = self_control, yi = g, sei = se_g, cluster = studyid, 
#>     steps = 0.025, estimator = "CML", bootstrap = "none")
#> 
#> Number of clusters = 33; Number of effects = 158
#> 
#> Steps: 0.025 
#> Estimator: composite marginal likelihood 
#> Variance estimator: robust 
#> 
#> Log composite likelihood of selection model: -54.97404
#> Inverse selection weighted partial log likelihood: 87.11211 
#> 
#> Mean effect estimates:                                                
#>                                     Large Sample
#>  Coef. Estimate Std. Error  p-value Lower  Upper
#>   beta     0.22     0.0525 2.85e-05 0.117  0.322
#> 
#> Heterogeneity estimates:                                                 
#>                                      Large Sample
#>  Coef. Estimate Std. Error p-value   Lower  Upper
#>   tau2   0.0394     0.0286     --- 0.00951  0.163
#> 
#> Selection process estimates:
#>  Step: 0 < p <= 0.025; Studies: 18; Effects: 32                                                 
#>                                      Large Sample
#>    Coef. Estimate Std. Error p-value Lower  Upper
#>  lambda0        1        ---     ---   ---    ---
#> 
#>  Step: 0.025 < p <= 1; Studies: 24; Effects: 126                                                 
#>                                      Large Sample
#>    Coef. Estimate Std. Error p-value Lower  Upper
#>  lambda1     1.03      0.506   0.944 0.397    2.7

# configure progress bar
progressr::handlers(global = TRUE)
#> Error in globalCallingHandlers(condition = global_progression_handler): should not be called with handlers on the stack

res_hybrid <- selection_model(
  data = self_control,
  yi = g,
  sei = se_g,
  cluster = studyid,
  steps = 0.025,
  estimator = "ARGL",
  bootstrap = "multinomial",
  CI_type = "percentile",
  R = 19
)

res_hybrid
#>    param    Est     SE percentile_lower percentile_upper
#>     beta 0.2194 0.0483          0.07355            0.281
#>     tau2 0.0393 0.0296          0.00351            0.155
#>  lambda1 1.0332 0.1502          0.19581            2.674
summary(res_hybrid)
#> Step Function Model with Cluster Bootstrapping 
#>  
#> Call: 
#> selection_model(data = self_control, yi = g, sei = se_g, cluster = studyid, 
#>     steps = 0.025, estimator = "ARGL", CI_type = "percentile", 
#>     bootstrap = "multinomial", R = 19)
#> 
#> Number of clusters = 33; Number of effects = 158
#> 
#> Steps: 0.025 
#> Estimator: augmented and reweighted Gaussian likelihood 
#> Variance estimator: robust 
#> Bootstrap type: multinomial 
#> Number of bootstrap replications: 19 
#> 
#> Log composite likelihood of selection model: -54.9741
#> Inverse selection weighted partial log likelihood: 87.26052 
#> 
#> Mean effect estimates:                                               
#>                            Percentile Bootstrap
#>  Coef. Estimate Std. Error      Lower     Upper
#>   beta    0.219     0.0483     0.0735     0.281
#> 
#> Heterogeneity estimates:                                               
#>                            Percentile Bootstrap
#>  Coef. Estimate Std. Error      Lower     Upper
#>   tau2   0.0393     0.0296    0.00351     0.155
#> 
#> Selection process estimates:
#>  Step: 0 < p <= 0.025; Studies: 18; Effects: 32                                                 
#>                              Percentile Bootstrap
#>    Coef. Estimate Std. Error      Lower     Upper
#>  lambda0        1        ---        ---       ---
#> 
#>  Step: 0.025 < p <= 1; Studies: 24; Effects: 126                                                 
#>                              Percentile Bootstrap
#>    Coef. Estimate Std. Error      Lower     Upper
#>  lambda1     1.03       0.15      0.196      2.67