Pool Model Parameters — pool_parameters • parameters

This function "pools" (i.e. combines) model parameters in a similar fashion as mice::pool(). However, this function pools parameters from parameters_model objects, as returned by model_parameters().

Usage

pool_parameters(
  x,
  exponentiate = FALSE,
  effects = "fixed",
  component = "all",
  verbose = TRUE,
  ...
)

Arguments

x: A list of parameters_model objects, as returned by model_parameters(), or a list of model-objects that is supported by model_parameters().
exponentiate: Logical, indicating whether or not to exponentiate the coefficients (and related confidence intervals). This is typical for logistic regression, or more generally speaking, for models with log or logit links. It is also recommended to use exponentiate = TRUE for models with log-transformed response values. For models with a log-transformed response variable, when exponentiate = TRUE, a one-unit increase in the predictor is associated with multiplying the outcome by that predictor's coefficient. Note: Delta-method standard errors are also computed (by multiplying the standard errors by the transformed coefficients). This is to mimic behaviour of other software packages, such as Stata, but these standard errors poorly estimate uncertainty for the transformed coefficient. The transformed confidence interval more clearly captures this uncertainty. For compare_parameters(), exponentiate = "nongaussian" will only exponentiate coefficients from non-Gaussian families.
effects: Should parameters for fixed effects ("fixed"), random effects ("random"), or both fixed and random effects ("all") be returned? By default, the variance components for random effects are returned. If group-level effects are requested, "grouplevel" returns the group-level random effects (BLUPs), while "random_total" return the overall (sum of fixed and random) effects (similar to what coef() returns). Using "grouplevel" is equivalent to setting group_level = TRUE. The effects argument only applies to mixed models. If the calculation of random effects parameters takes too long, you may use effects = "fixed".
component: Which type of parameters to return, such as parameters for the conditional model, the zero-inflation part of the model, the dispersion term, or other auxiliary parameters be returned? Applies to models with zero-inflation and/or dispersion formula, or if parameters such as sigma should be included. May be abbreviated. Note that the conditional component is also called count or mean component, depending on the model. There are three convenient shortcuts: component = "all" returns all possible parameters. If component = "location", location parameters such as conditional, zero_inflated, or smooth_terms, are returned (everything that are fixed or random effects - depending on the effects argument - but no auxiliary parameters). For component = "distributional" (or "auxiliary"), components like sigma, dispersion, or beta (and other auxiliary parameters) are returned.
verbose: Toggle warnings and messages.
...: Arguments passed down to model_parameters(), if x is a list of model-objects. Can be used, for instance, to specify arguments like ci or ci_method etc.

Value

A data frame of indices related to the model's parameters.

Details

Averaging of parameters follows Rubin's rules (Rubin, 1987, p. 76). The pooled degrees of freedom is based on the Barnard-Rubin adjustment for small samples (Barnard and Rubin, 1999).

Note

Models with multiple components, (for instance, models with zero-inflation, where predictors appear in the count and zero-inflation part, or models with dispersion component) may fail in rare situations. In this case, compute the pooled parameters for components separately, using the component argument.

Some model objects do not return standard errors (e.g. objects of class htest). For these models, no pooled confidence intervals nor p-values are returned.

References

Barnard, J. and Rubin, D.B. (1999). Small sample degrees of freedom with multiple imputation. Biometrika, 86, 948-955. Rubin, D.B. (1987). Multiple Imputation for Nonresponse in Surveys. New York: John Wiley and Sons.

Examples

# example for multiple imputed datasets
data("nhanes2", package = "mice")
imp <- mice::mice(nhanes2, printFlag = FALSE)
models <- lapply(1:5, function(i) {
  lm(bmi ~ age + hyp + chl, data = mice::complete(imp, action = i))
})
pool_parameters(models)
#> # Fixed Effects
#> 
#> Parameter   | Coefficient |   SE |          95% CI | Statistic |    df |      p
#> -------------------------------------------------------------------------------
#> (Intercept) |       18.85 | 3.53 | [ 10.94, 26.77] |      5.34 |  9.64 | < .001
#> age [40-59] |       -5.62 | 2.00 | [-10.04, -1.21] |     -2.81 | 10.73 | 0.017 
#> age [60-99] |       -7.05 | 2.50 | [-12.72, -1.37] |     -2.82 |  8.69 | 0.021 
#> hyp [yes]   |        2.23 | 2.13 | [ -2.54,  6.99] |      1.05 |  9.72 | 0.321 
#> chl         |        0.05 | 0.02 | [  0.01,  0.10] |      2.63 |  8.20 | 0.029 
#> 
#> Uncertainty intervals (equal-tailed) and p-values (two-tailed)
#>   computed using a Wald distribution approximation.

# should be identical to:
m <- with(data = imp, exp = lm(bmi ~ age + hyp + chl))
summary(mice::pool(m))
#>          term   estimate std.error statistic        df      p.value
#> 1 (Intercept) 18.8529658 3.5332535  5.335866  9.637102 0.0003741459
#> 2    age40-59 -5.6214485 2.0001740 -2.810480 10.729821 0.0173287192
#> 3    age60-99 -7.0451215 2.4952100 -2.823458  8.693991 0.0206115436
#> 4      hypyes  2.2276804 2.1295899  1.046061  9.722954 0.3208412270
#> 5         chl  0.0531414 0.0201819  2.633122  8.195111 0.0294228344

# For glm, mice used residual df, while `pool_parameters()` uses `Inf`
nhanes2$hyp <- datawizard::slide(as.numeric(nhanes2$hyp))
imp <- mice::mice(nhanes2, printFlag = FALSE)
models <- lapply(1:5, function(i) {
  glm(hyp ~ age + chl, family = binomial, data = mice::complete(imp, action = i))
})
m <- with(data = imp, exp = glm(hyp ~ age + chl, family = binomial))
# residual df
summary(mice::pool(m))$df
#> [1] 19.248074 19.248074 19.248074  5.431369
# df = Inf
pool_parameters(models)$df_error
#> [1] Inf Inf Inf Inf
# use residual df instead
pool_parameters(models, ci_method = "residual")$df_error
#> [1] 19.248074 19.248074 19.248074  5.431369