missDiag {missDiag}

Comparing Observed and Imputed Values under MAR and MCAR

Description

Function to compute discrepancy statistics comparing the (reweighted) density of imputed and observed values. To compute the weights balancing covariates that are part of the missing data mechanism, the function relies on either entropy balancing or stable balancing weights.

Usage

missDiag(
  original,
  imputed,
  formula = NULL,
  skip_n = 25,
  scale = FALSE,
  adjust = "ebal",
  use_imputed_cov = TRUE,
  convert = c("numeric"),
  categories = 3,
  verbose = 0,
  output_diag = FALSE,
  ebal_param = param_ebal(),
  sbw_param = param_sbw(),
  cobalt_param = param_cobalt()
)

Arguments

original

data frame with missing values.

imputed

an imputed data frame, a list of imputed data frames or a mids object from the mice::mice() package.

formula

two-sided formula with the variables to compute discrepancy statistics (right-hand side) and variables to balance (left-hand side).

skip_n

skip variables with fewer than skip_n missing values.

scale

scale the design matrix?

adjust

either 'none', 'sbw' or 'ebal'.

use_imputed_cov

use imputed covariates?

convert

vector of variable types to bin before coercion (ignored if use_imputed_cov=TRUE).

categories

how many bins (ignored if use_imputed_cov=TRUE).

verbose

one of three levels (0,1 or 2).

output_diag

add covariate balance statistics to output?

ebal_param

list of parameters passed to ebal.

sbw_param

list of parameters passed to sbw.

cobalt_param

list of parameters passed to cobalt.

Details

Let y be a variable with observed and imputed values and let m be a corresponding indicator if a value in y is observed (0) or imputed (1). We use X to denote all K covariates and x_k as the k^th covariate.

By default, missDiag computes discrepancy statistics (balance statistics) comparing the distribution of observed and imputed values, ie. comparing f(y|m=1) vs. f(y|m=0). The distribution are expected to be equal under MCAR.

If the data are missing at random (MAR), set adjust="ebal" or adjust="sbw", to construct weights to balance the covariate distribution X before computing the discrepancy statistics.

The left-hand side (lhs) of the formula gives the name of y while the right-hand side (rhs) defines the covariates X to balance under MAR. Rhs variables are transformed into a numeric matrix via the stats::model.matrix() function. Therefore factor and string variables are dummy encoded and functional transformations such as log() are applied.

To run missDiag on many y variables sequentially, supply a list of formulas or name all y variables on the lhs separating each variable with a "|", e.g. y1 | y2 ~ x1 + ... + xK.

If formula=NULL, missDiag runs on all variables with at least n_skip missing values in original. Weights are constructed such that all X covariates are balanced (if adjust!='none').

If use_imputed_cov=FALSE, all imputed values in the covariates X are deleted, variables are coerced to factor variables with missing values encoded as one category. Numerical variables are binned by quantiles before coercion. Use the parameter categories to define the number of bins. By default only variables of class "numeric" are binned. Use convert = c("numeric", "integer") to also bin integer variables before coercion to factor variables.

To balance the covariates, missDiag computes weights using either the ebal::ebalance() function or the sbw::sbw() function. These two packages have to be installed separately by the user.

To pass parameters to the sbw::sbw() or ebal::ebalance() use the functions param_sbw() and param_sbw() to generate valid parameter lists and pass these lists via the parameters sbw_param or ebal_param.

To display information about the computations set verbose to the value 1 (some information) or 2 (more information when constructing weights).

To compute the discrepancy statistics, missDiag relies on the function cobalt::bal.tab() from the cobalt package. To pass parameters to this function use param_cobalt() to generate a valid parameter list and pass this list via the parameter cobalt_param.

Value

A single data.frame with the results for each imputed dataset and all lhs variables.

If output_diag=FALSE, the dataset only includes the discrepancy statistics comparing y's observed values and imputed values.

If y is continuous, there will be exactly one row per imputed dataset. The discrepancy statistics are reported in the respective columns. For a categorical y cobalt computes discrepancy statistics for all K categories which means that there will be K rows for each imputed dataset in the output. The label for each category is listed in vname.

If the default settings are adopted, the dataset includes the following discrepancy statistics for continuous variables:

• diff_adj: Standardized mean difference

• v_ratio_adj: Variance ratio

• ks_adj: Kolmogorov–Smirnov statistic

• ovl_adj: 1-Overlap coefficient

No variance ratio is reported for categorical variables.

If output_diag=TRUE, the dataset also includes the balance statistics for all K covariates.

These balance statistics are useful to diagnose if the fitted weights are successful in balancing the covariate distribution.

For these diagnostics the column vname lists the covariate name (for continuous variables) or the covariate category (for categorical variables).

References

Moritz Marbach. 2021. Choosing Imputation Models.

José R Zubizarreta. 2015. Stable Weights that Balance Covariates for Estimation with Incomplete Outcome Data, Journal of the American Statistical Association, 110(511): 910-922.

Jens Hainmueller. 2012. Entropy Balancing for Causal Effects: A Multivariate Reweighting Method to Produce Balanced Samples in Observational Studies, Political Analysis 20(1): 25–46.

Examples

# Compare random value imputation 
# with predictive mean imputation 
# under MCAR

diag_rng <- missDiag( 
 original=anes08, 
 imputed=anes08_rng, 
 verbose = 1,
 adjust = 'none',
 formula = time ~ .)

diag_pmm <- missDiag( 
 original=anes08, 
 imputed=anes08_pmm, 
 verbose = 1,
 adjust = 'none',
 formula = time ~ .)

# SMD: 

 mean(diag_pmm$diff_adj)
 mean(diag_rng$diff_adj)

# log(Variance ratio)
 mean(log(diag_pmm$v_ratio_adj))
 mean(log(diag_rng$v_ratio_adj))

# KS
 mean(diag_pmm$ks_adj)
 mean(diag_rng$ks_adj)

# 1-OVL
 mean(diag_pmm$ovl_adj)
 mean(diag_rng$ovl_adj)