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rMIDAS demonstration

rMIDAS’s core functionalities are demonstrated here by using it to impute missing responses to the 2018 Cooperative Congressional Election Study (CCES), an electoral survey conducted in the United States whose size and complexity poses computational difficulties for many existing multiple imputation algorithms.

The full CCES has 525 columns and 60,000 rows, the latter corresponding to individual survey respondents. After removing variables that either require extensive preprocessing or are unhelpful for imputation purposes — open-ended string variables, time indices, and ZIP code variables — the dataset contains 349 columns. The vast majority of these variables are categorical and must therefore be one-hot encoded for most multiple imputation software packages — that is, each 1 × 60,000 categorical variable with K unique classes must be expanded into a K × 60,000 matrix of 1s and 0s — increasing their number to 1,914.

Loading and preprocessing the data

We begin by loading rMIDAS. If R is used interactively, then by calling library(rMIDAS) a user will be prompted if rMIDAS should be set up automatically.

library(rMIDAS)
set.seed(89)

We then read in the formatted CCES data and sort variables into continuous, binary, and categorical types.

data_0 <- fread("cces_jss_format.csv")

We then preprocess the data into the format required by the MIDAS algorithm using the rMIDAS::convert() function, which only requires vectors of binary and categorical variables. We set minmax_scale = TRUE to scale continuous variables between 0 and 1.

vals <- apply(data_0,2, function (x) length(unique(x)[!is.na(unique(x))]))
cont_vars <- c("citylength_1","numchildren","birthyr")
cat_vars <- names(vals)[vals > 2 & !(names(vals) %in% cont_vars)]
bin_vars <- names(vals)[vals == 2]
data_conv <- convert(data_0,
                     bin_cols = bin_vars,
                     cat_cols = cat_vars,
                     minmax_scale = TRUE)

Imputation

To train the MIDAS network, we pass our preprocessed data to the rMIDAS::train() function and specify network hyperparameters. Unlike in MIDASpy, we do not need to additionally declare categorical variables and their classes with the softmax_columns argument.

data_train <- train(data_conv,
                    layer_structure= c(256,256),
                    vae_layer= FALSE,
                    seed= 89,
                    input_drop = 0.75,
                    training_epochs = 10)
## Initialising Python connection

We then generate 10 completed datasets using the rMIDAS::complete() function, saving them in memory. The function returns scaled continuous variables and one-hot encoded categorical variables to their original form using the parameters saved in the preprocessing step. Unlike in the MIDASpy demonstration, by default this function converts imputed probabilities for binary variables into binary categories by taking draws from a binomial distribution with $P(x = 1) = p$. Categorical labels are similarly assigned by taking a weighted random draw using the vector of predicted probabilities from the imputed data. This behavior can be disabled by setting fast = TRUE when calling rMIDAS::complete(), in which case binary variables are assigned 1 if $p$ ≥ 0.5, and the label with the highest predicted probability is chosen for categorical variables

imputations <- complete(data_train, m=10)
## Imputations generated. Completing post-imputation transformations.

Analysis of completed datasets

We estimate a linear probability model by means of the rMIDAS::combine() function.

for (d in 1:10) {
  imputations[[d]]$age <- 2018 - imputations[[d]]$birthyr
  imputations[[d]]$CC18_415a <- ifelse(imputations[[d]]$CC18_415a == 1, 1, 0)}

combine("CC18_415a ~ age", imputations)
## No model family specified -- assuming gaussian model.

##          term     estimate    std.error statistic       df       p.value
## 1 (Intercept)  0.861297604 0.0060302023 142.83063 310.3369 3.757040e-285
## 2         age -0.004141295 0.0001148537 -36.05713 531.2022 7.103309e-145

Users can ensure exact reproducibility of analytical results by saving completed datasets to disk. The trained rMIDAS model is also saved by default in the R session directory.