Demystifying the Black Box: How One Developer Rebuilt MICE from Scratch in R

By Tech & Data Science Desk
Published: Special Feature

Introduction: Unlocking the Statistical "Magic"

For many data scientists and statisticians, dealing with missing data often feels like navigating an arcane ritual. Among the most popular and robust tools for this task is MICE—Multiple Imputation by Chained Equations. To practitioners, MICE can frequently feel like a black box: feed in an incomplete dataset, run a few functions, and emerge on the other side with pristine, fully imputed data frames ready for analysis.

But how does it actually work beneath the hood?

Motivated by a desire to demystify this statistical wizardry, data enthusiast and developer Ken Koon Wong embarked on a grueling, multi-week coding journey to build a working version of MICE entirely from scratch using R. Eschewing the comfort of the industry-standard mice package—at least initially—Wong set out to write the machinery of chained equations line by line. The resulting experiment not only successfully mirrored the behavior of the professional package but also provided a masterclass in the foundational mechanics of missing data imputation.

Main Facts: The Anatomy of MICE and the Experiment

To understand the scope of Wong’s achievement, it is necessary to examine what MICE actually accomplishes. When datasets suffer from missing values, a naive approach is to plug in a single best guess, such as the column mean or median. However, this method artificially shrinks standard errors, tricking analysts into a false sense of precision because it acts as if the imputed values were known with absolute certainty.

MICE solves this by embracing uncertainty:

1. Plausible Draws: It fills in missing gaps several times with plausible random guesses, creating multiple complete datasets.
2. Chained Equations: Instead of building one massive, complex joint model for all variables simultaneously, MICE cycles through each incomplete variable one by one. It fits a simple regression using all other variables as predictors, feeding the freshly imputed values directly into the next step.
3. Pooling via Rubin’s Rules: Once multiple datasets are generated and analyzed independently, their results are synthesized using specialized pooling formulas to account for both within-imputation and between-imputation variance.

In his independent replication, Wong constructed a simulated Data Generating Process (DGP) containing 1,000 observations across continuous and binary variables (p1 through p5, alongside an outcome variable). He deliberately introduced missingness across three distinct mechanisms:

• MCAR (Missing Completely at Random)
• MAR (Missing at Random)
• MNAR (Missing Not at Random)

Working through the complex loops required to index missing values, fill initial random draws, iterate regressions, and pool the final coefficients, Wong ultimately created a from-scratch R implementation that stood shoulder-to-shoulder with the gold-standard package.

Chronology: A Bumpy Journey from Conception to Code

The path to decoding MICE was far from linear. Wong’s project timeline spans a rigorous developmental process fraught with conceptual hurdles, iterative debugging, and conceptual breakthroughs.

Phase 1: Conceptualization and Initial Setup (Early October)

The project kicked off with a deep dive into the theoretical literature surrounding chained equations. Recognizing that coding underlying optimization routines like Ordinary Least Squares (OLS) or Maximum Likelihood Estimation (MLE) from absolute scratch would unnecessarily bloat the project, Wong decided to leverage base R modeling functions (lm and glm) while building the structural iteration loops himself.

Phase 2: Indexing and the First False Start

The first major technical hurdle involved indexing every missing value and mapping them neatly into a tracking data frame alongside metadata detailing their data types (numeric vs. integer/binary).

However, progress stalled early on due to a fundamental conceptual misconception. In his initial drafts, Wong attempted to average out the imputed values across the 10 datasets prematurely—a mathematically flawed approach.

"My initial go was a wrong approach where I average out the 10 datasets imputed data… then realized that that is not the proper pooling," Wong noted.

Phase 3: Utilizing AI as a Conversational Tutor

To course-correct, Wong turned to Large Language Models (LLMs) as interactive debugging partners. Through an iterative back-and-forth dialogue, he refined his understanding of how chained equations must operate sequentially across multiple iterations and chains before the values stabilize.

Phase 4: Final Execution and Validation

By late October, the loops were fully operational. Wong successfully wrote functions to:

• Extract predictor vectors (grab_xvec)
• Dynamically generate formula strings (gen_formula)
• Fill missing matrix slots (missing_fill and missing_fill_full)
• Execute 10 independent chains running 10 iterations each

Finally, he applied Rubin’s rules and Barnard–Rubin degrees of freedom adjustments to pool the results properly, capping off the project by benchmarking his custom code against the official mice library.

Supporting Data: Code Architecture and Benchmark Results

Wong’s implementation relies heavily on modern tidyverse syntax, mapping functions, and base R statistical modeling. Below is an overview of how the core simulation and iteration pipeline was established.

1. Simulating the Data and Missingness Mechanisms

library(tidyverse)
library(broom)

set.seed(1)
n <- 1000
p1 <- rnorm(n)
p2 <- rnorm(n, 0.5*p1)
p3 <- rnorm(n, 0.4*p1 + 0.3*p2)
p4 <- rbinom(n, 1, 0.5)
p5 <- rbinom(n, 1, plogis(-0.5 + 0.3*p1 - 0.2*p2 + 0.1*p3))
outcome <- rbinom(n, 1, plogis(-0.5 + 0.3*p1 - 0.2*p2 + 0.1*p3 + 0.5*p4 + 0.4*p5))

df <- tibble(p1,p2,p3,p4,p5,outcome)

# Introducing Missing Data Mechanisms (MCAR, MAR, MNAR)
p1_miss <- ifelse(runif(n) < 0.1, NA, p1)
p3_miss <- ifelse(runif(n) < 0.2, NA, p3)
p2_miss <- ifelse(runif(n) < plogis(-0.5 + 0.3*p1), NA, p2)
p4_miss <- ifelse(runif(n) < plogis(-0.5 + 0.3*p1 - 0.2*p2), NA, p4)
p5_miss <- ifelse(runif(n) < plogis(-0.5 + 0.8*p5), NA, p5)

df_miss <- tibble(p1 = p1_miss, p2 = p2_miss, p3 = p3_miss, p4 = p4_miss, p5 = p5_miss, outcome = outcome)

2. The Iterative Chained Equations Loop

The core engine of Wong’s script cycles through missing columns across multiple chains and iterations, fitting linear and logistic regressions dynamically:

col_missing <- empty_df |&gt; distinct(col) |&gt; pull()
empty_df_mice <- tibble()

for (chain in 1:10) 
  impute_df <- fill_empty_df(empty_df)

  for (iter in 1:10) 
    for (i in col_missing) &gt; filter(col == i) 

    if (iter == 10) &gt; mutate(chain = chain)) 
    
  

Comparative Visual Results

When comparing the final pooled coefficients against standard benchmarks, the results were striking:

• Custom MICE (Purple): Lined up remarkably close to the official mice package (Red) across every single model coefficient.
• Full-Data Fit (Teal): Maintained tight confidence intervals based on complete, uncorrupted data.
• Complete-Case Analysis (Green): Suffered from severe wandering estimates and vastly wider confidence intervals due to dropping rows with missing values entirely.

Official Responses and Expert Observations

While Wong’s project was executed as an independent educational exercise, the implications of building statistical tools from the ground up resonate deeply within the broader data science community.

Data engineering experts emphasize that recreating established algorithms is one of the most effective pedagogical strategies for mastering advanced analytics. By forcing oneself to handle edge cases—such as distinguishing continuous numeric modeling from binary logistic modeling within automated loops—practitioners transition from passive tool consumers to active algorithmic architects.

Furthermore, statisticians reviewing the experiment noted intriguing behavior regarding the MNAR (Missing Not at Random) variable p5. Technical theory dictates that standard MICE implementations can struggle or yield biased estimates when data is MNAR without specialized auxiliary variables. However, in this single simulation run, both the custom script and the official package performed surprisingly well—a reminder of the stochastic quirks inherent to random sampling and single-run simulations.

Implications: Why Demystifying "Magic" Matters

Ken Koon Wong’s successful recreation of MICE carries several vital takeaways for the data science ecosystem:

1. Bridging Theory and Practice: Algorithms like MICE often suffer from adoption hurdles because users are intimidated by their mathematical complexity. By breaking the process down into manageable coding blocks (indexing, filling, iterating, fitting, and pooling), complex statistical theory becomes accessible.
2. The Value of AI-Assisted Learning: The project highlights the evolving role of Large Language Models as interactive, patient programming tutors. Rather than replacing human critical thinking, LLMs served as a sounding board to help troubleshoot logical flaws in the pooling methodology.
3. Robustness of Established Standards: That a from-scratch script written by an independent developer could independently converge on results nearly identical to a mature, highly optimized package speaks volumes about the transparent, logical nature of modern statistical theory when correctly translated into code.

Ultimately, Wong’s messy, iterative journey proves that statistical magic is rarely magic at all—it is simply rigorous logic, well-sequenced equations, and a healthy dose of persistence.