MNAR means the probability of missingness still depends on the unobserved value even after conditioning on observed data. Standard imputation under MAR may then be biased unless the missingness mechanism is modelled or sensitivity analysis is performed.
MNAR means the probability of missingness still depends on the unobserved value even after conditioning on observed data. Standard imputation under MAR may then be biased unless the missingness mechanism is modelled or sensitivity analysis is performed.
The practical value of MNAR: missing not at random comes from understanding both the transformation and the boundary around it: what information is allowed to enter, what assumption is being made, and how you know the result is still valid after the transformation.
A beginner-friendly way to reason about it is to start with a tiny case where the correct result can be checked independently. Once the mechanism is clear, scale the exact same reasoning to larger tables, pipelines or models.
Use domain knowledge to identify self-selection or censoring mechanisms and perform sensitivity analyses under plausible alternative assumptions.
The interactive view uses a concept-specific plot when the topic maps naturally to one; otherwise it uses a workflow view instead of leaving a broken placeholder.
People with very high debt may be systematically less likely to report debt even after accounting for observed income and age.
A useful diagnostic question is: Could the same code still run successfully if the analytical assumption were wrong? If yes, add an explicit validation check rather than relying on execution success.
Keep the example small enough that you can inspect each stage manually.
# Purpose: demonstrate MNAR: missing not at random with a small, inspectable example.
# Follow the comments and printed stages to connect each operation with its result.
# Import the library or helper used in this example.
# Step 1 — Import the module so its functions/classes are available to the rest of this example.
import numpy as np
# Import the library or helper used in this example.
# Step 2 — Import the module so its functions/classes are available to the rest of this example.
import pandas as pd
# Import the library or helper used in this example.
# Step 3 — Import only the named objects needed by the following steps, keeping dependencies explicit.
from sklearn.compose import ColumnTransformer
# Import the library or helper used in this example.
# Step 4 — Import only the named objects needed by the following steps, keeping dependencies explicit.
from sklearn.impute import SimpleImputer
# Import the library or helper used in this example.
# Step 5 — Import only the named objects needed by the following steps, keeping dependencies explicit.
from sklearn.preprocessing import OneHotEncoder
# Create a small labelled dataset that is easy to inspect by eye.
# Step 6 — Construct `X` as a tabular object with named columns for inspectable analysis.
X = pd.DataFrame({
"age": [22,25,np.nan,31,35,38,41,44,48,np.nan,56,60],
"income": [42,45,48,np.nan,55,59,62,66,70,74,np.nan,82],
"city": ["A","B","A","B",None,"C","A","C","B","A","C",None]
})
# Print this intermediate result so you can verify the workflow step by step.
# Step 7 — Display the current value explicitly so the result/state can be inspected during execution.
print("STEP 1 · Shape:", X.shape)
# Print this intermediate result so you can verify the workflow step by step.
# Step 8 — Display the current value explicitly so the result/state can be inspected during execution.
print("STEP 1 · Missing counts:", X.isna().sum().to_dict())
# Store this intermediate value with a descriptive name for the next step.
# Step 9 — Compute the right-hand expression and store its result in `pre` for the next step.
pre = ColumnTransformer([
("num", SimpleImputer(strategy="median"), ["age","income"]),
("cat", SimpleImputer(strategy="most_frequent"), ["city"])
], verbose_feature_names_out=False)
# Learn the transformation from this data and apply it in one step.
# Step 10 — Fit the transformation on the training input and immediately transform that same input.
Xt = pre.fit_transform(X)
# Print this intermediate result so you can verify the workflow step by step.
# Step 11 — Display the current value explicitly so the result/state can be inspected during execution.
print("STEP 2 · Missing after imputation:", int(pd.isna(Xt).sum()))
# Print this intermediate result so you can verify the workflow step by step.
# Step 12 — Display the current value explicitly so the result/state can be inspected during execution.
print("STEP 3 · First four transformed rows:")
# Print this intermediate result so you can verify the workflow step by step.
# Step 13 — Display the current value explicitly so the result/state can be inspected during execution.
print(Xt[:4])STEP 1 · Shape: (12, 3)
STEP 1 · Missing counts: {'age': 2, 'income': 2, 'city': 2}
STEP 2 · Missing after imputation: 2
STEP 3 · First four transformed rows:
[[22.0 42.0 'A']
[25.0 45.0 'B']
[39.5 48.0 'A']
[31.0 60.5 'B']]