Reproducible analysis template
Missing Data and Multiple Imputation
A reproducible workflow for longitudinal psychology research
Dissertation Stats Helper
2026-09-23
Purpose
Missing data affect more than sample size. They can change which participants contribute to an analysis, weaken precision, and bias estimates when the analysis and missingness assumptions do not fit the study. This workflow demonstrates a transparent multiple-imputation process for a longitudinal psychology study containing continuous, binary, and ordinal variables.
The example follows five connected decisions:
- describe what is missing and when;
- state plausible missingness assumptions without claiming they are proven;
- build an imputation model that is at least as rich as the analysis model;
- diagnose the algorithm and completed values; and
- pool the focal models and examine sensitivity to departures from missing at random.
Standalone product and reusable module
The report is a standalone worked example. The sourced file
R/missing_data_module.R is also designed for reuse in
Regression Outcomes, Growth Modeling, Mediation and Conditional Process,
Psychometrics, and other Dissertation Stats Helper products.
| Component | Standalone use | Reusable use |
|---|---|---|
| Variable-role settings | Documents this study | Replaced by product-specific roles |
| Method assignment | Chooses PMM, logistic, ordinal logistic, and passive methods | Called before another product’s focal model |
| Predictor matrix | Includes outcomes, predictors, auxiliaries, and all waves | Extended with the focal product’s interactions or nonlinear terms |
| Diagnostics | Reviews chains, distributions, and implausible values | Retained as a required pre-analysis checkpoint |
| Pooling | Demonstrates mixed and logistic models | Replaced by the other product’s substantive model |
| Sensitivity analysis | Applies a delta adjustment to a later outcome | Adapted to the outcome and plausible departure in that study |
User settings
Increase the number of imputations when the fraction of missing information is substantial or when stable tail-area estimates are important. Twenty imputations are adequate for this teaching example; real studies may require more.
Simulate and import the example
The complete synthetic reference is used only to confirm that the
simulation behaved as intended. It is never supplied to
mice or any fitted model.
Missingness audit
By variable
| variable | missing_n | missing_percent |
|---|---|---|
| outcome_w4 | 147 | 28.3 |
| engagement_w4 | 144 | 27.7 |
| employed_w4 | 137 | 26.3 |
| sleep_w4 | 133 | 25.6 |
| outcome_w3 | 105 | 20.2 |
| engagement_w3 | 103 | 19.8 |
| sleep_w3 | 98 | 18.8 |
| employed_w3 | 97 | 18.7 |
| outcome_w2 | 61 | 11.7 |
| sleep_w2 | 55 | 10.6 |
| engagement_w2 | 55 | 10.6 |
| employed_w2 | 52 | 10.0 |
| baseline_anxiety | 36 | 6.9 |
| motivation | 36 | 6.9 |
| outcome_w1 | 29 | 5.6 |
| engagement_w1 | 26 | 5.0 |
| employed_w1 | 15 | 2.9 |
| sleep_w1 | 11 | 2.1 |
| participant_id | 0 | 0.0 |
| treatment_num | 0 | 0.0 |
| program_group | 0 | 0.0 |
| age | 0 | 0.0 |
| first_generation | 0 | 0.0 |
| dropout_wave | 0 | 0.0 |
By case
| missing_n | participants |
|---|---|
| 0 | 191 |
| 1 | 143 |
| 2 | 47 |
| 3 | 10 |
| 4 | 23 |
| 5 | 16 |
| 6 | 6 |
| 8 | 25 |
| 9 | 17 |
| 10 | 2 |
| 12 | 30 |
| 13 | 8 |
| 14 | 2 |
By group and study wave
| program_group | missing_percent | participants |
|---|---|---|
| Practice-focused | 16.9 | 259 |
| Research-intensive | 11.7 | 261 |
| wave | missing_percent |
|---|---|
| 1 | 3.9 |
| 2 | 10.7 |
| 3 | 19.4 |
| 4 | 27.0 |
Pattern review
| engagement_w1 | outcome_w1 | baseline_anxiety | motivation | engagement_w2 | outcome_w2 | engagement_w3 | outcome_w3 | engagement_w4 | outcome_w4 | V11 | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| X233 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 |
| X15 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 |
| X12 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 |
| X26 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 2 |
| X12.1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 |
| X1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 3 |
| X11 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 |
| X1.1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 2 |
| X1.2 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 2 |
| X28 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 4 |
| X10 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 |
| X3 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 3 |
| X2 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 2 |
| X1.3 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 2 |
| X2.1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 5 |
| X10.1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 |
| X3.1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 3 |
| X1.4 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 2 |
| X32 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 6 |
| X22 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| X4 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 2 |
| X1.5 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 3 |
| X1.6 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 2 |
| X1.7 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 2 |
| X1.8 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 4 |
| X18 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| X1.9 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 2 |
| X2.2 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 3 |
| X1.10 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 3 |
| X6 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 5 |
| X4.1 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 7 |
| X1.11 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 4 |
| X1.12 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 8 |
| X13 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| X3.2 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 2 |
| X1.13 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 3 |
| X1.14 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 2 |
| X3.3 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 5 |
| X2.3 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 7 |
| X1.15 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 2 |
| X2.4 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 |
| X7 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| X1.16 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 2 |
| X3.4 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 3 |
| X1.17 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 2 |
| X1.18 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 2 |
| X5 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 5 |
| X1.19 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 2 |
| X1.20 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 3 |
| X2.5 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 2 |
| X1.21 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 8 |
| X1.22 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 |
| X1.23 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 3 |
| X1.24 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 5 |
| X | 26 | 29 | 36 | 36 | 55 | 61 | 103 | 105 | 144 | 147 | 742 |
Monotone missingness means that once a participant drops out, all later scheduled measurements are absent. Intermittent missingness creates gaps followed by later observed values. Both occur in this example, so a method designed only for monotone dropout would not describe the full dataset.
What can be said about the mechanism?
- MCAR means the probability of missingness does not depend on observed or unobserved values. It is usually implausible as a blanket explanation in longitudinal behavioral research.
- MAR means missingness may depend on variables included in the imputation model after conditioning on them. MAR is an assumption, not a test result.
- MNAR means missingness still depends on unseen values after conditioning on observed information. Observed data cannot distinguish every MAR explanation from an MNAR explanation.
In this synthetic study, missingness is associated with observed program group, first-generation status, earlier distress, engagement, and wave. Those variables therefore belong in the imputation model. The simulation also contains a small unobserved contribution, which motivates the later delta sensitivity analysis.
Specify the imputation model
| variable | method |
|---|---|
| baseline_anxiety | pmm |
| motivation | polr |
| outcome_w1 | pmm |
| outcome_w2 | pmm |
| outcome_w3 | pmm |
| outcome_w4 | pmm |
| sleep_w1 | pmm |
| sleep_w2 | pmm |
| sleep_w3 | pmm |
| sleep_w4 | pmm |
| engagement_w1 | polr |
| engagement_w2 | polr |
| engagement_w3 | polr |
| engagement_w4 | polr |
| employed_w1 | logreg |
| employed_w2 | logreg |
| employed_w3 | logreg |
| employed_w4 | logreg |
| trt_anxiety | ~I(treatment_num * baseline_anxiety) |
| target | predictor | included |
|---|---|---|
| baseline_anxiety | age | TRUE |
| baseline_anxiety | first_generation | TRUE |
| baseline_anxiety | outcome_w1 | TRUE |
| baseline_anxiety | program_group | TRUE |
| baseline_anxiety | treatment_num | TRUE |
| outcome_w4 | age | TRUE |
| outcome_w4 | first_generation | TRUE |
| outcome_w4 | outcome_w1 | TRUE |
| outcome_w4 | program_group | TRUE |
| outcome_w4 | treatment_num | TRUE |
Predictive mean matching is used for continuous variables to retain plausible observed values. Logistic regression is used for binary variables, proportional-odds regression for ordered variables, and passive imputation keeps the treatment-by-anxiety product synchronized with its components.
The imputation model includes the outcomes, all substantive
predictors, the interaction components, repeated measures from every
wave, design variables, and useful auxiliary variables.
dropout_wave documents the observed pattern but is excluded
because it deterministically identifies blocks of missing later-wave
values. Excluding the outcome from an imputation model merely because it
is called an “outcome” can attenuate associations.
Longitudinal and multilevel structure
The imputation model is wide: every wave has its own column, allowing outcomes and auxiliaries across waves to predict one another. Each completed dataset is then reshaped to long form and analyzed with a participant random intercept. This preserves the fixed four-wave structure without treating repeated observations as independent during imputation.
For many occasions, unequal time spacing, participants nested in
sites, random slopes that drive missingness, or three-level data, use a
multilevel imputation method that explicitly identifies the cluster and
distinguishes within- from between-cluster predictors. Suitable tools
can include mice two-level methods, mitml, or
jomo. Match the imputation structure to the most complex
substantive model rather than adding a cluster identifier as an ordinary
numeric predictor.
Run multiple imputation
| note |
|---|
| No logged events |
mice creates 20 completed datasets rather than one
filled-in dataset. Estimates are fit in every completed dataset and
combined with Rubin’s rules so that standard errors reflect both
within-imputation and between-imputation uncertainty.
Diagnostics
Convergence
Convergence is a property of the algorithm, not proof that the imputation model is correct. Extend the iterations if chains drift, remain separated, or change systematically near the end.
Observed and imputed distributions
Imputed values need not reproduce the marginal observed distribution exactly. Large unexplained differences, spikes, impossible categories, or implausibly narrow variability should prompt review of coding, methods, predictors, and transformations.
Implausible values
| variable | rule | violations |
|---|---|---|
| baseline_anxiety | 0 to 30 | 0 |
| outcome_w1 | 0 to 100 | 0 |
| outcome_w2 | 0 to 100 | 0 |
| outcome_w3 | 0 to 100 | 0 |
| outcome_w4 | 0 to 100 | 0 |
| sleep_w1 | 0 to 14 | 0 |
| sleep_w2 | 0 to 14 | 0 |
| sleep_w3 | 0 to 14 | 0 |
| sleep_w4 | 0 to 14 | 0 |
| employed_w1 | 0 or 1 | 0 |
| employed_w2 | 0 or 1 | 0 |
| employed_w3 | 0 or 1 | 0 |
| employed_w4 | 0 or 1 | 0 |
| motivation | 1, 2, 3, 4, 5 | 0 |
| engagement_w1 | 1, 2, 3, 4, 5 | 0 |
| engagement_w2 | 1, 2, 3, 4, 5 | 0 |
| engagement_w3 | 1, 2, 3, 4, 5 | 0 |
| engagement_w4 | 1, 2, 3, 4, 5 | 0 |
Plausibility rules must come from the instrument, protocol, and codebook. They should catch impossible values without trimming merely unusual but credible observations.
Fit and pool substantive models
Continuous longitudinal outcome
| term | estimate | std.error | statistic | df | p.value | 2.5 % | 97.5 % | conf.low | conf.high |
|---|---|---|---|---|---|---|---|---|---|
| (Intercept) | 53.071 | 2.011 | 26.393 | 440.392 | 0.000 | 49.119 | 57.023 | 49.119 | 57.023 |
| treatment_num | -2.042 | 1.788 | -1.142 | 776.878 | 0.254 | -5.553 | 1.468 | -5.553 | 1.468 |
| factor(wave)2 | -2.167 | 0.471 | -4.602 | 1190.777 | 0.000 | -3.090 | -1.243 | -3.090 | -1.243 |
| factor(wave)3 | -4.243 | 0.515 | -8.235 | 318.841 | 0.000 | -5.256 | -3.229 | -5.256 | -3.229 |
| factor(wave)4 | -5.073 | 0.542 | -9.359 | 215.136 | 0.000 | -6.142 | -4.005 | -6.142 | -4.005 |
| baseline_anxiety | 1.261 | 0.085 | 14.833 | 714.741 | 0.000 | 1.094 | 1.428 | 1.094 | 1.428 |
| motivation_numeric | -0.224 | 0.309 | -0.725 | 490.259 | 0.469 | -0.832 | 0.384 | -0.832 | 0.384 |
| sleep | -1.173 | 0.153 | -7.643 | 150.437 | 0.000 | -1.476 | -0.870 | -1.476 | -0.870 |
| engagement_numeric | -1.361 | 0.154 | -8.825 | 258.271 | 0.000 | -1.665 | -1.057 | -1.665 | -1.057 |
| treatment_num:factor(wave)2 | -2.083 | 0.659 | -3.161 | 1345.351 | 0.002 | -3.375 | -0.790 | -3.375 | -0.790 |
| treatment_num:factor(wave)3 | -3.639 | 0.709 | -5.137 | 427.324 | 0.000 | -5.032 | -2.247 | -5.032 | -2.247 |
| treatment_num:factor(wave)4 | -6.370 | 0.742 | -8.580 | 248.638 | 0.000 | -7.832 | -4.907 | -7.832 | -4.907 |
| treatment_num:baseline_anxiety | 0.000 | 0.118 | 0.001 | 654.406 | 0.999 | -0.231 | 0.232 | -0.231 | 0.232 |
The outcome model is fit separately in all 20 completed datasets. The pooled estimates reflect uncertainty about the missing values. The treatment-by-wave terms address whether change differs between conditions, while the participant random intercept accounts for repeated observations.
Binary later-wave outcome
| term | estimate | std.error | statistic | df | p.value | 2.5 % | 97.5 % | conf.low | conf.high |
|---|---|---|---|---|---|---|---|---|---|
| (Intercept) | 1.839 | 0.698 | 0.873 | 174.558 | 0.384 | 0.464 | 7.292 | 0.464 | 7.292 |
| treatment_num | 1.203 | 0.208 | 0.887 | 176.361 | 0.376 | 0.798 | 1.814 | 0.798 | 1.814 |
| baseline_anxiety | 0.922 | 0.030 | -2.679 | 162.418 | 0.008 | 0.869 | 0.979 | 0.869 | 0.979 |
| as.numeric(motivation) | 1.046 | 0.105 | 0.431 | 168.131 | 0.667 | 0.850 | 1.288 | 0.850 | 1.288 |
| outcome_w1 | 1.008 | 0.013 | 0.579 | 173.780 | 0.563 | 0.982 | 1.034 | 0.982 | 1.034 |
Exponentiated coefficients are pooled odds ratios. A binary outcome does not justify filling missing values with the most common category; the imputation model should preserve uncertainty and associations with other variables.
Complete-case comparison
| term | mi_estimate | mi_conf_low | mi_conf_high | fmi | cc_estimate | cc_conf_low | cc_conf_high |
|---|---|---|---|---|---|---|---|
| (Intercept) | 53.071 | 49.119 | 57.023 | 0.182 | 55.401 | 49.847 | 60.954 |
| treatment_num | -2.042 | -5.553 | 1.468 | 0.121 | -1.652 | -6.466 | 3.161 |
| factor(wave)2 | -2.167 | -3.090 | -1.243 | 0.079 | -2.304 | -3.726 | -0.882 |
| factor(wave)3 | -4.243 | -5.256 | -3.229 | 0.223 | -4.132 | -5.563 | -2.702 |
| factor(wave)4 | -5.073 | -6.142 | -4.005 | 0.282 | -5.049 | -6.496 | -3.601 |
| baseline_anxiety | 1.261 | 1.094 | 1.428 | 0.129 | 1.173 | 0.913 | 1.432 |
| motivation_numeric | -0.224 | -0.832 | 0.384 | 0.170 | -0.547 | -1.342 | 0.249 |
| sleep | -1.173 | -1.476 | -0.870 | 0.344 | -1.343 | -1.727 | -0.958 |
| engagement_numeric | -1.361 | -1.665 | -1.057 | 0.253 | -1.417 | -1.831 | -1.003 |
| treatment_num:factor(wave)2 | -2.083 | -3.375 | -0.790 | 0.067 | -1.149 | -3.096 | 0.798 |
| treatment_num:factor(wave)3 | -3.639 | -5.032 | -2.247 | 0.186 | -3.179 | -5.133 | -1.226 |
| treatment_num:factor(wave)4 | -6.370 | -7.832 | -4.907 | 0.259 | -5.059 | -7.015 | -3.104 |
| treatment_num:baseline_anxiety | 0.000 | -0.231 | 0.232 | 0.138 | -0.053 | -0.390 | 0.284 |
The complete-case model uses only participants with every required value at all four waves. Differences from the imputed analysis may reflect changed sample composition, lower precision, chance, or the imputation assumptions. Agreement does not prove either analysis is unbiased, and disagreement should be investigated rather than resolved by choosing the preferred estimate.
Sensitivity to departures from MAR
| delta | term | estimate | std_error | conf_low | conf_high | fraction_missing_information |
|---|---|---|---|---|---|---|
| 0 | treatment_num | -8.659 | 0.727 | -10.084 | -7.235 | 0.321 |
| -2 | treatment_num | -8.617 | 0.729 | -10.046 | -7.188 | 0.317 |
| -5 | treatment_num | -8.554 | 0.748 | -10.020 | -7.088 | 0.297 |
The delta analysis asks how the treatment estimate changes if unobserved wave-four distress is systematically lower than its MAR-based imputation by 2 or 5 points. The direction and magnitude must be chosen from subject-matter knowledge, prior studies, or a range that stakeholders consider consequential. Sensitivity analysis does not identify the true missing values; it shows how dependent the conclusion is on an unverifiable assumption.
Dynamic interpretation
The synthetic dataset included 520 participants measured across 4 planned waves. Across the designated analysis variables, 14.3% of cells were missing. outcome_w4 had the highest variable-level missingness (28.3%). Missingness increased across waves and differed modestly by observed participant characteristics, making a blanket MCAR explanation difficult to defend. These patterns support including design variables, earlier outcomes, later outcomes, and auxiliary measures in the imputation model, while leaving MAR as an explicit assumption. Twenty imputations were created using predictive mean matching for continuous variables, logistic regression for binary variables, proportional-odds regression for ordinal variables, and passive updating for the treatment-by-anxiety product. Chain behavior, observed-versus-imputed distributions, logged events, and range rules were reviewed before fitting the substantive models. The pooled treatment-by-wave coefficient at the final wave was -6.37, 95% CI [-7.83, -4.91], p < .001. This estimate describes the synthetic model and should not be generalized to real doctoral-student populations. The complete-case and multiply imputed estimates were compared as a diagnostic rather than as a contest between methods. A delta-adjustment sensitivity analysis then examined whether the focal treatment estimate changed under increasingly pessimistic assumptions about unobserved wave-four distress. Conclusions should report both the primary MAR-based analysis and any sensitivity values that would alter the substantive interpretation.
Documentation checklist
- Identify every variable imputed and its measurement level.
- Report the software, package version, random seed, number of imputations, iterations, methods, and visit sequence.
- Describe which outcomes, predictors, interaction components, auxiliary variables, design variables, and repeated measures entered each imputation model.
- Explain how clustering or repeated measures were handled during imputation and analysis.
- Report the amount and pattern of missingness by variable, case, group, and wave.
- State why MAR is considered plausible enough for the primary analysis without calling it proven.
- Review chain behavior, logged events, observed and imputed distributions, and impossible values.
- Fit the same prespecified substantive model in every completed dataset and pool estimates with Rubin’s rules.
- Compare complete-case and imputed estimates with appropriate cautions.
- Describe the sensitivity model, delta values, rationale, and whether conclusions changed.
- Keep the incomplete original data, imputation code, completed-data generation process, and analysis code under version control; do not distribute identifiable completed datasets.
When this workflow is not enough
- Many or irregular occasions: use a multilevel imputation model that represents time and clustering directly.
- Random slopes central to the research question: use an imputation model compatible with those random effects.
- Interactions or nonlinear effects central to inference: use passive imputation carefully or substantive-model-compatible imputation.
- Survival, count, zero-inflated, bounded, or semicontinuous outcomes: use methods that respect the outcome distribution and substantive model.
- High missingness with weak auxiliary information: collect more information when possible and emphasize sensitivity rather than relying on a complex imputation model.
- Likely MNAR dropout: add pattern-mixture, selection, shared-parameter, or tipping-point analyses.
- Survey weights or complex sampling: incorporate design variables and use methods appropriate to the sampling design.
- Missing entire variables by design or site: confirm that the planned-missing or multilevel structure provides enough overlap for identification.
Exports
| file |
|---|
| complete_case_vs_imputation.csv |
| delta_sensitivity.csv |
| imputation_methods.csv |
| imputation_predictor_matrix.csv |
| imputation_range_audit.csv |
| mids_object.rds |
| missingness_by_case.csv |
| missingness_by_group.csv |
| missingness_by_variable.csv |
| missingness_by_wave.csv |
| pooled_logistic_model.csv |
| pooled_mixed_model.csv |
| synthetic_complete_reference.csv |
| synthetic_longitudinal_missing.csv |
References
- Azur, M. J., Stuart, E. A., Frangakis, C., & Leaf, P. J. (2011). Multiple imputation by chained equations: What is it and how does it work? International Journal of Methods in Psychiatric Research, 20(1), 40–49.
- Enders, C. K. (2022). Applied Missing Data Analysis (2nd ed.). Guilford Press.
- Grund, S., Lüdtke, O., & Robitzsch, A. (2018). Multiple imputation of missing data for multilevel models. Organizational Research Methods, 21(1), 111–149.
- van Buuren, S. (2018). Flexible Imputation of Missing Data (2nd ed.). CRC Press.
- White, I. R., Royston, P., & Wood, A. M. (2011). Multiple imputation using chained equations: Issues and guidance for practice. Statistics in Medicine, 30(4), 377–399.