STATISTICAL METHOD
Multiple Imputation Analysis
Statistical Consulting for Imputation and Pooling
We carry out multiple imputation analysis within your study design, building an imputation model that fits your analysis, creating enough imputed datasets and pooling results with Rubin's rules, checked by diagnostics and reported in publication-ready form.
No Commitment Required
Strictly Confidential
In-House PhD-Level Statisticians
Fixed Project Fee
Same-Day Response
METHOD OVERVIEW
What Is Multiple Imputation?
Multiple imputation replaces each missing value with several plausible draws from a model fitted to the observed data, analyzes each completed dataset identically, and combines the estimates and their uncertainty with Rubin’s rules. Under missing at random, where missingness depends only on observed data, it gives valid inference when the imputation model is compatible with the analysis model. It does not rescue data missing not at random, and it adds no information the data lack. OnlineSPSS, a specialist statistical consultancy for academic, clinical and professional research, provides multiple imputation analysis within your study design, with the relevant checks, effect estimates, uncertainty measures, interpretation and publication-ready reporting.
WHEN TO ENGAGE
When Is Multiple Imputation Appropriate?
Multiple imputation fits analyses in which missing values are plausibly explained by observed data, and these are the research situations in which researchers most often ask us to apply it.
Missing Covariates in a Model Predictors in a regression are missing for many participants, and dropping incomplete cases would cost precision and could bias the estimates.
Missing Outcomes or Follow-Up Some outcomes are absent from a trial or cohort, and observed predictors and auxiliary variables can make the missing-at-random assumption plausible.
Incomplete Scales and Derived Terms Questionnaire items, ratios or interaction terms are built from incomplete variables, and the imputation has to respect how each score is defined.
Imputation Results Questioned Completed datasets were averaged or analyzed once. Independent Statistical Review checks the imputation model and the pooling.
ANALYTICAL APPROACH
How We Apply Multiple Imputation
Within the family of Bayesian & Computational Methods, imputation is applied after the missingness has been assessed and its assumptions stated.
The Imputation Model It includes the outcome, every variable, interaction and nonlinear term of the analysis model, and auxiliary variables tied to missingness, so that relationships are preserved.
Congeniality and Method We choose chained equations or a joint model by variable types, and keep the imputation model at least as rich as the analysis, since omitting the outcome or an interaction attenuates it.
Imputations and Pooling We create enough imputations, commonly at least the percentage of incomplete cases, and pool each estimate with Rubin's rules, so between-imputation variance enters every interval.
Diagnostics and Sensitivity We compare imputed with observed values and check convergence, and where data may be missing not at random, delta-adjusted imputations test whether the pooled conclusion survives.
DELIVERABLES
What You Receive
Within our Quantitative Data Analysis service, the imputation is delivered with the model, checks and files needed to report and defend it.
Data & Variable Review Missing values are quantified, and variable types, the analysis model, auxiliary candidates and derived variables are documented before the imputation model is set.
Method-Specific Checks Imputed versus observed distributions, convergence of the chained equations and the stability of estimates across imputations are inspected, not only the pooled coefficient table.
Statistical Results Pooled estimates with standard errors and 95% confidence intervals from Rubin's rules, the fraction of missing information, and complete-case results shown for comparison.
Publication-Ready Tables & Figures Tables of imputation settings, pooled and complete-case results and diagnostic plots, formatted to STROBE, CONSORT or APA 7 as the journal requires.
Interpretation Findings are interpreted under the stated missing-at-random assumption, with the delta-adjusted results beside them and the limits of imputation openly acknowledged.
Reproducible Analysis Files R scripts, Stata do-files, SPSS syntax or SAS code are provided with the seed, imputation model and number of imputations, so every pooled estimate can be rerun.
ALTERNATIVE METHODS
When Another Method May Be More Appropriate
Imputation is one way to use incomplete data. These approaches fit when the handling method is still undecided, or a likelihood or weighting model can use the observed data directly.
01
Missing Data Analysis
When the open question is why values are missing and which handling method suits the design, assessing missingness and choosing the approach comes first.
02
Linear Mixed Models (Multilevel Modeling)
For repeated outcomes with missing visits and complete covariates, maximum likelihood estimation is already valid under MAR, so imputing the outcomes usually adds little.
03
Structural Equation Modeling (SEM)
When the analysis is already a latent variable model, full information maximum likelihood uses all observed indicators, and auxiliary variables enter as saturated correlates.
04
Generalized Estimating Equations (GEE)
For a population-averaged effect, weighting observed visits by the inverse probability of remaining in the study avoids imputation, but needs a well-specified dropout model.
CASE EXAMPLE
How We Work in Practice
An illustration of how an imputation analysis moves from a planned model to a reportable, defensible result.
ILLUSTRATIVE EXAMPLE · PUBLIC HEALTH SURVEILLANCE · UNITED STATES
A public health surveillance unit used a logistic model to relate smoking status and body mass index to a chronic condition, with both exposures missing for a share of the cohort.
Complete records over-represented frequent clinic attenders. Before the outcome model was run, we specified multiple imputation by chained equations (MICE) under a missing-at-random working assumption. The imputation model included the outcome, the analysis covariates, the age-by-smoking interaction, and auxiliary variables such as visit frequency and area. Body mass index was derived from height and weight, so we imputed those and calculated it passively. We checked imputed against observed distributions and convergence, pooled with Rubin’s rules, and prespecified a delta-adjusted analysis for smoking status.
Outcome: The unit received the pooled adjusted odds ratios with their 95% confidence intervals, the diagnostic checks, the delta-adjusted sensitivity results, a methods paragraph and the code with its seed.
This example does not describe a real client or project. We never share details of actual client work, in line with the confidentiality we promise every researcher. This illustrative example is included to show the type, scope, and standard of work involved in this kind of analysis.
SOFTWARE
Statistical Software for Multiple Imputation
Multiple imputation is run in IBM SPSS, R, Stata or SAS, each with established imputation and pooling routines, with code provided where applicable.
RESEARCH DISCIPLINES
Imputation Across Research Fields
Multiple imputation appears across research fields, each with its own reasons for missing values, study designs and reporting conventions.
A Defined Process for Your Analysis
We review your dataset, research question and design before any work begins, so the scope, deliverables, timeline and fixed project fee are clear from the outset.
01
Share Your Research Materials
Send your dataset, research question, study design and any existing analysis plan or output. We will let you know if anything else is needed to assess the project.
02
Receive Your Assessment
Your statistically trained Research Coordinator reviews the project and confirms the required analysis, deliverables, timeline and fixed project price before work begins.
03
Analysis & Delivery
Once you confirm the scope, an in-house statistician completes the agreed analysis and delivers the outputs, interpretation and reporting files.
RESEARCHER VOICE
What Researchers Say
Feedback from a researcher whose imputation results needed the model checked and the reporting made defensible.
“I had results from Multiple Imputation, but the interpretation still felt shaky because of how missing data should be handled without distorting the estimates. They checked the model, corrected the parts that needed attention, and made the final reporting much more defensible. The final output was concise, clearly interpreted, and ready to use in our research reporting.”
RESEARCH RESPONSIBILITY
Statistical Support Without Taking Over Your Research
We provide the statistical work for your imputation analysis, and the study, its meaning and its authorship stay entirely with you.
Agreed Statistical Support We provide the agreed methodological, analytical and statistical reporting support for your imputation analysis, within the scope confirmed before work begins.
No Intellectual Contribution OnlineSPSS claims no intellectual contribution to your research. Our work is statistical support, and authorship remains yours.
Your Research Decisions The research question, the plausibility of missing at random, interpretation and conclusions remain with you, and our interpretation stays within what the data support.
Confidential Handling Research data and project details are handled confidentially and are not published. An NDA is available where required, and can be arranged before sensitive materials are shared.
FREQUENTLY ASKED QUESTIONS
Questions About Multiple Imputation
Short answers to what researchers ask before an imputation analysis, from pooling and the imputation model to confidentiality and the assessment process.
Can I average the imputed datasets and analyze once?
No. Averaging the completed datasets treats imputed values as observed and understates uncertainty. Each dataset is analyzed separately and the estimates are pooled with Rubin’s rules, which add the variation between imputations to the variation within them, so the intervals reflect the missing values.
Which variables belong in the imputation model?
The outcome, every variable in the analysis model, including interactions and nonlinear terms, and auxiliary variables that predict missingness or the incomplete variables. A model simpler than the analysis, for example one that omits the outcome, biases the associations toward zero, so the two models must be compatible.
Is multiple imputation better than complete-case analysis?
Not always. When few records are incomplete and missingness is unrelated to the outcome given the covariates, complete-case results are similar and imputation adds work. When missing covariates are substantial or related to the outcome, imputation under MAR is more efficient and usually less biased, although it does not solve data missing not at random, which needs sensitivity analysis.
Can you review an analysis that has already been completed?
Yes, we can review a completed imputation analysis before submission or a response to reviewers. We check the imputation model against the analysis model, the number of imputations and seed, the diagnostics, whether estimates were pooled with Rubin’s rules and the sensitivity analysis, and confirm what stands or needs to change.
How do you protect my dataset and research confidentiality?
Your dataset, imputation code and any protocol or analysis plan are handled confidentially, and project information is not published. An NDA is available where required and can be arranged before sensitive materials are shared. Read more about confidentiality and data security.
What happens when I request an assessment, and how long does it take?
You share your research question, design and relevant materials, and a statistically trained Research Coordinator reviews the request and responds the same day. The analysis, deliverables, timeline and one fixed project fee are then confirmed before any work begins, so the timeline follows from the agreed scope.
Still have a question? Find more answers in our full FAQ.
NEXT STEP
Need Support With
Multiple Imputation?
Share your research question, study design and data. We assess whether imputation fits your missing values and confirm the approach before any work begins.
No Commitment Required
Strictly Confidential
Fixed Project Fee
In-House PhD-Level Statisticians
Same-Day Response
Serving Researchers Since 2014