Complex Survey & Missing Data

Statios provides complex survey design analysis and missing data handling. Covers design-based inference (Taylor linearization, replicate weights, Rao-Scott corrections) and advanced imputation (MICE, EM, PMM) with proper uncertainty propagation.

18 procedures. Every result is computed by the open Python engine and is exportable to APA tables and reports.

Procedure	What it does	Status	Key reference
Survey design definition	Specify strata, clusters, sampling weights, and finite population correction; summarize design.	✅ Full	Horvitz & Thompson (1952); Kish (1965)
Survey-adjusted means	Design-based estimates with Taylor linearization variance; includes DEFF per variable.	✅ Full	Horvitz & Thompson (1952); Binder (1983)
Survey-adjusted totals	Weighted population totals with design-adjusted standard errors and DEFFs.	✅ Full	Horvitz & Thompson (1952); Binder (1983)
Survey proportions	Design-based category proportions with confidence intervals and design effects.	✅ Full	Horvitz & Thompson (1952); Binder (1983)
Survey-weighted regression	Linear or logistic regression via WLS with design-adjusted sandwich covariance.	✅ Full	Binder (1983); Lumley (2004)
Design Effect (DEFF)	Ratio of design variance to SRS variance for a mean; includes interpretation guide.	✅ Full	Kish (1965)
Replicate weights analysis	Jackknife, BRR, or bootstrap SE/CI from replicate weight methodology.	✅ Full	Wolter (2007); Rust & Rao (1996)
Survey t-test	Two-sample design-adjusted t-test on difference of weighted means.	✅ Full	Binder (1983); Lumley (2004)
Rao-Scott chi-square	Chi-square test for categorical association; first-order design effect correction.	✅ Full	Rao & Scott (1981); Rao & Scott (1984)
Missing value summary	Comprehensive report of missing counts, patterns, and complete-case counts per variable.	✅ Full	Pedregosa et al. (2011)
Little's MCAR test	Test whether missingness is completely random; EM-based ML with chi-square inference.	✅ Full	Rubin (1976); Little (1988)
Simple imputation	Mean, median, or mode imputation for a single variable.	✅ Full	Rubin (1976)
KNN imputation	Impute missing via k nearest neighbors; standardizes features to avoid scale-dependence.	✅ Full	Rubin (1976)
MICE imputation	Multiple imputation by chained equations; pooled estimates via Rubin's rules.	✅ Full	Rubin (1976); van Buuren & Groothuis-Oudshoorn (2011)
EM imputation	EM algorithm for missing data assuming multivariate normality; returns imputed dataset.	✅ Full	Rubin (1976); Dempster et al. (1977)
Predictive Mean Matching (PMM)	Imputation via OLS prediction + nearest-neighbor donor draw; preserves observed distribution.	✅ Full	Rubin (1976); van Buuren & Groothuis-Oudshoorn (2011)
Missing data patterns	Identify missing patterns; check monotone vs non-monotone structure; Little's MCAR suggestion.	✅ Full	Pedregosa et al. (2011)
MNAR sensitivity analysis	Shift imputed values by delta range; track regression coefficient changes to find tipping point.	✅ Full	Rubin (1976)