Post-Estimation & Diagnostics
Statios provides 31 post-estimation and regression diagnostic procedures spanning heteroskedasticity tests, serial correlation diagnostics, influence measures, marginal effects, contrasts, and model comparison tools.
47 procedures · 1 with documented limitations. Every result is computed by the open Python engine and is exportable to APA tables and reports.
| Procedure | What it does | Status | Key reference |
|---|---|---|---|
| Normality tests (comprehensive suite) | Shapiro-Wilk, Kolmogorov-Smirnov, D'Agostino-Pearson, Anderson-Darling; includes skewness/kurtosis and Q-Q plot data. | ✅ Full | Shapiro & Wilk (1965); D'Agostino & Pearson (1973) |
| Homogeneity of variance test | Levene and Bartlett tests for equality of variances across groups; concludes on Levene (robust). | ✅ Full | Levene (1960); Bartlett (1937) |
| Outlier detection (multiple methods) | IQR, Z-score (|z|>3), and modified Z-score (MAD-based) methods with index identification. | ✅ Full | Virtanen et al. (2020) |
| Multicollinearity check | Variance Inflation Factor (VIF) analysis with concern classification (low/moderate/high). | ✅ Full | Virtanen et al. (2020) |
| Automatic test suggestion | Recommends appropriate statistical tests based on data characteristics. | ✅ Full | Virtanen et al. (2020) |
| Breusch-Pagan test for heteroskedasticity | LM and F variants test if residual variance depends on predictors; requires n > k+2. | ✅ Full | Breusch & Pagan (1979) |
| White test for heteroskedasticity | General heteroskedasticity test not assuming specific form; more flexible than Breusch-Pagan. | ✅ Full | White (1980) |
| Goldfeld-Quandt heteroskedasticity test | Sorts by first predictor, splits at the midpoint, drops a block of observations starting at the midpoint, and F-tests the lower vs upper group residual variances. | ✅ Full | Goldfeld & Quandt (1965) |
| Breusch-Godfrey serial correlation test | LM and F tests for autocorrelation up to specified lags in OLS residuals. | ✅ Full | Breusch (1978); Godfrey (1978) |
| Durbin-Watson autocorrelation statistic | DW near 2 indicates no autocorrelation; <1.5 positive, >2.5 negative autocorrelation. | ✅ Full | Durbin & Watson (1950) |
| Ljung-Box autocorrelation test | Tests joint significance of autocorrelations at specified lags; generic for series/residuals. | ✅ Full | Ljung & Box (1978) |
| Heteroskedasticity-robust LM test | Wooldridge robust LM test that a set of regressors are jointly zero, valid under heteroskedasticity of unknown form (n − SSR auxiliary regression on residualized products). | ✅ Full | Wooldridge (2010) |
| AR(1) serial-correlation test | Wooldridge's t-test for first-order serial correlation: regress OLS residuals on their own lag (plus the regressors) and test ρ = 0. | ✅ Full | Wooldridge (2010) |
| Durbin's h Test | Durbin's h test for first-order serial correlation in OLS models that include a lagged dependent variable, where the Durbin-Watson statistic is biased toward 2. | ✅ Full | Durbin (1970) |
| Moulton Factor (clustered SE inflation) | Moulton (1986) standard-error inflation factor: estimates the residual intra-class correlation across groups and reports naive OLS vs Moulton-adjusted standard errors. | ✅ Full | Moulton (1986) |
| Vuong Test (non-nested) | Vuong's (1989) likelihood-ratio test for two non-nested models (OLS/logit/Poisson), comparing per-observation log-likelihoods to decide which specification is closer to the true data-generating process, with AIC/BIC complexity-corrected variants. | ✅ Full | Vuong (1989, Econometrica) |
| Cox Test (non-nested) | Pesaran-Cox test discriminating between two non-nested linear regression models via the difference in log-likelihoods adjusted by its expectation under each model, reported in both directions as standard-normal statistics with a preferred-model verdict. | ✅ Full | Cox (1961); Pesaran (1974, Rev. Econ. Stud.) |
| Encompassing Test (non-nested) | Mizon-Richard (1986) encompassing test that asks, by artificial nesting, whether one non-nested linear model explains everything its rival adds: each direction adds the rival's non-overlapping regressors to the base model and F-tests their joint significance (insignificant => the base model encompasses the rival), returning F/df/p, per-direction verdicts, and a preferred model. | ✅ Full | Mizon & Richard (1986, Econometrica) |
| J Test (non-nested models) | Davidson-MacKinnon J test that discriminates between two non-nested linear specifications by adding each model's OLS fitted values to the other and testing their t-statistic in both directions, returning per-direction rejection verdicts and a preferred model. | ✅ Full | Davidson & MacKinnon (1981) |
| Information-Matrix Test (White) | White's (1982) omnibus information-matrix specification test for OLS: IM = n*R^2 of the auxiliary regression of squared residuals on the unique squares and cross-products of the regressors (chi-square), detecting general misspecification — wrong functional form, heteroskedasticity, or non-normality — not just heteroskedasticity. | ✅ Full | White (1982) |
| Harvey Multiplicative Heteroskedasticity | Harvey's (1976) LM test for multiplicative heteroskedasticity, regressing the log of squared OLS residuals on chosen variables to estimate the variance model Var(e)=exp(z'alpha) and test whether the variance depends on them. | ✅ Full | Harvey (1976) |
| LM / Score Test (omitted regressors) | Classic Lagrange-multiplier (score) test for omitted regressors: regresses the residuals of the restricted OLS (dependent on kept) on the full regressor set and reports LM = n*R-squared of that auxiliary regression as a chi-square(q) test that the tested coefficients are jointly zero, with the equivalent F-form and a reject/not verdict. | ✅ Full | Breusch & Pagan (1980); Engle (1984) |
| Multivariate Normality (Doornik-Hansen) | Tests whether a set of variables (or VAR residuals) is jointly multivariate normal via Mardia's multivariate skewness and kurtosis statistics and the Doornik-Hansen omnibus chi2(2p) test, returning each statistic with its df and p-value, per-variable skew/kurtosis, and an overall normal/non-normal verdict. | ✅ Full | Mardia (1970); Doornik & Hansen (2008) |
| Ramsey RESET specification test | Tests for functional form misspecification by adding polynomial terms of fitted values. | ✅ Full | Ramsey (1969) |
| Hosmer-Lemeshow goodness-of-fit test | Groups logit predictions by deciles, compares observed vs expected event counts via chi-square. | ✅ Full | Hosmer et al. (1980) |
| Variance Inflation Factor (VIF) analysis | VIF per predictor with concern thresholds (VIF>5 moderate, >10 high); includes mean VIF. | ✅ Full | Marquardt (1970) |
| Cook's distance influence measure | Identifies observations with disproportionate influence on regression; threshold default 4/n. | ✅ Full | Cook (1977) |
| Leverage (hat values) analysis | Detects high-leverage observations (unusual X values); threshold 2*(k+1)/n. | ✅ Full | Belsley et al. (1980) |
| DFBETAS parameter-specific influence | Measures change in each coefficient when one observation removed; threshold 2/sqrt(n). | ✅ Full | Belsley et al. (1980) |
| Marginal effects (logit/probit) | Average Marginal Effects (AME) or Marginal Effects at Means (MEM) for binary choice models. | ✅ Full | Seabold & Perktold (2010) |
| Predicted probabilities with CI | Logit/probit predictions on observed data or at specified covariate values with 95% CI. | ✅ Full | Seabold & Perktold (2010) |
| Post-hoc multiple comparisons | Tukey, Bonferroni, Holm step-down, Scheffe, Games-Howell with p-value adjustments. | ✅ Full | Tukey (1949); Games & Howell (1976) |
| Effect sizes across designs | Cohen's d, Glass's delta, Hedges' g, eta-squared, partial eta-squared, omega-squared, Cohen's f. | ✅ Full | Cohen (1988) |
| Planned contrasts (pairwise/polynomial) | Pairwise, polynomial (Legendre), Helmert, deviation contrasts with t-tests and CI. | ✅ Full | Seabold & Perktold (2010) |
| Prediction intervals (OLS) | Confidence and prediction intervals for fitted values; wider than CI due to residual variance. | ✅ Full | Seabold & Perktold (2010) |
| Coefficient table (with VIF/robust SE) | Formatted OLS results with standardized betas, VIF, HC3 robust SE option; significance stars. | ✅ Full | Seabold & Perktold (2010) |
| Model comparison (R-sq, AIC, BIC) | Side-by-side OLS models with delta AIC/BIC relative to best; RMSE and F-stat per model. | ✅ Full | Seabold & Perktold (2010) |
| Marginal effects at specified values | Conditional marginal effects (OLS/logit/probit/Poisson) at user-supplied covariate values. | ✅ Full | Seabold & Perktold (2010) |
| Margins contrast (difference in effects) | Compare marginal effects of one predictor across two or more levels; delta-method SE. | ✅ Full | Seabold & Perktold (2010) |
| Conditional marginal effects (interaction) | Marginal effect of focal variable at 10th, 25th, 50th, 75th, 90th percentiles of moderator. | ✅ Full | Seabold & Perktold (2010) |
| Nested contrasts (hierarchical) | Two-sample Welch t-tests on specified pairs within a grouping variable. | ✅ Full | Seabold & Perktold (2010) |
| Elasticities (full/partial/arc) | dy/dxx/y (full), dy/dxx (partial), or arc elasticity across specified predictor values. | ✅ Full | Seabold & Perktold (2010) |
| Semi-elasticities (dy/dx/y and dy/dx*x) | Proportional change in y and linear change in y per unit change in x. | ✅ Full | Seabold & Perktold (2010) |
| Predicted means over groups (Stata-style) | Marginal cell means with 95% CI; pairwise comparisons across factor levels. | ✅ Full | Seabold & Perktold (2010) |
| Adjusted predictions (holding covariates constant) | Linear predictor at specified covariate values (mean/median/min/max); 95% CI included. | ✅ Full | Seabold & Perktold (2010) |
| Probability profile (logit/probit curve) | Binary outcome probability as function of one predictor; other predictors at mean. | ✅ Full | Seabold & Perktold (2010) |
| Treatment effect contrasts (ATE/ATT/ATC) | Average treatment effect via regression-based g-computation; balanced or flexible interaction. | ⚠️ Limited | Seabold & Perktold (2010) |
Notes & limitations
- Treatment effect contrasts (ATE/ATT/ATC) — Uses OLS-based potential outcomes, not designed for instrumental variables.