Statsmodels Robust Robust Linear Model Rlm Statsmodels 0 14 4

Leo Migdal

-Dec 4, 2025, 1:23 PM

statsmodels robust robust linear model rlm statsmodels 0 14 4

Robust linear models with support for the M-estimators listed under Norms. See Module Reference for commands and arguments. PJ Huber. ‘Robust Statistics’ John Wiley and Sons, Inc., New York. 1981. PJ Huber.

1973, ‘The 1972 Wald Memorial Lectures: Robust Regression: Asymptotics, Conjectures, and Monte Carlo.’ The Annals of Statistics, 1.5, 799-821. R Venables, B Ripley. ‘Modern Applied Statistics in S’ Springer, New York, Estimate a robust linear model via iteratively reweighted least squares given a robust criterion estimator. A 1-d endogenous response variable. The dependent variable.

A nobs x k array where nobs is the number of observations and k is the number of regressors. An intercept is not included by default and should be added by the user. See statsmodels.tools.add_constant. The robust criterion function for downweighting outliers. The current options are LeastSquares, HuberT, RamsayE, AndrewWave, TrimmedMean, Hampel, and TukeyBiweight. The default is HuberT().

See statsmodels.robust.norms for more information. Available options are ‘none’, ‘drop’, and ‘raise’. If ‘none’, no nan checking is done. If ‘drop’, any observations with nans are dropped. If ‘raise’, an error is raised. Default is ‘none’.

Fits the model using iteratively reweighted least squares. The IRLS routine runs until the specified objective converges to tol or maxiter has been reached. Indicates the convergence criteria. Available options are “coefs” (the coefficients), “weights” (the weights in the iteration), “sresid” (the standardized residuals), and “dev” (the un-normalized log-likelihood for the M estimator). The default is “dev”. ‘H1’, ‘H2’, or ‘H3’ Indicates how the covariance matrix is estimated.

Default is ‘H1’. See rlm.RLMResults for more information. Specifies method for the initial estimates of the parameters. Default is None, which means that the least squares estimate is used. Currently it is the only available choice. Huber’s T norm with the (default) median absolute deviation scaling

Huber’s T norm with ‘H2’ covariance matrix Andrew’s Wave norm with Huber’s Proposal 2 scaling and ‘H3’ covariance matrix See help(sm.RLM.fit) for more options and module sm.robust.scale for scale options Note that the quadratic term in OLS regression will capture outlier effects. p x p scaled covariance matrix specified in the model fit method. The default is H1.

H1 is defined as k**2 * (1/df_resid*sum(M.psi(sresid)**2)*scale**2)/ ((1/nobs*sum(M.psi_deriv(sresid)))**2) * (X.T X)^(-1) where k = 1 + (df_model +1)/nobs * var_psiprime/m**2 where m = mean(M.psi_deriv(sresid)) and var_psiprime = var(M.psi_deriv(sresid)) H2 is defined as k * (1/df_resid) * sum(M.psi(sresid)**2) *scale**2/ ((1/nobs)*sum(M.psi_deriv(sresid)))*W_inv H3 is defined as 1/k * (1/df_resid * sum(M.psi(sresid)**2)*scale**2 * (W_inv X.T X W_inv)) where k is defined as above and W_inv = (M.psi_deriv(sresid) exog.T exog)^(-1) Return linear predicted values from a design matrix.

Design / exogenous data. Model exog is used if None. Robust regression methods in statsmodels provide a way to fit regression models that are resistant to outliers and violations of the usual OLS assumptions. Traditional linear regression using Ordinary Least Squares (OLS) can be heavily influenced by outliers, potentially leading to misleading results. Robust regression techniques minimize the influence of outliers by using alternative fitting criteria and iterative methods. The statsmodels implementation offers several robust regression approaches, including:

For other regression approaches, see Linear and Generalized Linear Models for standard regression methods or Mixed Effects Models for grouped data analysis. Below is a diagram showing the main components of the robust regression system: Sources: statsmodels/robust/robust_linear_model.py36-331 statsmodels/robust/norms.py16-90 statsmodels/robust/scale.py30-73 In the world of data analysis and statistical modeling, Linear Regression (specifically Ordinary Least Squares or OLS) is a fundamental tool. It’s widely used for understanding relationships between variables and making predictions. However, OLS has a significant vulnerability: it’s highly sensitive to outliers.

Outliers—data points that deviate significantly from other observations—can disproportionately influence OLS regression results, leading to biased coefficients and misleading conclusions. This is where Robust Linear Models (RLM) come into play, offering a more resilient approach. In this post, we’ll explore how to leverage Python’s powerful Statsmodels library to perform robust regression, ensuring your models are less susceptible to anomalous data. OLS works by minimizing the sum of the squared residuals (the differences between observed and predicted values). Squaring these differences means that large errors, often caused by outliers, have a much greater impact on the model’s parameters than smaller errors. An outlier can pull the regression line towards itself, distorting the slope and intercept, and misrepresenting the true underlying relationship in the majority of the data.

Robust regression methods aim to fit a model that is less affected by outliers. Instead of strictly minimizing the sum of squared residuals, they often employ different objective functions that downweight or even ignore the influence of extreme observations. This results in parameter estimates that are more representative of the bulk of the data, providing a more reliable understanding of the relationships between variables. Statsmodels is a fantastic Python library that provides classes and functions for estimating many different statistical models, as well as for conducting statistical tests and statistical data exploration. It’s built on top of NumPy and SciPy, integrating seamlessly into your data science workflow. For robust linear models, Statsmodels offers the RLM class, which implements various M-estimators.

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Statsmodels Robust Robust Linear Model Rlm Statsmodels 0 14 4

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Robust Linear Models With Support For The M-estimators Listed Under

1973, ‘The 1972 Wald Memorial Lectures: Robust Regression: Asymptotics, Conjectures,

A Nobs X K Array Where Nobs Is The Number

See Statsmodels.robust.norms For More Information. Available Options Are ‘none’, ‘drop’,

Fits The Model Using Iteratively Reweighted Least Squares. The IRLS