How do you interpret and communicate the results of robust regression to stakeholders?

2 How to apply robust regression?

Different robust regression methods can be implemented depending on the software or programming language used. For instance, R offers the rlm() function from the MASS package to fit models with different weighting schemes. LAD minimizes the sum of absolute deviations of the errors, making it less sensitive to outliers, but less efficient than OLS. Huber uses a hybrid weighting function that gives equal weight to errors within a certain range and lower weight to those outside of it, with a tuning parameter controlling the trade-off between robustness and efficiency. Bisquare utilizes a quadratic weighting function that gives full weight to errors within a certain range, and zero weight to those outside of it, with a tuning parameter controlling the degree of robustness.

3 How to interpret robust regression?

The output of robust regression methods usually includes the estimates of the slope and the intercept of the regression line, as well as some measures of fit and accuracy. For instance, the residual standard error reflects the variability of the data around the regression line, with a lower value indicating a better fit. Additionally, R-squared is the proportion of the variance in the response variable that is explained by the predictor variable, with a higher value showing a stronger relationship. Moreover, coefficient of variation is the ratio of the residual standard error to the mean of the response variable, and it reflects the relative error of the regression model, with a lower value indicating a more precise model.

4 How to communicate robust regression?

When communicating the results of robust regression to stakeholders, you should explain why you chose this method over a standard linear regression, and report the estimates of the slope and intercept of the regression line, and their confidence intervals. Additionally, you should provide measures of fit and accuracy such as the residual standard error, R-squared, and coefficient of variation. Graphical displays of the data and regression line, such as scatterplots or leverage plots, can also help to visualize the effect of outliers on the regression estimates and identify potential sources. Comparing these values with those of a standard linear regression model can also provide insight into how well the robust regression model fits the data and how reliable it is.

5 How to evaluate robust regression?

When selecting a robust regression method, you should consider the characteristics of your data such as the number and severity of outliers, the distribution and variance of the errors, and the shape and strength of the relationship between the predictor and response variables. To evaluate your model, you should investigate some diagnostic criteria like the distribution of weighted errors (ideally normally distributed with no skewness or kurtosis), homogeneity of weighted errors (ideally constant variance across different levels of predictor variable), and influence of outliers (ideally low leverage and low influence on regression estimates). Histograms, boxplots, normal probability plots, scatterplots, variance function plots, leverage plots, or Cook's distance plots can be used to check these criteria.