diagnostic plots

To generate diagnostic plots in R, you can use various functions and libraries. These plots help you assess the quality and assumptions of your statistical models. Here are the steps to create and interpret these diagnostic plots:

  1. Fit your model: Use a suitable modeling function, such as lm() for linear regression or glm() for generalized linear models, to fit your statistical model to the data.

  2. Residuals: Obtain the residuals from your model using the residuals() function. Residuals are the differences between the observed values and the predicted values from your model.

  3. Scatterplot of Residuals: Create a scatterplot of the residuals against the predicted values. This plot helps you assess if there is any pattern or relationship between the residuals and the predicted values. A random scatter of points around zero usually indicates a good model fit.

  4. Histogram of Residuals: Generate a histogram of the residuals to check their distribution. Ideally, the residuals should follow a normal distribution. Any deviations from normality may suggest problems with the model assumptions.

  5. Q-Q Plot: Create a Q-Q plot (quantile-quantile plot) to assess the normality assumption of the residuals. The Q-Q plot compares the quantiles of the residuals to the expected quantiles of a normal distribution. If the points on the plot fall along a straight line, it suggests the residuals are normally distributed.

  6. Scale-Location Plot: Construct a scale-location plot to check for homoscedasticity, which means the variability of the residuals should be constant across all levels of the predicted values. In this plot, the square root of the absolute residuals is plotted against the predicted values. A horizontal line indicates constant variance.

  7. Cook's Distance: Calculate Cook's distance for each observation using the influence.measures() function. Cook's distance measures the influence of each data point on the model fit. Values greater than 1 indicate influential points that may have a significant impact on the model.

  8. Outlier Plot: Create an outlier plot to identify any influential points that may be outliers. This plot displays the standardized residuals against the observation number. Points outside the dashed lines are potential outliers.

  9. Leverage Plot: Generate a leverage plot to identify observations with high leverage, which have a large impact on the model fit. The plot displays the leverage values against the standardized residuals. Points outside the dashed lines are observations with high leverage.

By following these steps and interpreting the diagnostic plots, you can assess the assumptions and performance of your statistical model in R. Remember to consider the context of your data and consult relevant literature or experts to ensure accurate interpretation.