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Chapter 14 Model diagnostics

In this chapter we investigate how ADAM models can be diagnosed and improved. The majority of topics will build upon the typical model assumptions discussed in Section 12 of Svetunkov (2021c) textbook. Some of the assumptions cannot be diagnosed properly, but for the others there are existing and well established instruments. We will consider the following assumptions and discuss how to check whether they are violated or not:

  1. Model is correctly specified:
  1. No omitted variables;
  2. No redundant variables;
  3. The necessary transformation of the variables are applied;
  4. No outliers in the model.
  1. Residuals are i.i.d.:
  1. They are not autocorrelated;
  2. They are homoscedastic;
  3. The expectation of residuals is zero, no matter what;
  4. The residuals follow the specified distribution;
  5. The distribution of residuals does not change over time.
  1. The explanatory variables are not correlated with anything but the response variable;

All the model diagnostics is aimed at spotting patterns in residuals. If there are some, then something is probably missing in the model. In this chapter we will discuss, which instruments can be used to diagnose different types of assumptions

In order to make this more actionable, we will consider a conventional regression model on Seatbelts data. This can be estimated equally well either with adam() from smooth or alm() from greybox. In general, I recommend using alm(), when no dynamic elements are present in the model. Otherwise, use adam() as shown below:

adamModelSeat01 <- adam(Seatbelts, "NNN",
                        formula=drivers~PetrolPrice+kms)
plot(adamModelSeat01,7)
Basic regression model for the data of Road Casualties in Great Britain 1969–84.

Figure 14.1: Basic regression model for the data of Road Casualties in Great Britain 1969–84.

This model has several issues, and in this chapter we will discuss how to diagnose and fix them.

References

• Svetunkov, I., 2021c. Statistics for business analytics. https://openforecast.org/sba/ (version: [01.09.2021])