Question

10) What test should you run to determine if your residuals are not spatially dependent (i.e. they are independent)? If that test proves to be significant, what corrective action can you take?

Answer 1

The given can also be said as autocorrelation in econometrics.

When you have a series of numbers, and there is a pattern such that values in the series can be predicted based on preceding values in the series, the series of numbers is said to exhibit autocorrelation. This is also known as serial correlation and serial dependence. The existence of autocorrelation in the residuals of a model is a sign that the model may be unsound. Autocorrelation is diagnosed using a correlogram (ACF plot) and can be tested using the Durbin-Watson test.

Sampling error alone means that we will typically see some autocorrelation in any data set, so a statistical test is required to rule out the possibility that sampling error is causing the autocorrelation. The standard test for this is the Durbin-Watson test. This test only explicitly tests first-order correlation, but in practice, it tends to detect most common forms of autocorrelation as most forms of autocorrelation exhibit some degree of first-order correlation.

Solution:

When autocorrelation is detected in the residuals from a model, it suggests that the model is misspecified (i.e., in some sense wrong). A cause is that some key variable or variables are missing from the model. Where the data has been collected across space or time, and the model does not explicitly account for this, autocorrelation is likely. For example, if a weather model is wrong in one suburb, it will likely be wrong in the same way in a neighboring suburb. The fix is to either include the missing variables, or explicitly model the autocorrelation (e.g., using an ARIMA model).

The existence of autocorrelation means that computed standard errors, and consequently p-­values, are misleading.