# Definition of 'Model Diagnostics'

Can anyone help me out with explaining what the term 'model diagnostics' refers to when applied to multiple regression please?

In particular, what tests are necessary to check whether your estimated model is congruent?

Thanks, L

After a regression model is fitted, it is necessary to check that the assumptions of the classical regression model are met, otherwise estimates based on the Ordinary Least Squares estimator may be biased or inefficient and inference based on OLS may be unreliable.

Some of the assumptions of the classical regression model rely on the structure of the disturbance term. Although the disturbances (shocks or errors) are not observed, they can be estimated as the residuals of the fitted model. Upon the residuals, we should test whether they are independent and homoscedastic. For that, the following tests are common:

If autocorrelation or heteroscedasticity is detected, then we have to consider choosing other estimator, e.g. Generalized Least Squares, in order to improve the efficiency of the estimates.

When the explanatory variables are not fixed, it should be checked whether they are uncorrelated with the disturbance term. The Durbin–Wu–Hausman test can be used to that end. If the null of uncorrelation between the explanatory variables and the disturbances is rejected, then the instrumental variables estimator has better properties than the standard OLS in large samples.

A test for the stability of the coefficients across the sample can be carried out for example by means of the Chow test.

The validity of the linear relationship among the variables against a non-linear relationship can be tested by means of the Ramsey test.

• I have never encountered the term model diagnostics before, my lecturer's background is economics and mine is psychology. I thought he may be referring to checking the assumptions of regression? Would this be something different altogether? – Lora Apr 19 '15 at 15:33
• @Lora "model diagnostics" refers to checking the assumptions of the linear regression model. The tests that I mentioned can be used to that end. – javlacalle Apr 19 '15 at 23:18
• Ok, that makes it more clear to me. Just a question on some of the tests you mentioned; I have also come across using Durbin Watson to test for 1st order autocorrelation, however I do not understand the difference between 1st order autocorrelation, and autocorrelation/serial correlation. Could you please clarify? Thank you – Lora Apr 20 '15 at 12:36
• @Lora First order autocorrelation is a particular form of autocorrelation where the observations at time $t$ depend on the previous observation $t-1$. Serial correlation refers to any form or degree of autocorrelation, it states that the current observation depends on the past observations (e.g. the last three observations, the first and the fourth previous observations,...). 1st order autocorrelation is a particular case of serial correlation. – javlacalle Apr 20 '15 at 18:15