Apart from the indicators automatically spitted out by gretl we can conduct a couple of additional test. Do not fear, cause it takes no more than a couple of mouse clicks. Once again the program will calculate everything for us, we only have to know where to look for the answers. Of course the question may arise what do we need all this testing for. Well, as mere human beings, we have a great capacity to err. Each mistake distorts the model, making it grow further apart from reality. Why building a model in a first place if we don’t want it to reflect anything?
#1: Testing for collinearity
Collinearity is simply a relationship between two independent variables. Think of a cat caressed only while he’s asleep. This would cause the values for sleep and caress to behave alike. Of course some level of collinearity doesn’t do any harm to the model. In economics it’s perfectly normal that some indicators sway together in a response to markets’ mood. We just have to make sure that those similarities in reactions lay within safe limits.
Having our previous model already calculated we select: Tests > Collinearity (menu bar).
Since everything has been already explained by the program I can only repeat. Check if any variable has VIF value exceeding 10. Our results seem ok (3.959 being the highest number in the column). A piece of cake.
#2: RESET (Regression Specification Error Test)
This test checks whether the model has a correct structure. At the beginning we’ve assumed that relation between independent variables and cat’s mood are linear. This is just the simplest possible form of relation between sets of values. As you know there are no squares nor logarithms in our formula, but they could’ve been. RESET won’t tell us what the appropriate formula should be, it would just inform us that the one we’ve chosen is wrong, and how wrong it is.
Once again select: Tests > Romney’s Reset
The result of the test is a new model with two new variables yhat^2 and yhat^3. These are squares and cubes of the cat’s mood values. In a correctly constructed model those should be valid, I mean their p values of t-ratio should be less than 0.05 (α ). They are not.
Another approach would be checking the F statistics as we did it in Wald test.
Ho : variables are not valid
H1 : the opposite
p value 0.227 > α 0.05 so we stick to Ho what only confirms our previous assumptions.
#3: Omitted variable test
This one is the most comprehensible one. We indicate a variable we don’t like and the program checks if we are better off without it. If you like to you can repeat the test for each variable, but at the higher level of initiation you would already be able to tell which one stinks.
Select: Tests > Omit variable > Wald omit test, and choose a variable you don’t like the most.
I’ve chosen the H. One more time we are given the Wald test statistics (F). Every time it works the same way. Two hypothesis, H0: the variable is useless, H1: it’s not.
p-value 0.457033 > α 0.05 , we throw out the H
#4: Davidson Mc-Kinnon test
Time for dessert. It’s a bit more complicated meaning it requires more clicking. We have to get back to creation of a model. Then instead of the one we already have construct two models with divergent variables sets. This is:
M = F + C
M = H + S
or any other combination you can think of. Just remember that both models have to include the same number of variables. I wonder what happens when the original model has an odd number of those.
After creating the first model we select Save > Fitted value
What we’ll get is a new variable yhat1 that has been automatically added to the list of variables in the first gretl’s window. Repeat the procedure for the second model (Save> Fitted...) and therefore you’ll obtain another variable yhat2.
Another name for fitted value is predicted value what is a bit more clear. So yhat1 is a column of cats’ moods predicted by model based on F and C. The same with yhat2. Now once again we create two separate models.
1: M = F + C + yhat2
2: M= H + S + yhat1
In each model we have to check whether yhat variable is valid or not. Hope you remember that it’s the p-value of t-ratio that decides. In this exemplary model yhat2 has a p-value of 0.1946. It’s greater than α meaning it lacks statistical significance. It means that this little model F+C is complete without it, it works.
In the Davidson McKinnon test we can accept or reject both models. There’s no need to choose between the winner and the loser.
I guess we are done testing for now. Though it’s one of the most important part of the modeling process. After creation of a hypothetic model there’s always a list of possible defects waiting to be ticked off. Never skip it . A defective model can do more harm than good.