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.
