@Logit conversion estimated negative coefficient ?

[acemi]

Hello,

In order to constrain coefficient c(2), used a @logit on all c(2)'s in the model.
As a result NLS estimation produces negative (-) values for c(2).
Since @logit(c(2)) = 1/(1+exp(c(2))) it should not be a negative number. Moreover in the model copied below there is both -@logit(c(2)) term and also *@logit(c(2)) term, so even if eviews estimates - value for -@logit(c(2)) term, this does not work for @logit(c(2)) term.

Can anyone comment on this issue ?
Thank you.it(c(2))

starting values = c(1) to c(5) are 0.08, 0.1, 0.1, 0.1, 0.1
results are frozen in table logit_forum
model :

log(y) = (1/((1-@logit(c(2)))*(1-c(3))-c(5)))*(((1-exp(-c(1)*@trend))*@log*(1-c(3))*log(s))+((1-exp(-c(1)*@trend))*c(5)*log(l))+((1-exp(-c(1)*@trend))*c(4)*log(fi))+((1-exp(-c(1)*@trend))*log(gamma+(1-@logit(c(2)))*c(5)*n))+((1-exp(-c(1)*@trend))*@logit(c(2))*(1-c(3))*log((n+delta)+(c(5)*n)))+((exp(-c(1)*@trend))*log(y(-1))))

[EViews Gareth]

I think you're confused as to what you're doing.

If c(2) is -1.08, then @logit(c(2)) is 0.25, which is a positive number.

[acemi]

Sorry, may have misphrased it out in earlier post but doesnt eviews estimate logit(c(2)) ?
then logit(c(2)) = -1.08 not c(2)itself. Then we have to work out c(2) by solving through :

-1.08 = 1/(1+exp(c(2)))
2.08=-1.08*exp(c(2))
2.08/-1.08 ? exp(c(2)) which is not possible and the basis of my question.
LN(2.08/-1.08)= c(2) you cant take LN of negative number.
So what am I missing can you elaborate please.
Thank you.

[EViews Gareth]

No, EViews estimates c(2).

[acemi]

From below reply by eviews moderator to my post on @logit transformation I understood it was the opposite.
Thanks again..

http://forums.eviews.com/posting.php?mo ... 4&p=57353

Thank you!

The whole purpose for @logit transformation is to impose/force limits for c(2). For the @logit(c(2)) conversion, the NLS estimation of c(2) is 3,475962 which is clearly not within intended range limits of 0<c(2)<1. So in order to obtain value for @logit(c(2)), substitute this value in 1/(1+exp(-3,475962)) = 0,969996 which is between intended limits. But is it OK to conclude that I have constrained c(2) in this case ?

acemi

In most cases like this people want the coefficient to between 0 and 1, not specifically the parameter c(2). As you say, using @logit does this. So think of the coefficient as being the value of @logit(c(2)).

[startz]

Define beta = logit(c(2))

In the equation y = beta*x, the effect of x on y is beta. When estimated, beta will be between 0 and 1, although no restriction is placed on c(2).

[acemi]

very clear now, thank you.