In "Credit Scoring for Risk Managers: The Handbook for Lenders" by
Elizabeth Mays, chapter 4 page 68, it says that the coeffients from
the logistic regression are multiplied by a factor equal to the number
of points for which we want a doubling of the odds to occur, and then
divided by ln(2). Is the multiplication a standard practice? Why it is
multiplied by say 20/ln(2)? How do we determine what factor to
multiply? Is 20 a standard factor?

In "Credit Scoring for Risk Managers: The Handbook for Lenders" by
Elizabeth Mays, chapter 4 page 68, it says that the coeffients from
the logistic regression are multiplied by a factor equal to the number
of points for which we want a doubling of the odds to occur, and then
divided by ln(2). Is the multiplication a standard practice?

Why it is multiplied by say 20/ln(2)? How do we determine what factor
to multiply? Is 20 a standard factor?

Panchu wrote:
In "Credit Scoring for Risk Managers: The Handbook for Lenders" by
Elizabeth Mays, chapter 4 page 68, it says that the coeffients from
the logistic regression are multiplied by a factor equal to the number
of points for which we want a doubling of the odds to occur, and then
divided by ln(2). Is the multiplication a standard practice? Why it is
multiplied by say 20/ln(2)? How do we determine what factor to
multiply? Is 20 a standard factor?

It might help if you explain what is being regressed on what.

--
David Marcus

On Feb 13, 1:44 am, David Marcus <DavidMar...@alumdotmit.edu> wrote:
Panchu wrote:
In "Credit Scoring for Risk Managers: The Handbook for Lenders" by
Elizabeth Mays, chapter 4 page 68, it says that the coeffients from
the logistic regression are multiplied by a factor equal to the number
of points for which we want a doubling of the odds to occur, and then
divided by ln(2). Is the multiplication a standard practice? Why it is
multiplied by say 20/ln(2)? How do we determine what factor to
multiply? Is 20 a standard factor?

It might help if you explain what is being regressed on what.

I will be involved in Credit Scoring project. Prior to that I am going
through thos book. It is written as follows in the book:

Once the logistic regression model has been estimated,

we can put in
the X values for a given loan and calculate a scoring using the
equation
SCORE = B1*X1 + ... + Bn*Xn.
The resulting score, however, is on the hard-to-interpret
natural log scale. A standard practice in the scoring world is to
transform the score to a linear scale where a given number of points
will result in a doubling of the odds that the event will happen.
To do the transformation, we multiply the score by a factor
equal to the number of points for which we want a doubling of the odds
to occur and then divided by ln(2). Say we seek a score where the odds
of going bad are expected to double each time the score increases 20
points. To obtain the scaled score, we would multiply the score that
comes directly from the regression model by 20 and divide by the
natural log of 2. That is we would calculate
(B1*X1 + ... + Bn*Xn)*(20/ln(2))

My question is "How do we determine what factor to multiply?". I tried
through calculations, but unable to find!

Panchananawrote:
On Feb 13, 1:44 am, David Marcus <DavidMar...@alumdotmit.edu> wrote:
Panchu wrote:
In "Credit Scoring for Risk Managers: The Handbook for Lenders" by
Elizabeth Mays, chapter 4 page 68, it says that the coeffients from
the logistic regression are multiplied by a factor equal to the number
of points for which we want a doubling of the odds to occur, and then
divided by ln(2). Is the multiplication a standard practice? Why it is
multiplied by say 20/ln(2)? How do we determine what factor to
multiply? Is 20 a standard factor?

It might help if you explain what is being regressed on what.

I will be involved in Credit Scoring project. Prior to that I am going
through thos book. It is written as follows in the book:

Once the logistic regression model has been estimated,

Does the book define/describe this model?





we can put in
the X values for a given loan and calculate a scoring using the
equation
SCORE = B1*X1 + ... + Bn*Xn.
The resulting score, however, is on the hard-to-interpret
natural log scale. A standard practice in the scoring world is to
transform the score to a linear scale where a given number of points
will result in a doubling of the odds that the event will happen.
To do the transformation, we multiply the score by a factor
equal to the number of points for which we want a doubling of the odds
to occur and then divided by ln(2). Say we seek a score where the odds
of going bad are expected to double each time the score increases 20
points. To obtain the scaled score, we would multiply the score that
comes directly from the regression model by 20 and divide by the
natural log of 2. That is we would calculate
(B1*X1 + ... + Bn*Xn)*(20/ln(2))

My question is "How do we determine what factor to multiply?". I tried
through calculations, but unable to find!

--
David Marcus- Hide quoted text -

- Show quoted text -- Hide quoted text -

- Show quoted text -

"Panchu" <panchan...@gmail.com> wrote in news:1171293538.248577.211090
@q2g2000cwa.googlegroups.com:

In "Credit Scoring for Risk Managers: The Handbook for Lenders" by
Elizabeth Mays, chapter 4 page 68, it says that the coeffients from
the logistic regression are multiplied by a factor equal to the number
of points for which we want a doubling of the odds to occur, and then
divided by ln(2). Is the multiplication a standard practice?

That does sound fairly standard. A simplistic starting point would be :
ln(OR)=beta*(difference in variables).
If you want doubling, then set OR=2 and solve. Remember: you have a linear
model in the log-odds scale.

Why it is multiplied by say 20/ln(2)? How do we determine what factor
to multiply? Is 20 a standard factor?

Tell us where you got 20 and perhaps someone can answer.

--
David Winsemius

On Feb 13, 8:24 am, David Winsemius <doe_s...@comcast.n0T> wrote:
"Panchu" <panchan...@gmail.com> wrote in
news:1171293538.248577.211090 @q2g2000cwa.googlegroups.com:

In "Credit Scoring for Risk Managers: The Handbook for Lenders" by
Elizabeth Mays, chapter 4 page 68, it says that the coeffients from
the logistic regression are multiplied by a factor equal to the
number of points for which we want a doubling of the odds to occur,
and then divided by ln(2). Is the multiplication a standard
practice?

That does sound fairly standard. A simplistic starting point would be
:
ln(OR)=beta*(difference in variables).
If you want doubling, then set OR=2 and solve. Remember: you have a
linear model in the log-odds scale.

Why it is multiplied by say 20/ln(2)? How do we determine what
factor to multiply? Is 20 a standard factor?

Tell us where you got 20 and perhaps someone can answer.

--
David Winsemius

To do the calculation, intercept is not present in the model!

"Panchanana" <panchan...@gmail.com> wrote innews:1171446560.161487.81860@s48g2000cws.googlegroups.com:





On Feb 13, 8:24 am, David Winsemius <doe_s...@comcast.n0T> wrote:
"Panchu" <panchan...@gmail.com> wrote in
news:1171293538.248577.211090 @q2g2000cwa.googlegroups.com:

In "Credit Scoring for Risk Managers: The Handbook for Lenders" by
Elizabeth Mays, chapter 4 page 68, it says that the coeffients from
the logistic regression are multiplied by a factor equal to the
number of points for which we want a doubling of the odds to occur,
and then divided by ln(2). Is the multiplication a standard
practice?

That does sound fairly standard. A simplistic starting point would be
:
ln(OR)=beta*(difference in variables).
If you want doubling, then set OR=2 and solve. Remember: you have a
linear model in the log-odds scale.

Why it is multiplied by say 20/ln(2)? How do we determine what
factor to multiply? Is 20 a standard factor?

Tell us where you got 20 and perhaps someone can answer.

--
David Winsemius

To do the calculation, intercept is not present in the model!

If that was a question, then let me see if I understand it. You want to
know if I left out or forgot to consider the intercept term in error?
Then no, I did not.

The full linear model on the log odds scale would be:

logit(Y) = ln(odds(Y)) = ln(Y/1-Y)=
beta0 +beta1*X1 + beta2*X2 + beta3*X3... (1)

After the model is estimated you can ask the question: "What is the
estimated odds ratio for two cases who differ only in variable X1. Let's
say that the two values are X1_a and X1_b. The answer to that question
is:
pred(Y/(1-Y)|X1=X1a)
OR = ----------------------- = exp(beta_1*(X1_a-X1_b)) (2)
pred(Y/(1-Y)|X1=X1b)

Why no intercept? The intercept term would appear in the initial
calculations starting from the model for eq 1 in both the numerator and
the denominator, but they start out inside ln(.) and when you convert to
the odds scale, you would get beta0/beta0 = 1 as one of the terms. Any of
the other variables with identical values assumed would also have ratios
of unity and dissappear in a cloud of magical logistic smoke. Taking logs
of (2), the expression offered in my initial response then appears
immediately.

If you had two variables under question, and the differences are now
delta(.) then:
OR=exp(beta1*(delta(X1) +beta2*(delta(X2))

I did leave out a few details, but they can be supplied if further proof
is needed.

--
David Winsemius- Hide quoted text -

- Show quoted text -

From the explanation, I am able to make the following solution.

On Feb 14, 6:20 pm, David Winsemius <doe_s...@comcast.n0T> wrote:
"Panchanana" <panchan...@gmail.com> wrote
innews:1171446560.161487.81860@s48g2000cws.googlegroups.com:

On Feb 13, 8:24 am, David Winsemius <doe_s...@comcast.n0T> wrote:
"Panchu" <panchan...@gmail.com> wrote in
news:1171293538.248577.211090 @q2g2000cwa.googlegroups.com:

In "Credit Scoring for Risk Managers: The Handbook for Lenders"
by Elizabeth Mays, chapter 4 page 68, it says that the
coeffients from the logistic regression are multiplied by a
factor equal to the number of points for which we want a
doubling of the odds to occur, and then divided by ln(2). Is the
multiplication a standard practice?

Since I was away I am giving the response lately. Sorry for this:
From the explanation, I am able to make the following solution.

If there is one variable under question, and the differences is now 20
then:
{2* [P1/(1-P1)]}/ {[P1/(1-P1)]} = {exp(alpha+beta*(x+20))}/{exp(alpha
+beta*x)}
2 = exp (beta*20)
ln 2 = beta * 20
beta = (ln 2)/20

Is this correct?

If so, why are we multiplying the score by 20/(ln 2)
Please, explain.