Hello
everyone,
my
name
is
Raaed Fadhil
Mohammed.
I
am
a
statistician.
I
lecturer
in
University
of
Mustansiriyah.
My
paper title is
Estimating
the
Parameter
of
Poisson
Regression
Model
Under
the
Multicollinearity
Problem
.
Outline:
Poisson
Regression
Model,
Multicollinearity
problem,
Ridge Regression Estimator
Method,
Liu Estimators Method,
and
Real
Data
Example.
Conclusion
and
References.
Poisson Regression
Model.
One
of
the
types
of
regression
model
that
fall
under
linear-logarithmic
regression
model
as
by
taking
the
natural
logarithm
of
the
distribution
formula,
it turns
into
a
linear
procedure.
Random
errors
in the
model
follow a
Poisson
distribution
with
a
parameter
mu.
The
model
is
based
on
two
essential
assumptions
about
the
distribution
as
it
differs
from
the
distribution
of
random
errors in the linear regression
model and
the
properties
of
the
Poisson
distribution
parameter
mu
as
a
function
of
predictor
variables.
M
ulticollinearity
Problem.
Multicollinearity Problems occur
when
two
or
more
predictor
variables
are
correlated
to
a solid
linear
relation,
so
it's
difficult
to
separate
the
effect
of
each
predictor
variable
from
the
dependent
variable
in
practice.
Or
when
the
value
of
one
of
the
predictor variables
depends
on
one
or
more
of
the
other
predictor
variables
in
the
model
under
study,
as
well
as
if the
data
takes
the
form
of
a
time
series
or
across-
section
data.
The
multicollinearity
problem
can
be
classified
into
two
types:
Number
1,
Perfect multicollinearity.
The determinant of the
information
matrix
is zero,
x
transpose
x
determined
equal
zero.
It follows from
this
is
impossible
to
estimate,
the
parameters
of
the
regression
model
due
to
the
inability
to
calculate
the
inverse
of
matrix
x
transpose
x.
The
best
method
in
this
case
to
calculate
x
transpose x.
We
can
make
use
principal
component
analysis.
Number
2,
Semi-perfect
multicollinearity.
In
this
case,
if
the
value
of
the
determinant
information
matrix
is
minimal,
close
to
zero,
then
the
parameters
estimated
considerable
variance.
The
best
method
in
this
case
we
can
use
regression
method
or
Leo
estimator
method.
The
following
formula
here
can
express
the
variance-
covariance
matrix
of the
parameters
estimated.
Perhaps
the
best
statistical
method
for
measuring
the
multicollinearity
intensity
is
the
variance
in
flation
factor
VIF,
whose
formula is
as
follows.
VIF
equal
one
over
one
minus
R
square.
R
square
here
determined
coefficient.
Ridge Regression
Estimator
Method.
One
of
the
important
alternatives
for
estimating
the
parameters
of
regression
module
when
there
is
m
ulticollinearity
between
predictor
variables.
This
method
established
according
to
the
principle
of
the
researchers
Hoerl
and
Kennard,
which
is
by
adding
a
small
positive
quantity
to
the
mine
diameter
elements
of
the
information
matrix.
The
regression
estimators
are
based
when
k
greater
than
zero
so
that
the
base
amount
can
be
expressed
by
the
formula,
Z minus
identity
by
beta.
Liu
Estimators
method.
The researcher
Liu 1993
laid
the
foundations
of
this
method
to
address
the
issue
of
the
variance
inflation
of
the
estimated
parameters
in
the
presence
of
multicollinearity
a problem.
The
Liu
estimator
for
the
parameter
Poisson
regression
can
be
expressed
in
the
following
formula.
Also
Liu
estimators
are
biased
when
d
greater
than
zero
and
the
magnitude
of
the
bias
is
z
minus
identity
by
beta.
Liu
estimators
are
biased,
the
reason
of
the
bias
is
the
added
value
d,
which
ranges
between
zero
and
one.
Also,
the
calculated
mean
squared
error
according
to
Liu
estimators'
method
is
less
than
the
mean
squared
error
for
the
same
parameters
if
estimated
according
to
the
maximum
likelihood
method.
Real
Data
example.
We
will
obtain
real
data
concerning
congenital
defects
of
the
heart
and
circulatory
system
in
a
new
borns
from
the
Central
Child T
eaching
Hospital
in
Baghdad,
Iraq,
where
the
distribution
of
a
dependent
variable
y represents
abnormalities
of
the
heart
and
circulatory
system
in
children
was
studied.
Also the
revealing
existence
of
a
multicollinearity
problem
among
the
predictor
variables
under
study.
The
case
of
congenital
disabilities
arriving
at
the
Central
Child
Teaching
Hospital
are
recorded
in
a
form
prepared
by
the
Statistics
Division
in
the
hospital
in
the
form
of
count
data
and
totals
within
semi
monthly
periods,
the
sample
was
taken
for
the
period
from
2012
to
end
2019,
and a Poisson
regression
model
was
built
as
one
of
the
appropriate
models
to
describe
this phenomenon as
the
following
formula:
yi equ
al
exponential
beta
one
xi 1
plus
beta
2
xi
2
plus
beta
3
xi
3 plus beta
4 xi 4 plus beta 5 xi 5 plus beta 6 xi 6 plus beta 7 xi plus ui.
That y represent
the
total
number
of
children
with
congenital
heart
and
circulatory
defects
in
each
period.
Xi1, the total weighted
of
infected
children
within
each
period.
Xi2, the
total
ages
fathers
of
inflected
children
within
each
period.
Xi3, the total ages mothers of inflected children within each period.
Xi
4,
represents
the
number
of
infected
male
children
within
each
period.
Xi5
represents
the
number
of
inected
female
children
within
each.
Xi
6,
the
number
of
infected children
born
from consanguineous
marriages
within
each
period.
Xi7,
the
number
of
infected
children
whose
mothers
were
exposed
to
radiation
or
life
influence
such
as
taking
certain
medications
and
drugs
during pregnancy.
Beta
one,
beta
two,
beta
three,
beta
four,
beta
five,
beta
six
and
beta
seven
beta.
The
slope
parameters
in
the
model
and
beta
note
represents
the
constant term.
ui
represent
the
random
error
in
the
model.
This
table,
Testing
Data
and
Diagnoising
Multicollinearity
to
find
out
probability
distribution
according
to
which
response
variable
can
be
distributed.
We
use
jump
pro
16.2
and
it
was
found
y,
dependent
variable
follows
the
Poisson
distribution
with
distributed
parameter,
mu
equals
6.5.
To
verify,
the
suitability
of
the
Poisson
distribution
to
the
response
variable y.
The
testing
goodness
of
it
was
conducted
for
the
variable
of
the
total
number
of
children
with
congenital
heart
and
circulatory
defense
in
each
period.
The
throw
which
we
make
show
that
the
poison
distribution
is
the
most
promoted
distribution
that
dependant
variable
can follow.
Where
we
not have
the
goodness
of
test
value
is
4958.4579
with
significance
level
close
to
zero.
As
on
the
table
in
the
front
of
you.
To
detect
whether
there
is
multicolliniarity
among
the
product
variable
under
study,
we
can
calculate
the
correlation
matrix
between
the
predictor
variables.
From
the
figure
we
observe
that
value
of
correlation
coefficient
are
significant
and
large
for
all
predictor
variables,
as
each
variable
is
associated
with
all
predictor
variables,
with
the
strong
direct
linear
correlation.
This
table
shown
the
value
of
various
function
factors.
As
the
largest
of
them,
well
those
of
the
projector variables, X2, X3 and X4
The variance inflation factor for undermining projector variables
exists the number 18.
From
this
we
conclude
that
there
is
a
linear
multiplicate
between
the
predictor
variables
and
the
[inaudible 00:16:24].
Application
of
Poisson
regression
method.
Parameter
estimator
of Poisson regression model using
method
regression,
we
observe
that
the
total
number
of
children
with
congenital
health,
and
circulatory
defects
in
each
period
depends
on
the
increase
and
all
parameters
of
[inaudible 00:17:11].
However,
most
variables
are
insignificant.
X1,
X4,
X5 and X6
because
of
the
effects
of
semi-
perfect
multi
collinearity.
Also,
the
result
indicates
that
the
base
parameter
is
k
equal
zero
point one, two.
[foreign language 00:17:53]
86.4959.
This
table
we
can
obtain
by
using
JMP.
When
we
are
applying
the
Liu
estimator
method
to
estimate
the
coefficient
of
the
Poisson
regression
module
in
the
presence
of
the
multicollinearity
problem.
We
use
the
JMP
secret
to
connect
between
our
language
and
JMP.
This
secret
to connect and run from
JMP,
the
package
of
Liu
regression
in
our
language.
While applying to
[inaudible 00:19:12], the coefficient, we obtained this result.
We
observed
that
the
total
number
of
children
with
the
congenital
hearts
and
circulatory
in
each
period
depends
on
the
extent
of
increase
in
all
parameters
of
the
model,
despite
the
insignificance
of
the
variable
xi
1.
Because
all
variables
under
study
are
increasing
the
number
of
children
with
congenital
disabilities,
but
it
is
very
good
properties.
Also
the
result
indicates
that
Hiaki
formation
criteria
35.
29
add
the
base
parameter
d
equal 4.1.
When
comparing
the
two
methods
regression
and
Liu estimator,
we
know
that
the
estimator
approach
given
a
low
value
of
information.
Has
more
significant
proficient
when
they
compare
to
the
regrasion
method.
Conclusions.
In
this
paper,
we
review
the
most
prominent
method
of
parameter
estimating
of
the
Poisson
regression
model
when
the
data
suffer
from
the
problem
of
semi-
perfect multicollinearity,
where
took
the ridge
regression
method
and
Liu
estimators'
method
and
compared
the
two
methods
based
on
Account
Information
Criteria
as
a
criterion
for
comparison.
By
applying
regression
analysis
method
in
the
presence
of
a
semi-perfect
multicollnearity
problem to real
data
regarding
congenital
heart
and
circulatory
defects
in
newborns,
obtained
from the
Central
Child
Teaching
Hospital
for
the
period
from
2012
to
2019,
we
find
the Liu
estimator's
method
is
more
efficient
than
the
regression
method
because
it
has
a
lower Akaike's
information
criterion.
It
also
gives
more
reliable
results
and
more
accurate
p-values.
Number
3:
Through Liu estimators'
method,
it
is
clear
that
all
predictor
variables
under
study are
influential
in
the
regression
model,
even
if
they
are
not
significant,
as
all
parameters
are
influential
in
increasing
the
number
of
children
with
congenital
disabilities
but
in varying
proportions.
Thank
you.
