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Logistic
Regression Model
(Applied Logistics
Regression (2013)
Hosmer David )
- The Multiple
Logistic
Regression Model
- INTRODUCTION
- ability to handle
many variables
- ability to handle
many variables
- MODEL
- TESTING THE
MODEL
- univariable
Wald test
statistics
- univariable
Wald test
statistics
- INTRODUCTION
- Simple
- INTRODUCTION
- outcome variable
is discrete, binary
or dichotomous.
- Example 1
Excel-Star
- Follow
Logistic
distribution
- logistic regression model
- Summary:
- 1. The
model for the
conditional mean
of the regression
equation must be
bounded between
zero and one. 2.
The binomial, not
the normal,
distribution
describes the
distribution of the
errors and is the
statistical
distribution on
which the
analysisis based
- 1. The
model for the
conditional mean
of the regression
equation must be
bounded between
zero and one. 2.
The binomial, not
the normal,
distribution
describes the
distribution of the
errors and is the
statistical
distribution on
which the
analysisis based
- outcome variable
is discrete, binary
or dichotomous.
- FITTING THE
LOGISTIC
REGRESSION
MODEL
- maximum likelihood.
- the method yields values
for the unknown
parameters that maximize
the probability of
obtaining the observed set
of data. In order to apply
this method we must first
construct a function,
called the likelihood
function
- The maximum
likelihood estimators of
the parameters are the
values that maximize
this function
- The maximum
likelihood estimators of
the parameters are the
values that maximize
this function
- the method yields values
for the unknown
parameters that maximize
the probability of
obtaining the observed set
of data. In order to apply
this method we must first
construct a function,
called the likelihood
function
- maximum likelihood.
- TESTING FOR THE
SIGNIFICANCE OF THE
COEFFICIENTS
- The statistic D is called the
deviance, and for logistic
regression, Is the same as the
sum-of-squares in linear
regression
- The statistic D is called the
deviance, and for logistic
regression, Is the same as the
sum-of-squares in linear
regression
- CONFIDENCE
INTERVAL
ESTIMATION
- INTRODUCTION
- Multinomial
and Ordinal
Outcomes
- nominal with
more than two
levels
- discrete
choice
model
- The variable has three levels
A,B or C is chosen.Possible
covariates might include
gender,age,income,family
size,and others.
- multinomial ,polychotomous, or
polytomous logistic regression
- The variable has three levels
A,B or C is chosen.Possible
covariates might include
gender,age,income,family
size,and others.
- discrete
choice
model
- Model
- p covariates and a constant
term, denoted by the vector x,of
length p+1,where x0=1.
- p covariates and a constant
term, denoted by the vector x,of
length p+1,where x0=1.
- nominal with
more than two
levels
- Interpretation of the
Fitted Logistic Regression
Model
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