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Terms in this set (115)
Logistic Regression Commonly used for modeling binary response
data. The response variable is a binary variable, and
thus, not normally distributed.
In logistic regression, we model the probability of a
success, not the response variable. In this model,
we do not have an error term
g-function We link the probability of success to the predicting
variables using the g link function. The g function is
the s-shape function that models the probability of
success with respect to the predicting variables
The link function g is the log of the ratio of p over
one minus p, where p again is the probability of
success
Logit function (log odds function) of the probability
of success is a linear model in the predicting
variables
The probability of success is equal to the ratio
between the exponential of the linear combination
of the predicting variables over 1 plus this same
exponential
,Odds of a success This is the exponential of the Logit function
Logistic Regression Assumptions Linearity: The relationship between the g of the
probability of success and the predicted variable,
is a linear function.
Independence: The response binary variables are
independently observed
Logit: The logistic regression model assumes that
the link function g is a logit function
Linearity Assumption The Logit transformation of the probability of
success is a linear combination of the predicting
variables. The relationship may not be linear,
however, and transformation may improve the fit
The linearity assumption can be evaluated by
plotting the logit of the success rate versus the
predicting variables.
If there's a curvature or some non-linear pattern, it
may be an indication that the lack of fit may be due
to the non-linearity with respect to some of the
predicting variables
,Logistic Regression Coefficient We interpret the regression coefficient beta as the
log of the odds ratio for an increase of one unit in
the predicting variable
We do not interpret beta with respect to the
response variable but with respect to the odds of
success
The estimators for the regression coefficients in
logistic regression are unbiased and thus the mean
of the approximate normal distribution is beta. The
variance of the estimator does not have a closed
form expression
Model parameters The model parameters are the regression
coefficients.
There is no additional parameter to model the
variance since there's no error term.
For P predictors, we have P + 1 regression
coefficients for a model with intercept (beta 0).
We estimate the model parameters using the
maximum likelihood estimation approach
Response variable The response data are Bernoulli or binomial with
one trial with probability of success
, MLE The resulting log-likelihood function to be
maximized, is very complicated and it is non-linear
in the regression coefficients beta 0, beta 1, and
beta p
MLE has good statistical properties under the
assumption of a large sample size i.e. large N
For large N, the sampling distribution of MLEs can
be approximated by a normal distribution
The least square estimation for the standard
regression model is equivalent with MLE, under the
assumption of normality.
MLE is the most applied estimation approach
Parameter estimation Maximizing the log likelihood function with respect
to beta0, beta1 etc in closed (exact) form
expression is not possible because the log
likelihood function is a non-linear function in the
model parameters i.e. we cannot derive the
estimated regression coefficients in an exact form
Use numerical algorithm to estimate betas
(maximize the log likelihood function). The
estimated parameters and their standard errors are
approximate estimates
Binomial Data This is binary data with repititions
Marginal Relationship Capturing the association of a predicting variable
to the response variable without consideration of
other factors
Correct Answers | Verified | Latest Update 2026
Save
Terms in this set (115)
Logistic Regression Commonly used for modeling binary response
data. The response variable is a binary variable, and
thus, not normally distributed.
In logistic regression, we model the probability of a
success, not the response variable. In this model,
we do not have an error term
g-function We link the probability of success to the predicting
variables using the g link function. The g function is
the s-shape function that models the probability of
success with respect to the predicting variables
The link function g is the log of the ratio of p over
one minus p, where p again is the probability of
success
Logit function (log odds function) of the probability
of success is a linear model in the predicting
variables
The probability of success is equal to the ratio
between the exponential of the linear combination
of the predicting variables over 1 plus this same
exponential
,Odds of a success This is the exponential of the Logit function
Logistic Regression Assumptions Linearity: The relationship between the g of the
probability of success and the predicted variable,
is a linear function.
Independence: The response binary variables are
independently observed
Logit: The logistic regression model assumes that
the link function g is a logit function
Linearity Assumption The Logit transformation of the probability of
success is a linear combination of the predicting
variables. The relationship may not be linear,
however, and transformation may improve the fit
The linearity assumption can be evaluated by
plotting the logit of the success rate versus the
predicting variables.
If there's a curvature or some non-linear pattern, it
may be an indication that the lack of fit may be due
to the non-linearity with respect to some of the
predicting variables
,Logistic Regression Coefficient We interpret the regression coefficient beta as the
log of the odds ratio for an increase of one unit in
the predicting variable
We do not interpret beta with respect to the
response variable but with respect to the odds of
success
The estimators for the regression coefficients in
logistic regression are unbiased and thus the mean
of the approximate normal distribution is beta. The
variance of the estimator does not have a closed
form expression
Model parameters The model parameters are the regression
coefficients.
There is no additional parameter to model the
variance since there's no error term.
For P predictors, we have P + 1 regression
coefficients for a model with intercept (beta 0).
We estimate the model parameters using the
maximum likelihood estimation approach
Response variable The response data are Bernoulli or binomial with
one trial with probability of success
, MLE The resulting log-likelihood function to be
maximized, is very complicated and it is non-linear
in the regression coefficients beta 0, beta 1, and
beta p
MLE has good statistical properties under the
assumption of a large sample size i.e. large N
For large N, the sampling distribution of MLEs can
be approximated by a normal distribution
The least square estimation for the standard
regression model is equivalent with MLE, under the
assumption of normality.
MLE is the most applied estimation approach
Parameter estimation Maximizing the log likelihood function with respect
to beta0, beta1 etc in closed (exact) form
expression is not possible because the log
likelihood function is a non-linear function in the
model parameters i.e. we cannot derive the
estimated regression coefficients in an exact form
Use numerical algorithm to estimate betas
(maximize the log likelihood function). The
estimated parameters and their standard errors are
approximate estimates
Binomial Data This is binary data with repititions
Marginal Relationship Capturing the association of a predicting variable
to the response variable without consideration of
other factors
