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Generalized Linear Model - 2 (Binary Logistic Regression Model (Fitted…
Generalized Linear Model - 2
Logistic Regression
Outcome is categorical
Binary/Nominal/Ordinal logistic regression
First used in dose-response models
(animal studies, doses,
look @ survival curve)
GLM that uses
logit link function
Epidemiology:
used for analysing odds ratios
Odds & odds ratios
Logit link function
If P is the proportion of people
for which an event occurred
then P/(1-P) is the odds
of the event occurring
Natural link to
odds & odds ratios
(natural log of the odds)
eg, simple scenario:
binary risk factor & outcome
Odds of event occurring
if you do not have risk factor
Odds of event occurring
if you have risk factor
odds: # times event occurred /
no. times event did not occur
Odds ratio for event occurring
if you have risk factor
relative to
not having risk factor
(note: referent in denominator)
Can re-write odds of
event occurring if you
have risk factor as a proportion
(sim to logit)
Binary Logistic
Regression Model
Expected Values
Fit the Model
Specify the model
Fitted values
2nd Class
3rd Class
1st Class
Visualise the data
Convert to
meaningful values
Proportion
Odds ratio
Odds
Pseudo R-square:
Nagelkerke R square
How much the model
improves
by including the va's
compared
to the null (constant only) model
Goodness of fit
Interpretation
Assumptions
Expanding on the model
Interactions
Interpreting sign.
terms in model
Calculate meaningful values
Interpreting Co-eff's
Interpretation of results
Confidence Intervals
re-run analysis with different referent
Comparison of Odds Ratios
Presentation of Results
Descriptive Statistics
% in each group
Crude odds ratio
Counts
Logistic Regression Output
Significance of
adjusted association
(Graph if there is
effect modification)
Adjusted odds ratios & CIs
Never
regression coeff's
convert to exp(b)
Summary of model