multilevel binary logistic regression
Click here to load reader
Post on 16-Apr-2017
Embed Size (px)
Eduard Ponarin Veronica Kostenko
Multilevel binary logistic regression
The basic logistic regression
X on Y in case of a binary outcome.
For example, if a candidate won or not during the elections, Y is either 0 or 1). Here X stands for the money spent on the campaign, Y the outcome.
Plotting X against proportion of successes
Where ni stands for the number of observations at X = h.
Why not a linear model for probabilities?
Linear approximation is problematic in this case because:
a) Residuals are non-randomly distributed
b) 0.2 < p < 0.8 is distributed otherwise then the tails of the function (p < 0.2; p > 0.8)
c) Regression line should fall into the interval between 0 and 1 which is hard to fit for a linear model
Estimated probabilities should be transformed into logits
Transformation of probabilities into logits
Plotting logit functions
Increasing logit function Decreasing logit function
Plotting probabilities for a single level logistic regression
Multilevel logistic regression formula
logit (Pr (Yi=1)) = j + i = 00 + 0j + i
logit (Pr (Yi=1)) = j + gender * gender + age * age + i.
j = 00 + 0j
Script for a simple model
Output for a logistic multilevel regression
Coefficients shouldnt be interpreted as in linear models, they should be transformed (exponential or divided-by-4 rule)
Signs of the coefficients stay the same
Coefficients can be compared with each other
Output for a simple model
Summary (more informative)
Adding 1st level interaction
Summary with interaction
Varying intercepts and slopes without group level predictor
Summary with varying slope
Adding a group-level predictor
A model with between-level interaction