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When does overdispersion not apply in logistic regression?
As already noted by others, overdispersion doesn’t apply in the case of a Bernoulli (0/1) variable, since in that case, the mean necessarily determines the variance. In the context of logistic regression, this means that if your outcome is binary, you can’t estimate a dispersion parameter. (N.B.
Can a logistic regression model have a binary outcome?
Remember, logistic regression with a purely binary outcome is just a special case of the more general logistic regression model in which the binomial index can exceed one (and can vary across observations).
Why does overdispersion occur in the generalized linear model?
The greater variability than predicted by the generalized linear model random component reflects overdispersion. Overdispersion occurs because the mean and variance components of a GLM are related and depends on the same parameter that is being predicted through the independent vector.
What is the logit of a logistic regression?
Logistic regression forms this model by creating a new dependent variable, the logit(P). If P is the probability of a 1 at for given value of X, the odds of a 1 vs. a 0 at any value for X are P/(1-P). The logit(P) is the natural log of this odds ratio. Definition : Logit(P) = ln[P/(1-P)] = ln(odds).
What should be included in a logistic regression analysis?
In the previous two chapters, we focused on issues regarding logistic regression analysis, such as how to create interaction variables and how to interpret the results of our logistic model. In order for our analysis to be valid, our model has to satisfy the assumptions of logistic regression.
Is there such a thing as overdispersion in GLM?
Overdispersion occurs because the mean and variance components of a GLM are related and depends on the same parameter that is being predicted through the independent vector. There is no such thing as overdispersion in ordinary linear regression. In a linear regression model
When does overdispersion occur in a response variable?
I’ve read that overdispersion is when observed variance of a response variable is greater than would be expected from the binomial distribution. But if a binomial variable can only have two values (1/0), how can it have a mean and variance? I’m fine with calculating the mean and variance of successes from x number of Bernoulli trials.