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Separation occurs when some classes of a categorical outcome can be perfectly distinguished by a linear combination of other variables.

2 votes

Complete separation in logistic regression with only one direction

The paper you linked do not have a correct definition of complete separation, it says that only occurs if it is caused by one variable $s_i$. … That is not correct, complete separation can well occur without any single variable causing it. …
kjetil b halvorsen's user avatar
1 vote

likelihood ratio test for logistic regression with a complete separation

You can still use the likelihood ratio test with separation. … For more details on logistic regression and separation see How to deal with perfect separation in logistic regression? and GLM high standard errors, but variables are definitely not collinear. …
kjetil b halvorsen's user avatar
5 votes

Why is it desirable to have linear separability in SVM?

In the example you show, point lie on concentric annular rings, which cannot be separated by any plane, but by introducing a new variable RADIUS---distance from center---you get complete linear separation
kjetil b halvorsen's user avatar
4 votes

Normally distributed estimated parameters in logistic regression

Well, you can define the $Z$ statistic by the same formulas (well, actually using asymptotic approximations) that is used in the normal case. There is no implication that the resulting statistic do h …
kjetil b halvorsen's user avatar
2 votes

instability of logistic regression

Well, if your goal is discrimination, it doesn't really matter if the estimated parameters are unstable---the class assignments could well be stable! Even, if your goal is risk estimation, even if the …
kjetil b halvorsen's user avatar
0 votes

any problems with Firths Logit model (to deal with separation)

Partially answered in comments: No time to provide an elaborate response, but Greenland recommends log-F(1,1) prior instead of Firth's bias correction method. And you can implement it by simply modif …
45 votes

Why does logistic regression become unstable when classes are well-separated?

(y ~ x, family=binomial, separation="test") Error in glm(y ~ x, family = binomial, separation = "test") : Separation exists among the sample points. … =binomial, separation="test") Error in glm(y ~ x, family = binomial, separation = "test") : Separation exists among the sample points. …
kjetil b halvorsen's user avatar
1 vote

Perfect separation error message for glm with binomial but not with quasibinomial family

for some ideas of what to do in this case of separation. …
kjetil b halvorsen's user avatar
1 vote

Dealing with quasi-complete separation in General Additive Model?

Your diagnosis is probably correct, and the big standard errors is because the loglikelihood function in this case is far from quadratic. Confidence intervals based on likelihood profiling might be be …
kjetil b halvorsen's user avatar
4 votes

If logistic regression is a linear classifier why does it fail on linearly separable data?

If the data are linearly separable with a positive margin, so that it can be separated by a plane in more than two (so infinitely many ways), then all those ways will maximize the probability, so the …
kjetil b halvorsen's user avatar
4 votes
Accepted

Binomial GLM - non-significant difference between 100% opposite groups of observations

As for diagnosing such separation problems, there is the useful R package safeBinaryRegression. See my answer here Why does logistic regression become unstable when classes are well-separated? …
kjetil b halvorsen's user avatar