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PERFECT SEPARATION in R I have run a logistic model using the probit transformation in R to model the probability of species = 1 (species

PERFECT SEPARATION in R

I have run a logistic model using the probit transformation in R to model the probability of species = 1 (species is binary) as a function of 4 independent variables.

So, it looks something like m=glm(Species~V1+V2+V3+V4, family = "binomial"("probit"). I've also done the same for the logit transformation. The dataset is has perfect separation and can perfectly predict whether species is 1 or 0, given values for the 4 independent variables. When a dataset has perfect separation, all z values in the output in R are 0. Pr(>|z|) are all 1. Given that probit and logit both show that this dataset has perfect separation, how can I logically explain this output? What do the z values tell me, etc? What does the AIC of 10 mean, given that there are 10 observations in this dataset? Really I'm just looking for a good verbal explanation here. I can't quite put this into words very well.

Here is the logit:

Deviance Residuals: 
 1 2 3 4 5 6 7 8 9 10 
-2.110e-08 -3.480e-06 -2.110e-08 -4.238e-06 -9.967e-06 5.774e-06 2.516e-06 9.366e-06 2.110e-08 2.110e-08 
 
Coefficients:
 Estimate Std. Error z value Pr(>|z|)
(Intercept) 4.047e+01 1.493e+06 0 1
Sepal.Length -1.373e+00 2.368e+05 0 1
Sepal.Width -2.255e+01 6.489e+05 0 1
Petal.Length 6.453e+00 1.829e+05 0 1
Petal.Width 2.558e+01 5.649e+05 0 1
 
(Dispersion parameter for binomial family taken to be 1)
 
 Null deviance: 1.3863e+01 on 9 degrees of freedom
Residual deviance: 2.5681e-10 on 5 degrees of freedom
AIC: 10
 
Number of Fisher Scoring iterations: 24

Here is the probit:

Deviance Residuals:

1 2 3 4 5 6 7 8 9

-2.110e-08 -3.917e-06 -2.110e-08 -4.824e-06 -1.266e-05 6.984e-06 2.588e-06 1.204e-05 2.110e-08

10

2.110e-08

Coefficients:

Estimate Std. Error z value Pr(>|z|)

(Intercept) 9.847e+00 2.076e+05 0 1

Sepal.Length -6.859e-01 3.096e+04 0 1

Sepal.Width -5.335e+00 8.943e+04 0 1

Petal.Length 1.827e+00 2.348e+04 0 1

Petal.Width 7.155e+00 7.554e+04 0 1

(Dispersion parameter for binomial family taken to be 1)

Null deviance: 1.3863e+01 on 9 degrees of freedom

Residual deviance: 3.9939e-10 on 5 degrees of freedom

AIC: 10

Number of Fisher Scoring iterations: 23

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