Hello;
I am working on a logistic regression model in which I have quasi-complete separation on an explanatory variable (see table below).  The response variable is Success of parrot reintroductions, and one of the explanatory variables is PredThreat, a 3 category variable designating the level of predator threat to the population.  When I fit the univariate logistic regression model Success ~ PredThreat, I get a huge standard error, which I believe is an indication of the optimization algorithm failing due to quasi-complete separation.  I am testing a variety of models using information-theoretic model selection to judge which variables are important to reintroduction success.  My question concerns what to do to about PredThreat, since it appears to be an informative variable.  First I'm wondering if I can trust the AIC value calculated from the model with PredThreat?  Second, to get at an effect size and also to include it in multivariate models, I thought of treating PredThreat as a continuous variable.  When I do that in the univariate model, I get a more reasonable parameter estimate and standard error, but a much lower AIC.  I'd really appreciate any insights in how to deal with this problem.

                        PredThreat
        Low     Med     High
  failure       12      3       10
  success       14      8        0



With 3-level categorical PredThreat
Call:
glm(formula = Success ~ PredThreat, family = binomial, data = Parrots)

Deviance Residuals:
     Min        1Q    Median        3Q       Max
-1.61201  -1.24354  -0.00013   1.11269   1.11269

Coefficients:
             Estimate Std. Error z value Pr(>|z|)
(Intercept)    0.1542     0.3934   0.392    0.695
PredThreat2    0.8267     0.7830   1.056    0.291
PredThreat3  -18.7202  2062.6395  -0.009    0.993

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 64.964  on 46  degrees of freedom
Residual deviance: 48.781  on 44  degrees of freedom
AIC: 54.781

Number of Fisher Scoring iterations: 17

With continuous PredThreat (treating levels as integer values)
Call:
glm(formula = Success ~ PredThreat, family = binomial, data = Parrots)

Deviance Residuals:
    Min       1Q   Median       3Q      Max
-1.3762  -1.1764  -0.6518   0.9909   1.3924

Coefficients:
            Estimate Std. Error z value Pr(>|z|)
(Intercept)   1.4046     0.7234   1.942   0.0522 .
PredThreat   -0.9485     0.4209  -2.254   0.0242 *
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 64.964  on 46  degrees of freedom
Residual deviance: 59.093  on 45  degrees of freedom
AIC: 63.093

Number of Fisher Scoring iterations: 4


Eric D. Stolen, Ph.D.
Mail Code: IHA-300
Kennedy Space Center, FL  32899
office: 321-476-4119; cell: 321-480-6799; fax: 321-853-2939; email: eric.d.stolen@nasa.gov<mailto:eric.d.stolen@nasa.gov>

"..in mathematics you don't understand things. You just get used to them."  - John von Neumann

"It is better to have an approximate answer to the right question, than an exact answer to the wrong question." -  John Tukey





	[[alternative HTML version deleted]]

