# Logistic regression with categorical predictor

I'm facing a problem with a binomial glmer model. I want to find if differences in flower presence in pine trees is due to procedence of the tree. My model is as follows: FlorMas ~ Proc + (1|Blq). Proc is a factor with nine levels, one of it (TAMR) presents no flower at all (variable value for all TAMR trees is 0). This model gives me this output:

Generalized linear mixed model fit by the Laplace approximation
Formula: FlorMas ~ Proc + (1 | Blq)
Data: flower.data
AIC   BIC logLik deviance
593 647.7 -285.5      571
Random effects:
Groups Name        Variance Std.Dev.
Blq    (Intercept) 0.18476  0.42983
Number of obs: 1067, groups: Blq, 8

Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept)   -1.7668     0.2958  -5.974 2.32e-09 ***
ProcTAMR     -16.8758  1080.5608  -0.016  0.98754
ProcARMY      -0.3543     0.3910  -0.906  0.36490
ProcASPE      -1.4891     0.5260  -2.831  0.00464 **
ProcCOCA      -2.4947     0.7619  -3.274  0.00106 **
ProcMIMI      -1.2040     0.4930  -2.442  0.01459 *
ProcORIA      -1.5360     0.5739  -2.676  0.00744 **
ProcPLEU      -1.9437     1.0538  -1.845  0.06511 .
ProcPTOV       0.1693     0.3508   0.483  0.62945
ProcSCRI       0.5060     0.3346   1.512  0.13050

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


I don't understand that values for TAMR procedence, as if it has all zero values it should be different from the others. Any help will be appreciated.

• Just to illustrate @Hong Ooi's excellent answer: Try to transform the log-odds back to probability: $\exp{(-16.8758)}/(1+\exp{(-16.8758)})\approx 0$. Commented Jul 15, 2013 at 11:48

The coefficient for TAMR of -16.87 is effectively negative infinity, on the log-odds scale. In other words, the estimated probability of an event for this level is zero which is correct for your data. The standard error in this case is numerically unstable, and should be ignored. Since the Z-statistic and P-value are based on the SE, they also should be ignored.
A better thing to do would be to remove that category from your dataset altogether (and fix the Proc factor to remove the level). If you know there can be no events, then there's no point including it in the model.