# Logistic Regression with categorical predictors - how to report?

Hello Stack Exchange.

I need to run a logistic regression to determine the significance of the effect of 5 categories of one variable on my dependent variable. I just can't find online anywhere how I report these findings? In papers I have read online I find people quoting "binomial logistic regression, regression coefficient: __, p < __ ... however in my output I always get multiple coefficients for each predictor, how would I know which to quote?

I found a really good previous blog post on here that recommended using the likelihood ratio test to compare my model and its effects to a model that doesn't include my predictor variable...

Significance of categorical predictor in logistic regression

However still here I don't see what I would quote in a written report of findings?

The output of my logistic regression model :

Call:
glm(formula = survival ~ cover - 1, family = "binomial")

Deviance Residuals:
Min       1Q   Median       3Q      Max
-1.0051  -0.7259  -0.6159  -0.4279   2.2073

Coefficients:
Estimate Std. Error z value Pr(>|z|)
cover0 -2.34455    0.16149 -14.519   <2e-16 ***
cover20 -1.56606    0.07024 -22.295   <2e-16 ***
cover40 -1.19915    0.07910 -15.160   <2e-16 ***
cover60 -0.90229    0.08670 -10.407   <2e-16 ***
cover80 -0.41985    0.26842  -1.564    0.118
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

Null deviance: 4854.8  on 3502  degrees of freedom
Residual deviance: 3418.9  on 3497  degrees of freedom
AIC: 3428.9

Number of Fisher Scoring iterations: 4


then I ran a likelihood ratio test to compare this to a model where cover did not predict survival outcome :

my.mod1 <- glm(survival ~ cover, family = "binomial")

my.mod2 <- glm(survival ~ 1 ,family = "binomial")

result <- anova(my.mod1, my.mod2, test="LRT")


The output of the likelihood ratio test:

anova(my.mod1, my.mod2, test="LRT")
Analysis of Deviance Table

Model 1: survival ~ cover
Model 2: survival ~ 1
Resid. Df Resid. Dev Df Deviance  Pr(>Chi)
1      3500     3424.3
2      3501     3517.5 -1  -93.262 < 2.2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


I still can't see here how I can quote an overall coefficient for my model.

I need to be able to say % cover (categorical) had an effect on survival (but then don't know how to report this from my above outputs)

Thank you so much

• Your model output appears to be a model that you have specified withoiut an intercept.. Why is that ? – Robert Long Apr 11 '19 at 8:57
• Hi Robert, I read in the blog linked in the post about how this way rather than each category being compared to the first category (cover = 0)... they are each compared to zero " Note that the intercept is gone now and that the coefficient of rank1 is exactly the intercept of the first model. Here, the Wald test checks not the pairwise difference between coefficients but the hypothesis that each individual coefficient is zero." – Becca Apr 11 '19 at 9:56
• Otherwise the intercept seems to just be for my reference/ dummy category of 0? – Becca Apr 11 '19 at 9:57
• Yes, that is true. I was just making sure that you understood this. Since the variable is categorical, obviously there will be an estimate for each level, and so you would report the point estimates for each one along with their confidence intervals – Robert Long Apr 11 '19 at 10:54
• Ah I see, so I could say something like " A likelihood ratio test of a binary logistic regression determined cover level to significantly predict survival (p = 2.2 e-16) ... then would I need to quote each categories coefficient estimate and standard error? – Becca Apr 11 '19 at 11:10