Dan Scott Dan Scott - 3 years ago 105
R Question

Determining Interpretation Direction of Logistic Model in R

I am trying to run a logistic regression to predict a variable called has_sed (binary, describes whether a sample has sediment or not, coded as 0 = does not have sediment and 1 = has sediment). See the summary output of this model below:

Call:
glm(formula = has_sed ~ vw + ws_avg + s, family = binomial(link = "logit"),
data = spdata_ss)

Deviance Residuals:
Min 1Q Median 3Q Max
-1.4665 -0.8659 -0.6325 1.1374 2.3407

Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 0.851966 0.667291 1.277 0.201689
vw -0.118140 0.031092 -3.800 0.000145 ***
ws_avg -0.015815 0.008276 -1.911 0.055994 .
s 0.034471 0.019216 1.794 0.072827 .
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

Null deviance: 296.33 on 241 degrees of freedom
Residual deviance: 269.91 on 238 degrees of freedom
AIC: 277.91

Number of Fisher Scoring iterations: 4


Now, I understand how to interpret a logistic model output like this in general, but I don't understand how R chooses the direction (may be a better word for that) of my dependent variable. How do I know if a unit increase in vw increases the log odds of a sample having sediment, or increases the log odds of that sample not having sediment (i.e., has_sed = 0 vs has_sed = 1)?

I plotted out each of these relationships with boxplots, and the sign on the estimates in the logistic model output looks reversed from what I'm seeing in the boxplots. So, does R calculate the log odds of has_sed being 0, or the log odds of it being 1?

Answer Source

This is best illustrated with an example, I will use iris data with two classes

data(iris)
iris2 = iris[iris$Species!="setosa",]
iris2$Species = factor(iris2$Species)
levels(iris2$Species)
#output[1] "versicolor" "virginica" 

Lets make a glm

   model = glm(Species ~ Petal.Length, data = iris2, family = binomial(link = "logit"))
summary(model)
#truncated output
    Coefficients:
             Estimate Std. Error z value Pr(>|z|)    
(Intercept)   -43.781     11.110  -3.941 8.12e-05 ***
Petal.Length    9.002      2.283   3.943 8.04e-05 ***


library(ggplot2)

  ggplot(iris2)+
  geom_boxplot(aes(x = Species, y = Petal.Length))

enter image description here

Chances of being "virginica" rise with increasing Petal.Length, the reference level was "versicolor" - the first level when we did levels(iris2$Species).

Lets change it

iris2$Species = relevel(iris2$Species, ref = "virginica")
levels(iris2$Species)
#output
[1] "virginica"  "versicolor"

model2 = glm(Species ~ Petal.Length, data = iris2, family = binomial(link = "logit"))
summary(model2)
#truncated output
Coefficients:
             Estimate Std. Error z value Pr(>|z|)    
(Intercept)    43.781     11.110   3.941 8.12e-05 ***
Petal.Length   -9.002      2.283  -3.943 8.04e-05 ***

Now the reference level is "virginica" the first level in levels(iris2$Species). Chances of being "versicolor" drop with increasing Petal.Length.

In short the order of levels in your response variable determines the reference level for treatment contrasts.

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