Dear list members,
I need some help in understanding whether I am doing correctly a binomial
logistic regression and whether I am interpreting the results in the
correct way. Also I would need an advice regarding the reporting of the
results from the R functions.
I want to report the results of a binomial logistic regression where I want
to assess difference between the 3 levels of a factor (called System) on
the dependent variable (called Response) taking two values, 0 and 1. My
goal is to understand if the effect of the 3 systems (A,B,C) in System
affect differently Response in a significant way. I am basing my analysis
on this URL: https://stats.idre.ucla.edu/r/dae/logit-regression/
This is the result of my analysis:
fit <- glm(Response ~ System, data = scrd, family = "binomial")
summary(fit)
Call:
glm(formula = Response ~ System, family = "binomial", data = scrd)
Deviance Residuals:
Min 1Q Median 3Q Max
-2.8840 0.1775 0.2712 0.2712 0.5008
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 3.2844 0.2825 11.626 < 2e-16 ***
SystemB -1.2715 0.3379 -3.763 0.000168 ***
SystemC 0.8588 0.4990 1.721 0.085266 .
---
Signif. codes: 0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 411.26 on 1023 degrees of freedom
Residual deviance: 376.76 on 1021 degrees of freedom
AIC: 382.76
Number of Fisher Scoring iterations: 6
Following this analysis I perform the wald test in order to understand
whether there is an overall effect of System:
library(aod)
wald.test(b = coef(fit), Sigma = vcov(fit), Terms = 1:3)
Wald test:
----------
Chi-squared test:
X2 = 354.6, df = 3, P(> X2) = 0.0
The chi-squared test statistic of 354.6, with 3 degrees of freedom is
associated with a p-value < 0.001 indicating that the overall effect of
System is statistically significant.
Now I check whether there are differences between the coefficients using
again the wald test:
# Here difference between system B and C:
l <- cbind(0, 1, -1)
wald.test(b = coef(fit), Sigma = vcov(fit), L = l)
Wald test:
----------
Chi-squared test:
X2 = 22.3, df = 1, P(> X2) = 2.3e-06
# Here difference between system A and C:
l <- cbind(1, 0, -1)
wald.test(b = coef(fit), Sigma = vcov(fit), L = l)
Wald test:
----------
Chi-squared test:
X2 = 12.0, df = 1, P(> X2) = 0.00052
# Here difference between system A and B:
l <- cbind(1, -1, 0)
wald.test(b = coef(fit), Sigma = vcov(fit), L = l)
Wald test:
----------
Chi-squared test:
X2 = 58.7, df = 1, P(> X2) = 1.8e-14
My understanding is that from this analysis I can state that the three
systems lead to a significantly different Response. Am I right? If so, how
should I report the results of this analysis? What is the correct way?
Thanks in advance
Best wishes
FJ
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