[R] Reporting binomial logistic regression from R results

[Frodo Jedi]

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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