[R] Reporting binomial logistic regression from R results

[Eik Vettorazzi]

Dear Jedi,
please use the source carefully. A and C are not statistically different 
at the 5% level, which can be inferred from glm output. Your last two 
wald.tests don't test what you want to, since your model contains an 
intercept term. You specified contrasts which tests A vs B-A, ie A- 
(B-A)==0 <-> 2*A-B==0 which is not intended I think. Have a look at 
?contr.treatment and re-read your source doc to get an idea what dummy 
coding and indicatr variables are about.

Cheers


Am 12.11.2018 um 02:07 schrieb 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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> 
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-- 
Eik Vettorazzi

Department of Medical Biometry and Epidemiology
University Medical Center Hamburg-Eppendorf

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20246 Hamburg

Phone: +49 (0) 40 7410 - 58243
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