# Reporting binomial logistic regression from R results

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## Reporting binomial logistic regression from R results

 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         [[alternative HTML version deleted]] ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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