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Reporting binomial logistic regression from R results

7 messages · Frodo Jedi, PIKAL Petr, Eik Vettorazzi +2 more

#
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:
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:
----------

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:
Wald test:
----------

Chi-squared test:
X2 = 22.3, df = 1, P(> X2) = 2.3e-06



# Here difference between system A and C:
Wald test:
----------

Chi-squared test:
X2 = 12.0, df = 1, P(> X2) = 0.00052



# Here difference between system A and B:
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
#
Dear Frodo (or Jedi)

The results seems to confirm your assumption that 3 systems are different. How you should present results probably depends on how it is usual to report such results in your environment.

BTW. It seems to me like homework and this list has no homework policy (Sorry, if I am mistaken).

Cheers
Petr
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#
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:

  
    
#
Yes, only one of the pairwise comparisons (B vs. C) is right. Also, the overall test has 3 degrees of freedom whereas a comparison of 3 groups should have 2. You (meaning Frodo) are testing that _all 3_ regression coefficients are zero, intercept included. That would imply that all three systems have response probablilities og 0.5, which is not likely what you want.

This all suggests that you are struggling with the interpretation of the regression coefficients and their role in the linear predictor. This should be covered by any good book on logistic regression.

-pd

  
    
#
Dear Peter and Eik,
I am very grateful to you for your replies.
My current understanding is that from the GLM analysis I can indeed
conclude that the response predicted by System A is significantly different
from that of System B, while the pairwise comparison A vs C leads to non
significance. Now the Wald test seems to be correct only for Systems B vs
C, indicating that the pairwise System B vs System C is significant. Am I
correct?

However, my current understanding is also that I should use contrasts
instead of the wald test. So the default contrasts is with the System A,
now I should re-perform the GLM with another base. I tried to use the
option "contrasts" of the glm:
contrasts = contr.treatment(3, base=1,contrasts=TRUE))
contrasts = contr.treatment(3, base=2,contrasts=TRUE))
contrasts = contr.treatment(3, base=3,contrasts=TRUE))
However, the output of these three summary functions are identical. Why?
That option should have changed the base, but apparently this is not the
case.


Another analysis I found online (at this link
https://stats.stackexchange.com/questions/60352/comparing-levels-of-factors-after-a-glm-in-r
)
to understand the differences between the 3 levels is to use glth with
Tuckey. I performed the following:
Simultaneous Tests for General Linear Hypotheses

Multiple Comparisons of Means: Tukey Contrasts


Fit: glm(formula = Response ~ System, family = "binomial", data = scrd)

Linear Hypotheses:
                      Estimate Std. Error z value Pr(>|z|)
B - A == 0  -1.2715     0.3379  -3.763 0.000445 ***
C - A == 0    0.8588     0.4990   1.721 0.192472
C - B == 0     2.1303     0.4512   4.722  < 1e-04 ***
---
Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
(Adjusted p values reported -- single-step method)


Is this Tukey analysis correct?


I am a bit confused on what analysis I should do. I am doing my very best
to study all resources I can find, but I would really need some help from
experts, especially in using R.


Best wishes

FJ
On Mon, Nov 12, 2018 at 1:46 PM peter dalgaard <pdalgd at gmail.com> wrote:

            

  
  
#
Generally speaking, this list is about questions on R programming, not
statistical issues. However, I grant you that your queries are in something
of a gray area intersecting both.

Nevertheless, based on your admitted confusion, I would recommend that you
find a local statistical expert with whom you can consult 1-1 if at all
possible. As others have already noted, you statistical understanding is
muddy, and it can be quite difficult to resolve such confusion in online
forums like this that cannot provide the close back and forth that may be
required (as well as further appropriate study).

Best,
Bert

On Mon, Nov 12, 2018 at 11:09 AM Frodo Jedi <frodojedi.mailinglist at gmail.com>
wrote:

  
  
#
Dear Bert,
I understand and thanks for your recommendation. Unfortunately I do not
have any possibility to contact a statistical expert at the moment. So this
forum experts' recommendation would be crucial to me to understand how R
works in relation to my question.
I hope that someone could reply to my last questions.

Best regards

FJ
On Mon, Nov 12, 2018 at 7:48 PM Bert Gunter <bgunter.4567 at gmail.com> wrote: