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I am trying to determine to what extent the age ( continuous variable) affect the outcome of the patient ( outcome - dead/recovered). So, I tried to build a model in R using glm(family = "binomial"). There are many other predictors, but my concern is about the variable "age" or how it is named in the output below "vecums". It's continuous variable, and as I understand the glm function, when using binomial regression, outputs log odds, so for variable age - the coefficient is equal to exp(2.309e-01) = 1.26.

> summary(fullModel)

Call:
glm(formula = Izn ~ ., family = "binomial", data = myData14)

Deviance Residuals: 
     Min        1Q    Median        3Q       Max  
-2.00942  -0.20697  -0.01299   0.00155   2.62596  

Coefficients: (1 not defined because of singularities)
              Estimate Std. Error z value Pr(>|z|)    
(Intercept) -1.868e+01  4.508e+00  -4.144 3.41e-05 ***
DZ           9.712e-01  7.510e-01   1.293 0.195917    
Vecums       2.309e-01  6.039e-02   3.824 0.000131 ***

So, if reference level for the response variable is recovered, then there are 1.26 people aged y+1 that have died per every y aged person. Somebody told me that that's not a correct way to interpret the coefficient, because the age variable is not linearly related to the outcome. So, I tried to cut data into several age groups, but in that case the coefficients were not significant, most probably due to the data size (300 patients). How precise is the coefficient 1.26 in case, I am not cutting age into groups? How to correctly interpret it?

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  • $\begingroup$ Try starting at the top of this search & reading through some of our threads on how to interpret logistic regression. $\endgroup$ – gung - Reinstate Monica May 14 at 13:02
  • $\begingroup$ @ReinstateMonica So, am I right about the interpretation of log odds coefficient? I read the thread, and that's what I understood from it: if the coefficient next to age (Vecums) is equal to 1.26, then for every 1.26 person aged y+1, there are 1 y aged person that dies. $\endgroup$ – user18942 May 14 at 13:28
  • $\begingroup$ That's not correct. (BTW, we typically use "y" to mean the outcome variable, & "x" for the regressor.) In a fitted logistic regression model, $\exp(\hat{\beta}_1)$ is an odds ratio. It is the multiplicative factor by which we increment the odds when moving from x to x+1. Thus, if the odds that y=1 when x=1 is $o$, the odds that y=1 when x=2 is $\exp(\hat{\beta}_1)\ \times \ o$. $\endgroup$ – gung - Reinstate Monica May 14 at 14:18
  • $\begingroup$ @ReinstateMonica But in this case the x is age. And y is binary. How do I now o?What are the odds that the person will day at age x=1 ? Do I even now this from the information that I have? $\endgroup$ – user18942 May 14 at 14:29
  • $\begingroup$ Keep reading the threads from that search. There's a bunch of stuff you need to know before you can understand these things. $\endgroup$ – gung - Reinstate Monica May 14 at 14:33

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