Suppose I run a binomial GLM (in R) with response variable [0,1] and 2 predictor variables that are both categorical. Let's call them
a has 3 factor levels (
b has 2 factor levels (
mod <- glm(y~a+b, family=binomial(logit),data=pretend)
Let's say the summary output of the coefficients looks like this:
Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) -0.62049 0.06988 -8.879 < 2e-16 *** a a2 -2.24304 0.16111 -13.923 < 2e-16 *** a.a3 -1.76965 0.14147 -12.509 < 2e-16 *** s.b2 -0.79545 0.07918 -10.046 < 2e-16 ***
So I understand
b1 are constrained in the intercept and the estimate values presented are log-odds ratios (I am familiar with interpreting them).
Let's say now I want to determine the estimate when
a2 is true or = 1 and
b1 is =1 (true), then I would just calculate it as B0 (intercept) + B1 (coeff of a2) = -0.62049 + -2.24304
a3 is true and
b2 then I would calculate it as
B0 (intercept) + B3 (coeff of a3) + B4(coeff of b2). = -0.62049 + -1.76965 + -0.79545
But now how do I calculate the Standard errors and/or 95% Confidence intervals for the last two scenarios? Can I just add the standard errors in the same way? Or I would think I leave out the SE's of B0 (the intercept)?
So that in my first scenario where a2 is true and b1 is true, then I would just calculate it as SE of B1 (SE of a2) = 0.16111
And in my second scenario where a3 is true and b2 then I would calculate it as SE of B3 (SE of a3) + SE of B4(SE of b2). = 0.14147 + 0.07918.
Am I correct in my assumptions of interpreting the model output or am I completely wrong here?