Hi R bayesians,
I need an advise how to resolve the two different estimates applying a
traditional glm (TG) and a bayes glm (BG), and different results depending
on the data formats of response data and the prior specs using bayesglm in
R. I'm not familiar with bayes estimate and my colleague asked me to look
into this because the EPA from France reported a quite different estimates
for the follwoing ethylene data applying bayes method using MCSIM. As seen
below glm give same results regardless of response data format, i.e.,
two-column or binary formats, but bayesglm would give different results.
The result from French report is -91.78+8*lnC+6.055*lnT which lie
between prior.df=1 and 2 appling binary data format in R.
My question are as follows:
1. What is advantage using bayes estimate? Is it better for small samples?
2. How to resolve different estimates depending on the format of response
data, and the prior specs (Ex: prior.df)?
3.Should we use interval estimate rather than point estimate for BG?
Two-Column format:
cppm Tmin lnC lnT Death Number
1 1850 240 7.52294 5.48064 5 5
2 1637 240 7.40062 5.48064 4 5
3 1443 240 7.27448 5.48064 1 5
4 1021 240 6.92854 5.48064 0 5
5 4827 60 8.48198 4.09434 5 5
6 4202 60 8.34332 4.09434 1 5
7 4064 60 8.30992 4.09434 5 5
8 3966 60 8.28551 4.09434 2 5
9 3609 60 8.19119 4.09434 0 5
Binary data format:
cppm Tmin lnC lnT resp
1 1850 240 7.52294 5.48064 1
2 1850 240 7.52294 5.48064 1
3 1850 240 7.52294 5.48064 1
4 1850 240 7.52294 5.48064 1
5 1850 240 7.52294 5.48064 1
6 1637 240 7.40062 5.48064 1
7 1637 240 7.40062 5.48064 1
8 1637 240 7.40062 5.48064 1
9 1637 240 7.40062 5.48064 1
10 1637 240 7.40062 5.48064 0
11 1443 240 7.27448 5.48064 1
12 1443 240 7.27448 5.48064 0
13 1443 240 7.27448 5.48064 0
14 1443 240 7.27448 5.48064 0
attach(ehtylene)
DL<-cbind(Death,Alive=Number-Death)
Call:
glm(formula = DL ~ lnC + lnT, family = binomial(link = "probit"),
data = ethylene)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -145.156 43.668 -3.324 0.000887 ***
lnC 12.972 3.918 3.311 0.000931 ***
lnT 9.122 2.736 3.335 0.000854 ***
Using binary data:
Call:
glm(formula = resp ~ lnC + lnT, family = binomial(link = "probit"),
data = ethylene.mod)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -145.157 43.670 -3.324 0.000887 ***
lnC 12.972 3.918 3.311 0.000931 ***
lnT 9.122 2.736 3.334 0.000855 ***
Using bayesglm with two-column data:
summary(result3)
Call:
bayesglm(formula = DL ~ lnC + lnT, family = binomial(link = "probit"),
data = ethylene)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -134.971 17.490 -7.717 1.19e-14 ***
lnC 12.060 1.570 7.680 1.59e-14 ***
lnT 8.485 1.095 7.751 9.11e-15 ***
Using bayesglm with binary data:
Call:
bayesglm(formula = resp ~ lnC + lnT, family = binomial(link = "probit"),
data = ethylene.mod)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -98.477 26.919 -3.658 0.000254 ***
lnC 8.792 2.423 3.628 0.000286 ***
lnT 6.208 1.681 3.694 0.000221 ***
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