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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