# [S] How to obtain SE in probit analysis

Park, Kyong H. (khpark@cbdcom-emh1.apgea.army.mil)
Mon, 23 Feb 1998 09:38:13 -0500

Dear S+ users,
I ran a Probit analysis for a dose-response relation and compared
standard deviation (SD) between S+ and my own, and found big differences
between two. I'd very much appreciate if somebody tell me where I made
mistakes. Data and summarized results are provided below. SD from S+ is
obtained by invoking object\$se.fit. SD from me is based on:
y = a + b *log(dose) + error, from which Var (y) = Var (a) + Var (b) *
log (dose) ^2 +2 * cov (a,b) *log(dose) +Var (error).
Var (a) and Var (b) are obtained from summary results from S+ and Cov
(a, b) is from correlation coefficient * SD ( a) *
SD (b). Correlation coefficient is also given in summary results. Var
(error) is:
p*(1-p)/(number of risk)*z^2, where z is from (1/sqrt(2*pi))*exp(-y^2/2)
and p is estimated probability from the above linear equation. As a
reference z and Var (error) as follows:
Z: 1 2 3
4 5 6
0.03815687 0.1059306 0.2176265 0.3363327 0.3985163
0.3583668

Var (error): 1.706005 0.7282885 0.4121203 0.2967073 0.2620027
0.2831471

Comparison of SD:
S+: 1 2 3 4
5 6
0.4884953 0.3640075 0.2580228 0.1964676 0.218965
0.304918

Mine: 1.459399 0.9816474 0.7282645 0.6043724 0.5892042
0.6695408

Data file:

dose resp risk
1 79 0 6
2 100 0 6
3 126 1 6
4 158 2 6
5 200 4 6
6 250 3 6

Summary Results:

[[1]]:
[1] "probit.analysis"

[[2]]:

Call: glm(formula = mat ~ log(dose), family = binomial(link = probit),
data = temp)
Deviance Residuals:
1 2 3 4 5 6
-0.4277536 -0.7981921 0.2167881 0.2886422 0.9139426 -0.9037637

Coefficients:
Value Std. Error t value
(Intercept) -12.141048 4.0678044 -2.984669
log(dose) 2.282767 0.7922293 2.881448

(Dispersion Parameter for Binomial family taken to be 1 )

Null Deviance: 13.5398 on 5 degrees of freedom

Residual Deviance: 2.602475 on 4 degrees of freedom

Number of Fisher Scoring Iterations: 4

Correlation of Coefficients:
(Intercept)
log(dose) -0.9979987

Fitted y and 95% confidence interval of y from S+:

lower y fitted y upper y
1 -3.5228956 -2.16661527 -0.81033490
2 -2.6391630 -1.62851601 -0.61786905
3 -1.8173279 -1.10094171 -0.38455550
4 -1.1298029 -0.58432148 -0.03884001
5 -0.6541664 -0.04622222 0.56172198
6 -0.3834255 0.46316260 1.30975072