/*
Number of Deaths by Horsekicks in the
Prussian Army from 1875-1894 for 14 Corps

Data from von Bortkiewicz (1898), given by
Andrews & Herzberg (1985), on number of deaths
by horse or mule kicks in 10 (of 14 reported)
corps of the Prussian army. 4 corps were not
considered by Fisher (1925) as they had a
different organization.

http://www.maths.lth.se/help/R/.R/library/vcd/html/HorseKicks.html

who in turn give as the Source

Michael Friendly (2000), Visualizing Categorical Data, p. 18.

and the

References
D. F. Andrews & A. M. Herzberg (1985), Data: A Collection of
Problems from Many Fields for the Student and Research Worker.
Springer-Verlag, New York, NY.

R. A. Fisher (1925), Statistical Methods for Research Workers.
Oliver & Boyd, London.

L. von Bortkiewicz (1898), Das Gesetz der kleinen Zahlen.
Teubner, Leipzig.

more on him at
http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Bortkiewicz.html

M. Friendly (2000), Visualizing Categorical Data.
SAS Institute, Cary, NC.

*/

* --- for SAS ---- ;

options ls= 85 ps=50; run;

data a;
input year corps1-corps14 total;
lines;
 1875 0 0 0 0 0 0 0 1 1 0 0 0 1 0  3
 1876 2 0 0 0 1 0 0 0 0 0 0 0 1 1  5
 1877 2 0 0 0 0 0 1 1 0 0 1 0 2 0  7
 1878 1 2 2 1 1 0 0 0 0 0 1 0 1 0  9
 1879 0 0 0 1 1 2 2 0 1 0 0 2 1 0 10
 1880 0 3 2 1 1 1 0 0 0 2 1 4 3 0 18
 1881 1 0 0 2 1 0 0 1 0 1 0 0 0 0  6
 1882 1 2 0 0 0 0 1 0 1 1 2 1 4 1 14
 1883 0 0 1 2 0 1 2 1 0 1 0 3 0 0 11
 1884 3 0 1 0 0 0 0 1 0 0 2 0 1 1  9
 1885 0 0 0 0 0 0 1 0 0 2 0 1 0 1  5
 1886 2 1 0 0 1 1 1 0 0 1 0 1 3 0 11
 1887 1 1 2 1 0 0 3 2 1 1 0 1 2 0 15
 1888 0 1 1 0 0 1 1 0 0 0 0 1 1 0  6
 1889 0 0 1 1 0 1 1 0 0 1 2 2 0 2 11
 1890 1 2 0 2 0 1 1 2 0 2 1 1 2 2 17
 1891 0 0 0 1 1 1 0 1 1 0 3 3 1 0 12
 1892 1 3 2 0 1 1 3 0 1 1 0 1 1 0 15
 1893 0 1 0 0 0 1 0 2 0 0 1 3 0 0  8
 1894 1 0 0 0 0 0 0 0 1 0 1 1 0 0  4
;
run;

* a new file where each count is on a different observation
  indexed by year and corps ;

data b;
keep year corps deaths;
array c(14) corps1-corps14;
set  a;
do corps = 1 to 14; deaths= c(corps) ; output; end;
run;

proc means data=b; var deaths;

proc univariate data=b; var deaths;

proc means data=b ; class  year; var deaths;
proc means data=b; class corps; var deaths;

proc genmod data=b;
model deaths = / distribution = poisson
                 link = identity;

proc genmod data=b;
model deaths = / distribution = normal
                 link = identity;


proc genmod data=b;
model deaths = / distribution = poisson
                 link = log;

run;

* --- for Stata ---- ;

clear
input year deaths1-deaths14 total
 1875 0 0 0 0 0 0 0 1 1 0 0 0 1 0  3
 1876 2 0 0 0 1 0 0 0 0 0 0 0 1 1  5
 1877 2 0 0 0 0 0 1 1 0 0 1 0 2 0  7
 1878 1 2 2 1 1 0 0 0 0 0 1 0 1 0  9
 1879 0 0 0 1 1 2 2 0 1 0 0 2 1 0 10
 1880 0 3 2 1 1 1 0 0 0 2 1 4 3 0 18
 1881 1 0 0 2 1 0 0 1 0 1 0 0 0 0  6
 1882 1 2 0 0 0 0 1 0 1 1 2 1 4 1 14
 1883 0 0 1 2 0 1 2 1 0 1 0 3 0 0 11
 1884 3 0 1 0 0 0 0 1 0 0 2 0 1 1  9
 1885 0 0 0 0 0 0 1 0 0 2 0 1 0 1  5
 1886 2 1 0 0 1 1 1 0 0 1 0 1 3 0 11
 1887 1 1 2 1 0 0 3 2 1 1 0 1 2 0 15
 1888 0 1 1 0 0 1 1 0 0 0 0 1 1 0  6
 1889 0 0 1 1 0 1 1 0 0 1 2 2 0 2 11
 1890 1 2 0 2 0 1 1 2 0 2 1 1 2 2 17
 1891 0 0 0 1 1 1 0 1 1 0 3 3 1 0 12
 1892 1 3 2 0 1 1 3 0 1 1 0 1 1 0 15
 1893 0 1 0 0 0 1 0 2 0 0 1 3 0 0  8
 1894 1 0 0 0 0 0 0 0 1 0 1 1 0 0  4
end

* reshape dataset from wide to long ...

reshape long deaths, i(year) j(corps)

drop total

* descriptively...

summ deaths, detail

inspect deaths

* fit (calculate) mean as the intercept in null regression

glm deaths, family(poisson) link(identity)

glm deaths, family(normal) link(identity)