!Daten Agresti, S. 136
$ass y0=19 132 0 9 11 52 6 97 $
$gfac 8 x1 2 x2 2 x3 2 $
$list list0=x1+x2+x3 $
                              !Daten Haslett:
$as y= 3 5 7 10 2 17 1 12 0 0 0 0 12 7 3 2 12 0 6 8 8 9 6 4 $
$gfac 24 a  3 b  4 c  2 $
$list LIST=a+b+c $
                              !Daten Conaway (LT5):
$ass y1=2 0 0 2 3 0 0 0 0 0 1 0 2 4 0 0 0 0 0 0 0 0 0 0 0 0
0 5 1 0 1 4 0 0 0 0 3 2 0 2 38 4 0 2 3 0 0 0 0 2 0 0 1 1 0
0 0 0 0 0 0 0 0 0 0 0 0 4 3 0 1 4 0 0 0 1 2 0 0 5 12  $
$gfac 81 w1 3 w2 3 w3 3 w4 3 $
$lis LIST1=w1+w2+w3+w4 $
                            !Daten Conaway (komplett):
$ass y2=2 0 0 2 3 0 0 0 0 0 1 0 2 4 0 0 0 0 0 0 0 0 0 0 0 0
0 5 1 0 1 4 0 0 0 0 3 2 0 2 38 4 0 2 3 0 0 0 0 2 0 0 1 1 0
0 0 0 0 0 0 0 0 0 0 0 0 4 3 0 1 4 0 0 0 1 2 0 0 5 12
1 2 0 2 0 0 0 0 0 1 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 0
5 15 1 0 0 0 2 2 0 6 53 6 0 5 1 0 0 0 0 1 1 0 3 1 0 0 1 0 0 0
0 0 0 0 0 0 1 13 0 0 0 0 0 0 0 1 7 2 0 2 7 $
$gfac 162 d 2 ww1 3 ww2 3 ww3 3 ww4 3 $
$lis LIST2=D+ww1+ww2+ww3+ww4 $

$in 'uep.mac' $
$page on $
$pr ; ; ; '                                UEP' ;
    '     Algorithm for calculating the number of unestimable parameters' ;
    '                        in sparse contingency tables'                ;
    '     =============================================================='
; ;  ;  ' Now comes a short demonstration of the macro UEP.'  ; ;
; ' 1. Example:' ;
' -----------' ; ; 'Consider the 2x2x2 table, taken from Agresti (1990):'
; ; $
$tprint y0 2,2,2 $
$pr ; ; ' The variate is named Y0, the factors are called X1 to X3 and are '
' collected in the list LIST0.' ;  ;
' To get the number of unestimable parameters, the following instruction'
' is necessary: ' ; ; ; ;
'$USE UEP Y0 LIST0 $'   ; ; ; $
$use uep y0 list0 $
$pr ; ; ; ; ; ; ; ; ;
' This means that no correction of degrees of freedom is necessary '
' because of the zero in the table above.' ; ;
' Remark: ' ;
' If a table only consists of zeros or, on the other hand, does not ' ;
' contain any zeros, an error message is printed.' ; ;
; ; ; '2. Example:' ; '-----------' ; ;
' The following 3x4x2 table is taken from Haslett (1990). The variate is' ;
' called Y and the factors A, B, C are collected in LIST.' ; ; $
$use uep y list  $
$pr ; ; ; ' From the output above we can see, that the configuration ' ;
' A, B, C - the table itself - contains 5 zeros and 2 unestimable ' ;
' parameters.' ;
' So the model X1.X2.X3=0 would have 18  parameters, but 2 parameters ';
' are unestimable, so the model has (24-2)-18 = 4 degrees of freedom. ' ; ; ;
' 3.Example:' ; '----------';;
' The last example comes from Conaway (1989).' ; ;
'$USE UEP Y1 LIST1 $' ; $
$use uep y1 list1 $
$pri ; 'e.g. If it is of interest to test the model M: W1.W2.W3.W4=0 ' ;
' the degrees of freedom for this model has to be calculated as follows: '
; ; ; ' Parameter of the saturated model    81 ';
' unestimable parameters            - 38 ';
' paramters of the model M          - 65 ';
' unestimable parameters in M       + 23 ';
'                                 ________';
' Degrees of freedom                   1 '; ; ; ;
$PR ;  ; ; ' This is the end of the demonstration.'; ;
' The following data is now available:' ; ;
 ; '  Data            Variate         factors    list of factors' ;
   ' ------------------------------------------------------------' ;
   ' Agresti             y0          X1,X2,X3         LIST0 ' ;
   ' Haslett             y             A,B,C          LIST' ;
   ' Conaway (LT5)       y1        W1,W2,W3,W4        LIST1' ;
   ' Conaway (full)      y2     D,WW1,WW2,WW3,WW4     LIST2' ;
   ' ------------------------------------------------------------' ; ; ;
 ' Macro UEP is already loaded, to load it again type ' ; ; ; '$IN ''UEP'' $'
 ; ; ; $

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