IPF Call

Chapter Contents

Language Reference

IPF Call

performs an iterative proportional fit

CALL IPF( fit, status, dim, table, config<, initab><, mod>);

The inputs to the IPF subroutine are as follows:

fit: is a returned matrix. The argument fit specifies an array of the estimates of the expected number in each cell under the model specified in config. This matrix conforms to table.
status: is a returned matrix. The status argument specifies a row vector of length 3. If you specify STATUS={error, obs-maxdev, no-iterate}, then error is 0 if there is convergence to the desired accuracy and is 3 if there is no convergence to the desired accuracy; obs-maxdev is the maximum difference between estimates of the last two iterations; and no-iterate is the number of iterations performed.
dim: is an input matrix. The dim argument is a vector specifying the number of variables and the number of their possible levels in a contingency table. If dim is 1 ×v, then there are v variables, and the value of the ith element is the number of levels of the ith variable.
table: is an input matrix. The table argument specifies an array of the number of observations at each level of each variable. Variables are nested across columns and then across rows.
config: an input matrix. The config argument gives an array specifying which marginal totals to fit. Each column specifies a distinct marginal in the model under consideration. Because the model is hierarchical, all subsets of specified marginals are included in fitting.
initab: is an input matrix. The initab argument is an array of initial values for the iterative procedure. If you do not specify values, 1s are used. For incomplete tables, initab is set to 1 if the cell is included in the design, and 0 if it is not.
mod: is an input matrix. The mod argument is a two-element vector specifying the stopping criteria. If mod= {maxdev, maxit}, then the procedure iterates until either maxit iterations are completed or the maximum difference between estimates of the last two iterations is less than maxdev. Default values are maxdev=0.25 and maxit=15.

The IPF subroutine performs an iterative proportional fit of the marginal totals of a contingency table. The arguments used with the IPF function can be matrix names or literals.

The matrix table must conform in size to the contingency table as specified in dim. In particular, if table is n ×m, the product of the entries in dim must equal nm. Furthermore, there must be some integer k such that the product of the first k entries in dim equals m. If you specify initab, then it must be the same size as table.

For example, consider the no-three-factor-effect model for interpreting Bartlett's data as described in Bishop, Fienberg, and Holland (1975):

   dim={2 2 2};
   table={156  84  84  156,
          107 133  31  209};
   config={1  1  2,
           2  3  3};
   call ipf(fit,status,dim,table,config);

The result is

               FIT
           161.062   78.938  78.907  161.093
           101.905  138.095  36.119  203.881


            STATUS
                 0   .166966     4

Equivalent results are obtained by the statement

   table={156  84,
           84 156,
          107 133,
           31 209};

or the statement

   table={156 84 84 156 107 133 31 209};

In the first specification, TABLE is interpreted as

             variable 2:            1                      2
                                _________              _________
variable 3   variable 1:         1     2                1     2
_________________________________________________________________

         1                      156   84               84    156
         2                      107  133               31    209

In the second specification, TABLE is interpreted as

variable 3  variable 2    variable 1:          1             2
__________________________________________________________________
        1           1                         156           84
                    2                          84          156
        2           1                         107          133
                    2                          31          209

And in the third specification, TABLE is interpreted as

  variable 3:            1                              2
               ________________________      _________________________
  variable 2:     1             2               1               2
               __________    __________      ___________    ___________
  variable 1:  1      2      1      2        1       2      1       2
              _______________________________________________________
              156     84     84     156     107     133     31     209 .

Chapter Contents
Previous
Next
Top