The MARG subroutine evaluates marginal totals in a multiway contingency table.

The input arguments to the MARG subroutine are as follows:

locmar

is a returned matrix that contains a vector of indices to each new set of marginal totals under the model specified by config. A marginal total is exhibited for each level of the specified marginal. These indices help locate particular totals.

marginal

is a return vector of marginal totals.

dim

is an input matrix. If the problem contains variables, then dim is row vector. The value dim[] is the number of possible levels for variable in a contingency table.

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

is an input matrix. The config argument specifies which marginal totals to evaluate. Each column of config specifies a distinct marginal in the model under consideration.

The matrix table must conform in size to the contingency table specified in dim. In particular, if table is , the product of the entries in the dim vector must equal . In addition, there must be some integer such that the product of the first entries in dim equals . See the description of the IPF function for more information about specifying table.

For example, consider the three-dimensional table discussed in the IPF call, based on data that appear in Christensen (1997). The table presents data on a person’s self-esteem for people classified according to their religion and their father’s educational level.

As explained in the IPF documentation, the father’s education level is Variable 1, self-esteem is Variable 2, and religion is Variable 3.

The following program encodes this table, uses the MARG call to compute a two-way marginal table by summing over the third variable and a one-way marginal by summing over the first two variables.

dim={5 2 3};

table={
/* Father's Education:
           NotHSGrad HSGrad Col ColGrad PostCol
          Self-
   Relig  Esteem                           */
/* Cath-   Hi */ 575   388  100    77   51,
/* olic    Lo */ 267   153   40    37   19,

/* Jew-    Hi */ 117   102   67    87   62,
/*  ish    Lo */  48    35   18    12   13,

/* Prot-   Hi */ 359   233  109   197   90,
/* estant  Lo */ 159   173   47    82   32
        };

config = { 1 3,
           2 0 };
call marg(locmar, marginal, dim, table, config);
print locmar, marginal;

The first marginal total is contained in locations 1 through 10 of the marginal vector, which is shown in Figure 23.171. It represents the results of summing table over the religion variable. The first entry of marginal is the number of subjects with high self-esteem whose fathers did not graduate from high school (). The second entry is the number of subjects with high self-esteem whose fathers were high school graduates (). The tenth entry is the number of subjects with low self-esteem whose fathers had some post-collegiate education ().

The second marginal is contained in locations 11 through 13 of the marginal vector. It represents the results of summing table over the education and self-esteem variables. The eleventh entry of the marginal vector is the number of Catholics in the study. The thirteenth entry is the number of Protestants.

You can also extract the marginal totals into separate vectors, as shown in the following statements:

/* Examine marginals: The name indicates the
   variable(s) that are NOT summed over.
   The locmar variable tells where to index
   into the marginal variable. */
Var12_Marg = marginal[1:(locmar[2]-1)];
Var12_Marg = shape(Var12_Marg, dim[2], dim[1]);
Var3_Marg  = marginal[locMar[2]:ncol(marginal)];
print Var12_Marg, Var3_Marg;