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 Language Reference

## MARG Call

evaluates marginal totals in a multiway contingency table

CALL MARG( locmar, marginal, dim, table, config);

The inputs to the MARG subroutine are as follows:

locmar
is a returned matrix containing 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[i] 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 appearing 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.

 Father's Educational Level Self- Not HS HS Some Coll Post Religion Esteem Grad Grad Coll Grad Coll High 575 388 100 77 51 Catholic Low 267 153 40 37 19 High 117 102 67 87 62 Jewish Low 48 35 18 12 13 High 359 233 109 197 90 Protestant Low 159 173 47 82 32

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 2-way marginal table by summing over the third variable and a 1-way marginal by summing over the first two variables.

```
dim={5 2 3};

table={
/* Father's Education:
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,

/* Prote-  Hi */ 359   233  109   197   90,
/* stant   Lo */ 159   173   47    82   32
};
```

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

/* 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)];
```

The results of this program are as follows:

```

LOCMAR

1        11

MARGINAL

COL1    COL2    COL3    COL4    COL5    COL6    COL7

ROW1   1051     723     276     361     203     474     361

MARGINAL

COL8    COL9   COL10   COL11   COL12   COL13

ROW1    105     131      64    1707     561    1481
```

```
VAR12_MARG

1051       723       276       361       203
474       361       105       131        64

VAR3_MARG

1707
561
1481
```

The first marginal total is contained in locations 1 through 10 of the marginal vector. 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.

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