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Marginal standardization of two-way tables

        mstdize varname rowtotvar coltotvar [if exp] [in range] , by(rowvar
                 colvar) [ generate(newvar) tolerance(#) tabdisp_options ]


Description

    mstdize takes a table of varname, with rows indexed by rowvar and columns
    indexed by colvar, and produces a new table containing varname scaled
    such that the row totals are given by rowtotvar and the column totals
    given by coltotvar.


Remarks

    The algorithm is

        0. Initialise
            guess = varname

        1. Loop until max (| guess - previous guess |) <= tolerance
            previous guess = guess
            guess = guess * target row total / guess row total
            guess = guess * target col total / guess col total

    The total over rows of the column totals should equal the total over
    columns of the row totals. That is, the two should lead to the same grand
    total.

    This procedure is known by many different names in several different
    disciplines, including statistics, economics and engineering. Some are

        biproportional matrices
        iterative proportional fitting
        raking
        RAS technique


Options

    by() indicates rowvar and colvar and is required.

    generate() generates a new variable containing scaled values.

    tolerance() is a technical option indicating the criterion for
        convergence. This is the largest acceptable absolute difference
        between each guess and the previous guess (and also between the two
        totals of totals). Default 0.001.

    tabdisp_options are options of tabdisp.  Default center format(%9.2f).


Examples

    Data used by Smith (1976), quoted by Agresti (1990, p.197; 2002, p.345):
    . input freq schooling attitude
    . 209 1 1
    . 101 1 2
    . 237 1 3
    . 151 2 1
    . 126 2 2
    . 426 2 3
    .  16 3 1
    .  21 3 2
    . 138 3 3
    . end
    . gen r = 100
    . gen c = 100
    . mstdize freq r c, by(schooling attitude)

    Data used by Friedlander (1961), quoted by Bishop et al. (1975, p.98):
    . input freq age status
    . 1306 1 1
    . 83 1 2
    . 0 1 3
    . 619 2 1
    . 765 2 2
    . 3 2 3
    . 263 3 1
    . 1194 3 2
    . 9 3 3
    . 173 4 1
    . 1372 4 2
    . 28 4 3
    . 171 5 1
    . 1393 5 2
    . 51 5 3
    . 159 6 1
    . 1372 6 2
    . 81 6 3
    . 208 7 1
    . 1350 7 2
    . 108 7 3
    . 1116 8 1
    . 4100 8 2
    . 2329 8 3
    . end
    . gen rt = .
    . tokenize 1412 1402 1450 1541 1681 1532 1662 7644
    . qui forval i = 1/8 {
    .         replace rt = ``i'' if age == `i'
    . }
    . gen ct = .
    . tokenize 3988 11702 2634
    . qui forval j = 1/3 {
    .         replace ct = ``j'' if status == `j'
    . }
    . mstdize freq rt ct , by(age status)


References

    Agresti, A. 1990.  Categorical data analysis.  New York: John Wiley.

    Agresti, A. 2002.  Categorical data analysis.  Hoboken, NJ: John Wiley.

    Bishop, Y.M.M., Fienberg, S.E. and Holland, P.W. 1975.  Discrete
        multivariate analysis.  Cambridge, MA: MIT Press.

    Friedlander, D. 1961.  A technique for estimating a contingency table
        given the marginal totals and some supplementary data.  Journal of
        the Royal Statistical Society Series A 124: 412-420.

    Smith, K.W. 1976.  Table standardization and table shrinking: aids in the
        traditional analysis of contingency tables.  Social Forces 54:
        669-693.


Author

    Nicholas J. Cox, Durham University, U.K.
    n.j.cox@durham.ac.uk