help sdlim
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Title

    sdlim -- Rescaled standard deviations for limited variables


Syntax

    Syntax 1: Rescaled standard deviations for many variables

        sdlim varlist [if] [in] [weight] , limits(# #)} [ simulate(# #)}
                 keep]


    Syntax 2: Rescaled standard deviations by groups

        sdlim varname [if] [in] [weight] , by(varname ) [ limits(# #)}
                 simulate(# #)} keep]

    aweights, and fweights are allowed; see weight.

    by is allowed; see by.


Description

    sdlim rescales the standard deviation of a variable such that the result
    is the proportion of the raw standard deviation at the maximum standard
    deviation for a given mean.

    The theoretical maximum of the standard deviation of the variable X with
    mean = mean(X) is

        max(SD) = sqrt((min(X) - mean(X)) * (mean(X)-max(X)) * N/(N-1))

    The formula assumes that the mimimum and the maximum of X is known and
    fixed. This is the case for variables measured with a rating scale, for
    example.

    sdlim has two syntaxes. Syntax 1 is used to to rescale the standard
    deviations of various variables. In this case the option limits() must be
    used. Syntax 2 is used to rescale the standard deviation of one variable
    for different groups. In this case the option by() is required, while the
    specification of a varlist behind the command is not allowed.

Options

    limits(# #) is used to set the theoretical limits of the variable(s) for
        which the standard deviation should be rescaled. Limits are set by
        two interger numbers. The first number is the theoretical minimum of
        the variable the second number is the theoretical maximum. Results
        are omitted if variables contain values outside its theoretical
        boundaries. Note that the option is required if the command is given
        without option by() (i.e. for Syntax 1). For Syntax 2 limits(# #)
        defaults to the minimum and maximum value of varname over all
        by-groups.

    by(varname) is used to compare rescaled standard deviations between
        groups defined by categories of varname. With option by(), rescaling
        of standard deviation can be done for only one variable.

    simulate(# #) uses a simulation to rescale the standard deviation of a
        variable measured with a limited rating scale. The simulation assumes
        a latent variable with the mean of the observed variable and a given
        standard deviation. It further assumes that all values of the latent
        variable that exceed the specified limits are set to the highest and
        lowest value of the observed variable. Inside the parentheses the
        option requires two numbers. The first number is the number of
        observations used in the simulation, the second number is the
        standard deviation of the latent variable.

    keep is used to keep in memory the results of sdlim as a Stata data set
        (i.e. a resultsset)


Examples

    . sysuse auto
    . sdlim rep78, l(1 5)
    . sdlim rep78, by(for)
    . sdlim rep78, by(for) l(1 9)

    . sdlim rep78, by(for) l(1 9) sim(1000 2)

Saved results

    sdlim does not save returns. However with option keep keep the results
    are kept in memory as a resultsset.

Acknowledgment

    The formula for the maximum standard deviation is published in Kalmijn,
    Wim and Ruut Veenhoven, 2005: Measuring inequality of happiness in
    nations. In search for proper statistics. Journal of Happiness Studies 6,
    357-396 (Special issue on "Inequality of Happiness in nations").

    The two methods for rescaling of standard deviations are discussed by
    Delhey, Jan and Kohler, Ulrich: Is Happiness Inequality Immune to Income
    Inequality? New Evidence through Instrument-Effect-Corrected Standard
    Deviations. This article is currently under review in Social Science
    Research.

Author

Ulrich Kohler, WZB
kohler@wzb.eu


Also see
Manual:  [R] summarize