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help for ^brier2^                                               (STB-32: sg55)
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Decompose Brier score
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   ^brier2^ outcome forecast [^if^ exp] [^in^ range] ^,^ ^g^roup^(^#^)^

Description
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^brier2^ computes the Yates, Sanders, and Murphy decompositions of the Brier
Mean Probability Score.  The ^outcome^ must be a 0-1 variable and the ^forecast^
is a predicted probability, such as might be produced by logit or probit,
or by an independent human forecaster.

Options
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^group(^#^)^ specifies the number of groups that will be used to compute
        the decomposition.  The default is 10.

Examples
--------

 . ^brier death myprdn, group(5)^

Remarks
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All of the scores are in mean square error terms with 0 meaning perfect
agreement and 1 meaning perfect disagreement.

^Brier score^ measures the total difference between an event and the
forecast probability of that event.

^Spiegelhalter's z score^ is a standard normal test statistic for testing
whether an individual Brier score is extreme

^ROC area^ is the same as produced by ^lroc^ (and by ^ranksum2^); the
associated test is a test of whether the area is GREATER than 0.5.

^Sanders Brier score^ measures the difference between a grouped forecast
measure and the event.

^Sanders decomposition^ measures error that arises from statistical
considerations in making a forecast.  For example, the error that arises
because a prediction of p=.4 does not predict the zeros and ones, is part
of this term.

^Reliability-in-the-small^ measures the error that comes from the average
forecast within group not measuring the average outcome within group.
This term measures lack of modeling quality.

^Murphy decomposition^ measures the tendency of outcome differences in
forecast groups to differ from the overall outcome.  The better the
"information" in the forecast, the larger this term will be.

^Outcome index variance^ is just the variance due to the outcome variable.

^Forecast variance^ measures the amount of forecast discrimination being
attempted.  In a logit model, this would tend to go up with the amount
of information available.

^Reliability-in-the-large^ is the ability of the mean forecast to match the
mean probability.  This should be zero for statistical forecasting methods
applied to the training dataset, since they always get the overall probability
right.

^Forecast-Outcome Covariance^ is a measure of how accurately the forecast
responds to the outcome.  It is similar in concept to R-squared.

Also see
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On-line:  ^help^ for @logistic@, @lfit@, @brier@

Author
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        Richard Goldstein
        Qualitas, Inc.
        richgold@@netcom.com