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help for ^psbayes6^
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Pseudo-Bayes smoothing of cell estimates
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^psbayes6^ datavar [priorvar] [^if^ exp] [^in^ range]
[ ^, by(^rowvar [colvar [layervar]]^) g^enerate^(^newvar^) p^rob
tabdisp_options ]
Description
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^psbayes6^ takes datavar, which should be a set of frequencies, and
shrinks or smooths it towards a set of frequencies implied by prior
probabilities. This will have the effect of replacing sampling
zeros by positive estimates whenever the priors are positive.
For a set of data frequencies n_i, summing to n, and a set of prior
probabilities q_i, the smoothed estimates are n * p_i, where
n n_i k
p_i = ----- --- + ----- q_i,
n + k n n + k
and shrinkage is tuned by the constant
2 2
n - sum ( n_i )
k = ----------------------.
2
sum (n_i - n * q_i)
These estimates minimise the total mean square error between
estimated and estimand probabilities. For more details, see the
References.
If priorvar is specified, it must sum to 1 for the data used. If
priorvar is not specified, it is taken to be a set of equal
probabilities.
^psbayes6^ is the original version of ^psbayes^, renamed on
the promotion of ^psbayes^ to Stata 8. Users of Stata 8 up
should change to ^psbayes^.
Options
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^by(^rowvar colvar layervar^)^ indicates that datavar refers to a table
with rows (and columns if specified (and layers if specified))
indexed by the variable(s) named, which will structure a display of
cell estimates using ^tabdisp^. If ^by( )^ is not specified, cell
estimates will be displayed according to observation numbers.
^generate(^newvar^)^ generates a new variable containing results.
^prob^ indicates that probabilities rather than estimated frequencies
are to be shown (and if desired kept).
tabdisp_options are options of ^tabdisp^. Default ^center format(%9.1f)^.
Examples
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. ^psbayes6 f prior, by(row col) g(sf)^
References
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Agresti, A. 1990. Categorical data analysis. New York: John Wiley.
Bishop, Y.M.M., Fienberg, S.E. and Holland, P.W. 1975. Discrete
multivariate analysis. Cambridge, MA: MIT Press.
Fienberg, S.E. and Holland, P.W. 1970. Methods for eliminating zero
counts in contingency tables. In Patil, G.P. (ed.) Random counts in
scientific work. Volume 1: Random counts in models and structures.
Pennsylvania State University Press, University Park, 233-260.
Fienberg, S.E. and Holland, P.W. 1972. On the choice of flattening
constants for estimating multinomial probabilities. Journal of
Multivariate Analysis 2, 127-134.
Fienberg, S.E. and Holland, P.W. 1973. Simultaneous estimation of
multinomial cell probabilities. Journal, American Statistical
Association 68, 683-691.
Good, I.J. 1965. The estimation of probabilities: an essay on modern
Bayesian methods. MIT Press, Cambridge, MA.
Sutherland, M., Holland, P.W. and Fienberg, S.E. 1975. Combining Bayes
and frequency approaches to estimate a multinomial parameter. In
Fienberg, S.E. and Zellner, A. (eds) Studies in Bayesian econometrics
and statistics in honor of Leonard J. Savage. North-Holland, Amsterdam,
585-617.
Author
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Nicholas J. Cox, University of Durham, U.K.
n.j.cox@@durham.ac.uk
Also see
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On-line: help for @tabdisp@