ORTH.ordinal.mac
J Perin
May 2014


An adaptation of generalized estimating equations
for modeling an ordinal outcome with an average or mean determined by
proportional odds, and the association modeled with an implementation
of orthogonalized residuals for Ordinal data.  Based on Richard Zink's
software for binary data.

Ordinal outcome should be coded such that the levels are
0,1, ..., C.  So the outcome has C+1 possible levels.

Questions and comments can be directed to

Jamie Perin
615 N Wolfe St
Department of International Health
Johns Hopkins Bloomberg School of Public Health
email: jperin@jhu.edu



References:  Perin, J., Preisser, J.S., Qaqish, B.F., and Phillips, C.
             "Regression analysis of correlated ordinal data using
             orthogonalized residuals".

             Qaqish, Bahjat F., Richard C. Zink, and John S. Preisser.
             "Orthogonalized residuals for estimation of marginally specified
             association parameters in multivariate binary data." Scandinavian
             Journal of Statistics 39.3 (2012): 515-527.




Description:

For ordinal outcome Y_it, the probability

    logit( P(Y_it <= c) ) =  X*Beta

is being modeled for the mean of Y_it, and the correlation
between clustered observations Y_is and Y_it is modeled through
the odds ratio

    log( Odds Ratio(Y_is, Y_it) ) =  Z*alpha,

for s \ne t.

Macro options:

            data = sas data set with outcome and covariates
            y = sas variable name of ordinal response, must be from 0,1,...,C.
            X = variable names of covariates in sas data set.
	    xpartial = variable names for covariates with non-proportional odds
                       (must also be named in X).
	    Z = variable names for association model
	    Zdata = dataset with Z matrix association modelling input
            cluster = sas variable name for cluster identifier, must be in format {1  to nrow(n)}
            miter   = maximum number of iterations
            crit    = critical value determining convergence
	    ibeta   = Initial beta estimate
	    out     = 1: print final parameter estimates
            detailOut =  1: print parameter estimates at each iteration.