/*
** expon.src - Exponential Regression Model
** (For the analysis of duration data)
**
** (C) Copyright 1988-1995  Aptech Systems, Inc.
** All Rights Reserved.
**
** This Software Product is PROPRIETARY SOURCE CODE OF APTECH
** SYSTEMS, INC.    This File Header must accompany all files using
** any portion, in whole or in part, of this Source Code.   In
** addition, the right to create such files is strictly limited by
** Section 2.A. of the GAUSS Applications License Agreement
** accompanying this Software Product.
**
** If you wish to distribute any portion of the proprietary Source
** Code, in whole or in part, you must first obtain written
** permission from Aptech Systems.
**
**-------------------**------------------**-------------------**-----------**
**-------------------**------------------**-------------------**-----------**
**
**  FORMAT:    { b,vc,llik } = EXPON(dataset,dep,ind);
**
**  INPUT:
**      dataset = name of Gauss dataset on disk or matrix in memory
**      dep     = dependent variable name, or column number of input matrix;
**                elements should be durations in time so that 0<y<infinity.
**      ind     = vector of independent variable names, or column numbers
**                of input matrix
**  OUTPUT:
**      b    = vector of effect parameters that maximize the likelihood
**      vc   = variance-covariance matrix of b
**      llik = value of the log-likelihood at the maximum
**
**  GLOBALS:
**    _cn_Inference    = MAXLIK for maximum likelihood estimates
**                    = BOOT for bootstrapped estimates
**                    = PROFILE for likelihood profile and profile t traces
**
**       _cn_Censor      0 = exponential gamma model, no censoring (default),
**                symbol = use this variable from dataset to censor.
**                         Code each row as 0 if censored or 1 if not.
**               integer = use this column of input matrix to censor.
**                        Code each row as 0 if censored or 1 if not.
**
**      _cn_Start   choose method of calculating starting values.
**                     0 = LS (default),
**                     1 = set to vector stored in _cn_StartValues,
**                     2 = rndu-0.5,
**                     3 = zeros, or set to vector
**
**      __output    1  =  print output to screen (default),
**                  0  =  do not print to screen
**
**  OTHER GLOBALS:
**      see MAXLIK.
**
**  EXAMPLE:
**      dataset="\\gauss\\prg\\coal";
**      let dep=months;
**      let ind=nparties unemp polariz;
**      let _cn_Censor=ciep;
**      call expon(dataset,dep,ind);
**
**  REFERENCE:  Gary King, Jim Alt, Nancy Burns, and Michael Laver. "A
**              Unified Model of Coalition Duration in Parlimentary
**              Democracies," photocopy, Department of Government, Harvard U.
*/

#include gauss.ext
#include count.ext
#include maxlik.ext

@ starting values @

proc _cn_svexp(dataset,dep,ind);
    local pars,b;
    if ind==0;
        pars = 1;
    else;
        pars = rows(ind)+1;
    endif;
    if _cn_Start==0;
        if pars==1;
            b = 0;
        else;
            b = -lols(dataset,dep,ind);
        endif;
    elseif _cn_Start==1;
        b = _cn_StartValues;
        if rows(b)/=pars;
            errorlog "ERROR:  b is the wrong size for _cn_Start.";
            end;
        endif;
    elseif _cn_Start==2;
        b = rndu(pars,1)-0.5;
    elseif _cn_Start==3;
        b = zeros(pars,1);
    else;
        b = _cn_Start;
        if rows(b)/=pars;
            errorlog "ERROR:  ROWS(_cn_Start) is wrong.";
            end;
        endif;
    endif;
    retp(b);
endp;


@ likelihood function @

proc _cn_liexp(b,dta);
    local y,x,xb,n,res,c,dd;
    y = dta[.,1];
    n = rows(dta);
    c = cols(dta)-(_cn_Censor/=0);
    x = ones(n,1);
    if c>1;
        x = x~dta[.,2:c];
    endif;

    if _cn_Censor/=0;
        dd = dta[.,cols(dta)];
    else;
        dd = 1;
    endif;

    xb = x*b;
    res = -(dd.*xb)-exp(-xb).*y;
    retp(res);
endp;

@ the main proc @
proc 3 = expon(dataset,dep,ind);
    local vars,b,logl,g,vc,st,ret;
    _max_CovPar = 3;
    _cn_fn = dataset;
    if dep$==0;
        errorlog "ERROR:  DEP must be a variable name or number.";
        end;
    endif;
    if ((type(dataset)/=13) and (_cn_Censor>cols(dataset)));
        errorlog "ERROR:  If dataset is a matrix in memory, "\
             "_cn_Censor must be the number of a column in the "\
             "matrix.";
        end;
    endif;
    if ((type(dataset)/=13) and ((maxc(ind)>cols(dataset)) or
        (dep>cols(dataset))) );
        errorlog "\nERROR:  If dataset is a matrix, the DEP "\
            "and IND must be column numbers.\n";
        end;
    endif;
    if (type(dataset)==13) and (type(_cn_Censor)==13);
        _cn_Censor = indcv(_cn_Censor,getname(dataset));
    endif;
    st = _cn_svexp(dataset,dep,ind);
    if __title $== "";
      if _cn_Censor/=0;
          __title = "Censored ";
      endif;
          __title = __title $+ "Exponential Regression Model";
    endif;
    if ind == 0;
        vars = dep;
    else;
        vars = dep|ind;
    endif;
    if _cn_Censor/=0;
        vars = vars|_cn_Censor;
    endif;
    _max_GradProc=&_cn_der1exp;
    _max_HessProc=&_cn_der2exp;
    local infm,inf0,lcInf;
    infm = { MAXLIK, BOOT };
    inf0 = { 1, 2 };
    LcInf = _ml_check(_cn_Inference,1,infm,inf0,1);
    if LcInf == 1;
        { b,logl,g,vc,ret } = maxlik(dataset,vars,&_cn_liexp,st);
    elseif LcInf == 2;
        { b,logl,g,vc,ret } = maxboot(dataset,vars,&_cn_liexp,st);
    endif;
    if ret /= 0;
        errorlog "ERROR: Model estimation failed.";
        end;
    endif;
    if type(dataset)==13;
        vars = "beta0";
        if ind/=0;
            vars = vars|ind;
        endif;
    else;
        vars = "beta0";
        if ind/=0;
            vars = vars|
            ((0 $+ "Col." $+ zeros(rows(ind),1))$+_cn_ftosm(ind,2));
        endif;
    endif;
    _cn_vr = vars;
    _cn_dp = dep;
    ndpclex;
    retp(b,vc,logl*_max_NumObs);
endp;



proc _cn_der1exp(b,dta);

@ First derivatives @

    local y,x,xb,n,res,c,dd;
    y = dta[.,1];
    n = rows(dta);
    c = cols(dta)-(_cn_Censor/=0);
    x = ones(n,1);
    if c>1;
        x = x~dta[.,2:c];
    endif;

    if _cn_Censor/=0;
        dd = dta[.,cols(dta)];
    else;
        dd = 1;
    endif;

    xb = x*b;
    res = (-dd+exp(-xb).*y).*x;
    retp(res);
endp;

proc _cn_der2exp(b,dta);

@ Second derivatives @

    local y,x,xb,n,res,c,dd;
    y = dta[.,1];
    n = rows(dta);
    c = cols(dta)-(_cn_Censor/=0);
    x = ones(n,1);
    if c>1;
        x = x~dta[.,2:c];
    endif;

    if _cn_Censor/=0;
        dd = dta[.,cols(dta)];
    else;
        dd = 1;
    endif;

    xb = x*b;
    res = sqrt(exp(-xb).*y);
    res = -moment(res.*x,0);
    retp(res);
endp;