*! Version 3.5 16September2019
*! Jean-Benoit Hardouin
************************************************************************************************************
* Stata program : pcm
* Estimate the parameters of the Partial Credit Model
* Version 1 : December 17, 2007 [Jean-Benoit Hardouin]
* Version 2 : July 15, 2011 [Jean-Benoit Hardouin]
* Version 2.1 : October 18th, 2011 [Jean-Benoit Hardouin] : -fixedvar- option, new presentation
* Version 2.2 : October 23rd, 2013 [Jean-Benoit Hardouin] : correction of -fixedvar- option
* Version 2.3 : April 10th, 2014 [Jean-Benoit Hardouin] : correction of -fixedvar- option
* Version 2.3 : April 10th, 2014 [Jean-Benoit Hardouin] : correction of -fixedvar- option
* Version 3 : July 6th, 2019 [Jean-Benoit Hardouin] : New version using gsem
* Version 3.1 : July 9th, 2019 [Jean-Benoit Hardouin] : Small corrections
* Version 3.2 : July 17th, 2019 [Jean-Benoit Hardouin] : Small corrections
* Version 3.3 : July 25th, 2019 [Jean-Benoit Hardouin] : -pce- option
* Version 3.4 : August 23th, 2019 [Jean-Benoit Hardouin] : Correction of a bug
* Version 3.5 : September 16th, 2019 [Jean-Benoit Hardouin] : Correction of bugs
*
*
*
* Jean-benoit Hardouin - University of Nantes - France
* INSERM UMR 1246-SPHERE "Methods in Patient Centered Outcomes and Health Research", Nantes University, University of Tours
* jean-benoit.hardouin@univ-nantes.fr
*
* News about this program : http://www.anaqol.org
*
* Copyright 2007, 2011, 2013, 2014, 2019 Jean-Benoit Hardouin
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
************************************************************************************************************/


program define pcm3, rclass 
syntax varlist(min=2 numeric) [iweight] [, CONTinuous(varlist) CATegorical(varlist) ITerate(int 100) TOLerance(real 0.01) model DIFFiculties(name) rsm Graphs noGRAPHItems filesave dirsave(string) docx(string) extension(string) PCE WMLiterate(int 1) GENLT(name) GENINF(name) postpce]

qui count
local nbobs=r(N)
/*************************************************************************************************************
GESTION DES VARIABLES CONTINUES ET CATEGORIELLES
*************************************************************************************************************/
local modcont
local nbpar=0
local nbcont=0
local nbcat=0
if "`continuous'"!="" {
	tokenize `continuous'
	local nbcont : word count `continuous'
	local continuous
	forvalues i=1/`nbcont' {
		local cont`i' ``i''
		local continuous `continuous' ``i''
		local modcont `modcont' ``i''
	    local ++nbpar
	}
	local modcont (`modcont'->T)
}

local modcat
if "`categorical'"!="" {
	tokenize `categorical'
	local nbcat : word count `categorical'
	local categorical
	forvalues i=1/`nbcat' {
		local cat`i' ``i''
		local categorical `categorical' ``i''
		local modcat `modcat' i.``i''
		qui levelsof ``i''
		local levelsof``i'' `r(levels)'
		local nbpar=`nbpar'+`r(r)'-1
	    *di "categorical : ``i'' levels : `levelsof``i'''"
	}
	local modcat (`modcat'->T)
}


if "`dirsave'"=="" {
   local dirsave `c(pwd)'
}
if "`genlt'"!=""|"`geninf'"!="" {
    capture confirm new variable `genlt' se`genlt' `geninf'
	if _rc!=0 {
	    di in red "The variables `genlt', se`genlt' and/or `geninf' alreday exist. Please modify the -genlt- and/or -geninf- option"
		exit 198
	}
}

/*************************************************************************************************************
GESTION DES ITEMS ET TESTS
*************************************************************************************************************/

tokenize `varlist'
local nbitems : word count `varlist'
marksample touse ,novarlist
*preserve

local modamax=1
local modamin=0
local pbmin
local nbdiff=0
forvalues i=1/`nbitems' {
     qui su ``i''
	 if `r(min)'!=`modamin' {
	     local modamin=r(min)
		 local pbmin `pbmin' ``i''
	 }
	 if `r(max)'>`modamax' {
	     local modamax=r(max)
	 }
	 local modamax``i''=r(max)
	 if "`rsm'"=="" {
	    local nbdiff=`nbdiff'+`modamax``i'''
	 }
}
if "`rsm'"!="" {
   local nbdiff=`nbitems'+`modamax'-1
}
if `modamin'!=0 {
   di as error "The minimal answer category of each item must be coded by 0. This is not the case for the following items: `pbmin' (`modamin') "
   error 198
}
qui count
local nbind=r(N)
*set trace on
local code
forvalues k=1/`modamax' {
   local code`k'
   forvalues i=1/`nbitems' {
       if `k'<=`modamax``i''' {
	      local code`k' `code`k'' `k'.``i''
	   }
   }
   local code`k' (`code`k''<-T@`k')
   local code `code' `code`k''
}

/*************************************************************************************************************
OPTION PCE
*************************************************************************************************************/

if "`pce'"!=""&"`difficulties'"=="" {
    tempname sedelta b
	qui raschpce `varlist'
	local ll=r(ll)
	matrix `sedelta'=r(sedelta)
	matrix `sedelta'=`sedelta''
	matrix `b'=r(b)
	*matrix `b'=`b''
	local difficulties `b'
	*matrix list `b'
	matrix loulou=`b'
	return matrix diff_parm=`b'
	`qui' pcm `varlist', diff(loulou)  geninf(TInf_0) genlt(lt_0) /*postpce*/
	*exit
}


/*************************************************************************************************************
RECUPERATION DES PARAMETRES DE DIFFICULTES ET DEFINITION DES CONTRAINTES
*************************************************************************************************************/
if "`difficulties'"!=""&"`rsm'"!="" {
   di as error "You can not defined in the same time the difficulties and the rsm options"
   error 198
}
if "`difficulties'"!="" {
    tempname beta
	matrix `beta'=J(`nbitems',`modamax',.)
	local t=1
	local constraints
	matrix list `difficulties'
	forvalues i=1/`nbitems' {
		forvalues k=1/`modamax``i''' {
			if `difficulties'[`i',`k']==. {
				 di as error "The kth difficulty parameter of the item ``i'' is not correctly defined in the difficulties matrix"
				 error 198
			}
			else {
				if `k'==1 {
					matrix `beta'[`i',1]=-`difficulties'[`i',1]
  			    }
				else {
				    matrix `beta'[`i',`k']=`beta'[`i',`=`k'-1']-`difficulties'[`i',`k']
				}
				constraint `t' [`k'.``i'']_cons=`beta'[`i',`k']
				local constraints `constraints' `t'
				local ++t
			}
		}
	}
}

/*************************************************************************************************************
DEFINITION DES CONTRAINTES POUR UN RSM
*************************************************************************************************************/

if "`rsm'"!="" {
   local t=1
   local constraints
   forvalues k=2/`modamax' {
       forvalues i=2/`nbitems' {
	       constraint `t'   [`=`k'-1'.``i'']_cons-[`k'.``i'']_cons+[1.``i'']_cons=[`=`k'-1'.`1']_cons-[`k'.`1']_cons+[1.`1']_cons
		   local constraints `constraints' `t'
		   local ++t
	   }
   }
}

/*************************************************************************************************************
MODELE
*************************************************************************************************************/


discard
*di "`qui' gsem `code' `modcont' `modcat' ,iterate(`iterate') tol(`tolerance') constraint(`constraints')"
local qui qui
if "`model'"!="" {
   local qui
}
`qui' gsem `code' `modcont' `modcat' ,iterate(`iterate') tol(`tolerance') constraint(`constraints')
local ll=e(ll)

*set trace on
tempvar latent score group selatent latent2
tempname groups
*capture qui predict mu, mu
*su mu 
qui predict `latent',latent se(`selatent')
if "`genlt'"!="" {
    gen `genlt'=`latent'
	gen se`genlt'=`selatent'
}
set seed 123456
qui gen `latent2'=`latent'+invnorm(uniform())*`selatent'
qui genscore `varlist',score(`score')
qui gengroup `latent',newvariable(`group') continuous
qui levelsof `group'
local nbgroups=r(r)
matrix `groups'=J(`nbgroups',`=`nbitems'+3',.)
forvalues g=1/`nbgroups' {
    matrix `groups'[`g',`=`nbitems'+3']=0
    forvalues i=1/`nbitems' {
	*tab ``i'' if `group'==`g'
        qui count if ``i''!=.&`group'==`g'
		local n=r(N)
		if `n'>0 {
			qui su ``i'' if `group'==`g'
			matrix `groups'[`g',`i']=r(mean)
			matrix `groups'[`g',`=`nbitems'+3']=`groups'[`g',`=`nbitems'+3']+`r(mean)'
		}
		else {
			matrix `groups'[`g',`i']=.
			matrix `groups'[`g',`=`nbitems'+3']=.
		}		
    }
	qui su `latent' if `group'==`g'
	matrix `groups'[`g',`=`nbitems'+1']=r(mean)
	qui count if `group'==`g'
	matrix `groups'[`g',`=`nbitems'+2']=r(N)
}
*matrix list `groups'
	
qui count if `score'!=.
local nbobsssmd=r(N)	
	
di
di as text "Number of individuals:" %6.0f as result `nbobs'
di as text "Number of complete individuals:" %6.0f as result `nbobsssmd'
di as text "Number of items:" %6.0f as result `nbitems'

di as text "Marginal log-likelihood:" %12.4f as result `ll'
di 
return scalar ll=`ll'



*set trace on
/*************************************************************************************************************
RECUPERATION DES ESTIMATIONS DES PARAMETRES DE DIFFICULTE
*************************************************************************************************************/

tempname diff diffmat vardiff diffmat2
*set trace on
qui matrix `diffmat'=J(`nbitems',`modamax',.)
qui matrix `diffmat2'=J(`nbitems',`modamax',.)
qui matrix `diff'=J(`nbdiff',6,.)
local rn
*qui matrix `vardiff'=J(`nbdiff',`nbdiff',.)
*matrix list `diff'
*set trace on
local t=1
forvalues i=1/`nbitems' {
    qui matrix `diffmat'[`i',1]=-_b[1.``i'':_cons]
    qui matrix `diffmat2'[`i',1]=-_b[1.``i'':_cons]
	qui lincom -_b[1.``i'':_cons]
    qui matrix `diff'[`t',1]=`r(estimate)'
    qui matrix `diff'[`t',2]=`r(se)'
    qui matrix `diff'[`t',3]=`r(z)'
    qui matrix `diff'[`t',4]=`r(p)'
    qui matrix `diff'[`t',5]=`r(lb)'
    qui matrix `diff'[`t',6]=`r(ub)'
    *qui matrix `vardiff'[`t',`t']=_se[1.``i'':_cons]^2
	local rn `rn' 1.``i''
	local ++t
	local sum _b[1.``i'':_cons]
	if "`rsm'"=="" {
	    forvalues k=2/`modamax``i''' {
			local sum "_b[`k'.``i'':_cons]-(`sum')"
			di "``i'' `k' `sum'"
			local sum2 "_b[`=`k'-1'.``i'':_cons]-_b[`k'.``i'':_cons]"
			qui lincom (`sum2')
			*set trace on
			qui matrix `diffmat'[`i',`k']=`r(estimate)'
			qui matrix `diffmat2'[`i',`k']=`diffmat2'[`i',`=`k'-1']+`diffmat'[`i',`k']
			qui matrix `diff'[`t',1]=`r(estimate)'
			qui matrix `diff'[`t',2]=`r(se)'
			qui matrix `diff'[`t',3]=`r(z)'
			qui matrix `diff'[`t',4]=`r(p)'
			qui matrix `diff'[`t',5]=`r(lb)'
			qui matrix `diff'[`t',6]=`r(ub)'
			*qui matrix `vardiff'[`t',`t']=`r(se)'^2
			*set trace off
			local rn `rn' `k'.``i''
			local ++t
		}
    }
}
if "`rsm'"!="" {
    forvalues k=2/`modamax' {
		qui lincom _b[`=`k'-1'.`1':_cons]-_b[`k'.`1':_cons]+_b[1.`1':_cons]
		qui matrix `diff'[`t',1]=`r(estimate)'
		qui matrix `diff'[`t',2]=`r(se)'
		qui matrix `diff'[`t',3]=`r(z)'
		qui matrix `diff'[`t',4]=`r(p)'
		qui matrix `diff'[`t',5]=`r(lb)'
		qui matrix `diff'[`t',6]=`r(ub)'
		forvalues i=1/`nbitems' {
		    qui matrix `diffmat'[`i',`k']=`diff'[`t',1]+`diffmat'[`i',1]
		    qui matrix `diffmat2'[`i',`k']=`diffmat'[`i',`k']+`diffmat2'[`i',`=`k'-1']
		}
		local rn `rn' tau`k'
		local ++t
	}
}
local cn Estimate S.e. z p "Lower bound" "Upper Bound"
matrix colnames `diff'=`cn'
matrix rownames `diff'=`rn'
*matrix list `diff'
*matrix list `diffmat'
*matrix list `diffmat2'
*matrix list `vardiff'



/*************************************************************************************************************
RECUPERATION DES ESTIMATIONS DES PARAMETRES POUR LES COVARIABLES ET LA VARIANCE
*************************************************************************************************************/

tempname covariates
qui matrix `covariates'=J(`=`nbpar'+1',6,.)

*set trace on
if "`continuous'"!=""|"`categorical'"!="" {
    qui lincom _b[/var(e.T)]
}
else {
    qui lincom _b[/var(T)]
}
qui matrix `covariates'[1,1]=`r(estimate)'
qui matrix `covariates'[1,2]=`r(se)'
qui matrix `covariates'[1,3]=`r(z)'
qui matrix `covariates'[1,4]=`r(p)'
qui matrix `covariates'[1,5]=`r(lb)'
qui matrix `covariates'[1,6]=`r(ub)'

local t=2
forvalues i=1/ `nbcont' {
   qui lincom `cont`i''
   qui matrix `covariates'[`t',1]=`r(estimate)'
   qui matrix `covariates'[`t',2]=`r(se)'
   qui matrix `covariates'[`t',3]=`r(z)'
   qui matrix `covariates'[`t',4]=`r(p)'
   qui matrix `covariates'[`t',5]=`r(lb)'
   qui matrix `covariates'[`t',6]=`r(ub)'
   local ++t
}
forvalues i=1/ `nbcat' {
   local first=0
   foreach j in `levelsof`cat`i''' {
	   if `first'==0 {
	      local ++first
	   }
	   else {
		   qui	lincom `j'.`cat`i''
		   qui matrix `covariates'[`t',1]=`r(estimate)'
		   qui matrix `covariates'[`t',2]=`r(se)'
		   qui matrix `covariates'[`t',3]=`r(z)'
		   qui matrix `covariates'[`t',4]=`r(p)'
		   qui matrix `covariates'[`t',5]=`r(lb)'
		   qui matrix `covariates'[`t',6]=`r(ub)'
		   local ++t
	   }
   }
}
* matrix list `covariates'

/*************************************************************************************************************
OUTPUTS
*************************************************************************************************************/

if "`postpce'"=="" {
	local t=1
	local diffname
	*set trace on
	di "{hline 73}"
	di  as text _col(60) "<--95% IC -->"
	di  "Items" _col(60) "Lower" _col(68) "Upper"
	di "parameters" _col(13) "category" _col(25) "Estimate" _col(37) "s.e." _col(48) "z" _col(56) "p" _col(59) " Bound" _col(68) "Bound"
	di "{hline 73}"
	*set trace on
	forvalues i=1/`nbitems' {
	   *local l=1
	   forvalues j=1/`modamax``i''' {
		  if "`rsm'"==""|`j'==1 {
			  if `j'==1 {
				 di as text abbrev("``i''",19) _c
			  }
			  di as text _col(20) %5.2f "`j'" as result _col(28) %5.2f `diff'[`t',1]  _col(36) %5.2f `diff'[`t',2] _col(44) %5.2f `diff'[`t',3] _col(52) %5.2f `diff'[`t',4] _col(60) %5.2f `diff'[`t',5] _col(68) %5.2f `diff'[`t',6] 
			  local ++t
			  *local ++l
			  local diffname `diffname' `j'.``i''
		  }
	   }
	}
	if "`rsm'"!="" {
		forvalues k=2/`modamax' {
			di as text "tau`k'"  as result _col(28) %5.2f `diff'[`t',1]  _col(36) %5.2f `diff'[`t',2] _col(44) %5.2f `diff'[`t',3] _col(52) %5.2f `diff'[`t',4] _col(60) %5.2f `diff'[`t',5] _col(68) %5.2f `diff'[`t',6] 
			local diffname `diffname' tau`k'
			local ++t
		}
	}
	di as text "{hline 73}"
	local t=1
	local n: word count  Variance `continuous' 
	forvalues i=1/`n' {
		local v: word `i' of Variance `continuous' 
		di as text _col(1) %5.2f "`v'" as result _col(28) %5.2f `covariates'[`t',1]  _col(36) %5.2f `covariates'[`t',2] _col(44) %5.2f `covariates'[`t',3] _col(52) %5.2f `covariates'[`t',4] _col(60) %5.2f `covariates'[`t',5] _col(68) %5.2f `covariates'[`t',6] 
		local ++t
	}

	local rn Variance `continuous'

	local n: word count of  `categorical' 
	local catname
	forvalues i=1/`n' {
		local v: word `i' of `categorical'
		local first=1
		local saute=1
		foreach j in `levelsof`cat`i''' {
			if `saute'==0 {
				if `first'==1 {
					di as text _col(1) abbrev("`v'",19) _c
				}
				di  as text _col(20) %5.2f "`j'" as result _col(28) %5.2f `covariates'[`t',1]  _col(36) %5.2f `covariates'[`t',2] _col(44) %5.2f `covariates'[`t',3] _col(52) %5.2f `covariates'[`t',4] _col(60) %5.2f `covariates'[`t',5] _col(68) %5.2f `covariates'[`t',6] 
				local ++first
				local rn `rn' `j'.`n'
				local ++t
				local catname `catname' `j'.`v'
			}
			else {
			   local saute=0
			}
		}
		*local ++t
	}
	di as text "{hline 73}"
	/*
	di
	qui su `latent'
	qui local PSI=1-(`r(sd)')^2/((`covariates'[1,1])^2)
	di as text "PSI:" as result %4.2f `PSI' 
	di
	*/

	di
	qui su `latent'
	tempvar se2latent
	qui gen `se2latent'=(`selatent')^2
	qui su `se2latent'
	di as text "Mean squared std error of the latent variable: " as result %4.2f `=(`r(mean)')'
	di as text "Global variance of the latent variable: " as result %4.2f `=((`covariates'[1,1])+(`r(mean)'))'
	local PSI=(`covariates'[1,1])/((`covariates'[1,1])+(`r(mean)'))
	di as text "PSI: " as result %4.2f `PSI' _c
	if "`continuous'"!=""|"`categorical'"!="" {
		di as text " (without adjustment on covariates)"
	}
	else {
		di
	}
	di


	matrix colnames `covariates'=`cn'
	matrix rownames `covariates'=`rn'
}

/*************************************************************************************************************
FIT TESTS
*************************************************************************************************************/

tempname fit
qui matrix `fit'=J(`nbitems',4,.)
matrix colnames `fit'=OUTFIT INFIT "Standardized OUTFIT" "Standardized INFIT"
matrix rownames `fit'=`varlist'
*matrix list `fit'

tempvar Tcum TInf cum
qui gen `Tcum'=0
qui gen `TInf'=0
if "`postpce'"=="" {
	di as text "{hline 90}"
	di as text _col(60) "<---  Standardized   --->"
	di as text "Items" _col(34) "OUTFIT" _col(50) "INFIT" _col(64) "OUTFIT" _col(80) "INFIT"
	di as text "{hline 90}"
	di as text "Referenced values*" _col(29) "[" %4.2f `=1-6/sqrt(`nbobs')' ";" %4.2f `=1+6/sqrt(`nbobs')' "]" _col(44) "[" %4.2f `=1-2/sqrt(`nbobs')' ";" %4.2f `=1+2/sqrt(`nbobs')' "]" _col(60) "[-2.6;2.6]" _col(75) "[-2.6;2.6]"
	di as text "Referenced values**" _col(29) "[0.75;1.30]" _col(44) "[0.75;1.30]" _col(60) "[-2.6;2.6]" _col(75) "[-2.6;2.6]"
	di as text "{hline 90}"
}
*set trace on
local chi2=0
local chi2_old=0
forvalues g=1/`nbgroups' {
   local chi2_g`g'=0
   local chi2_old_g`g'=0
}
forvalues i=1/`nbitems' {
	if "`rsm'"=="" {
		local mm=`modamax``i'''
	}
	else {
		local mm `modamax'
	}	
	tempvar cum_old``i'' c_old0_``i'' Inf_old``i'' y_old``i'' y2_old``i''  	
	tempvar cum``i'' c0_``i'' Inf``i'' C``i'' C2``i'' C3``i'' y``i'' y2``i'' z``i'' z2``i'' i``i'' 

	local d=1
	local d_old=1
	qui gen `cum``i'''=0
	qui gen `cum_old``i'''=0
	forvalues k=1/`mm' {
		local d `d'+exp(`k'*`latent2'-`diffmat2'[`i',`k'])
		local d_old `d_old'+exp(`k'*`latent'-`diffmat2'[`i',`k'])
	}
	qui gen `c0_``i'''=1/(`d')
	qui gen `c_old0_``i'''=1/(`d_old')
	forvalues k=1/`mm' {
		tempvar c`k'_``i'' c_old`k'_``i''
		qui gen `c`k'_``i'''=exp(`k'*`latent2'-`diffmat2'[`i',`k'])/(`d')
		qui gen `c_old`k'_``i'''=exp(`k'*`latent'-`diffmat2'[`i',`k'])/(`d')
		qui replace `cum``i'''=`cum``i'''+`c`k'_``i'''*`k'
		qui replace `cum_old``i'''=`cum_old``i'''+`c_old`k'_``i'''*`k'
	}
	qui gen `Inf``i'''=0
	qui gen `Inf_old``i'''=0
	qui gen `C``i'''=0
	forvalues k=0/`mm' {
		qui replace `Inf``i'''=`Inf``i'''+(`k'-`cum``i''')^2*`c`k'_``i'''
		qui replace `Inf_old``i'''=`Inf_old``i'''+(`k'-`cum_old``i''')^2*`c_old`k'_``i'''
		qui replace `C``i'''=`C``i'''+(`k'-`cum``i''')^4*`c`k'_``i'''
	}
	qui count if ``i''!=.
	local n``i''=r(N)
	
	qui gen `C2``i'''=`C``i'''/((`Inf``i''')^2)
	qui su `C2``i'''
	local q2o``i''=(`r(mean)'-1)/((`n``i'''))

	qui gen `C3``i'''=`C``i'''-(`Inf``i''')^2
	qui su `C3``i'''
	local n=r(sum)
	qui su `Inf``i'''
	local d=r(sum)
	local q2i``i''=`n'/((`d')^2)
	
	//di "``i'' qo = `=sqrt(`q2o``i''')' qi = `=sqrt(`q2i``i''')'"
	
	qui replace `Tcum'=`Tcum'+`cum``i'''
	qui replace `TInf'=`TInf'+`Inf``i'''
	qui gen `y``i'''=``i''-`cum``i'''
	qui gen `y_old``i'''=``i''-`cum_old``i'''
	qui gen `y2``i'''=(`y``i''')^2
	qui gen `y2_old``i'''=(`y_old``i''')^2
	qui gen `z``i'''=(`y``i'''/sqrt(`Inf``i'''))
	local chi2_``i''=0
	local chi2_old_``i''=0
	forvalues g=1/`nbgroups' {
		qui su `y2``i''' if `group'==`g'
		local n=r(sum)
		qui su ``i'' if `group'==`g'
		local n1=r(sum)
		qui su `cum``i''' if `group'==`g'
		local n2=r(sum)
		qui su `Inf``i''' if `group'==`g'
		local d=r(sum)
		*di "chi2_`g'_``i''=`chi2'+(`n1'-`n2')^2/(`d')"
		local chi2=`chi2'+(`n1'-`n2')^2/(`d')
		local chi2_``i''=`chi2_``i'''+(`n1'-`n2')^2/(`d')
		local chi2_g`g'=`chi2_g`g''+(`n1'-`n2')^2/(`d')
		qui su `y2_old``i''' if `group'==`g'
		local n_old=r(sum)
		qui su ``i'' if `group'==`g'
		local n1_old=r(sum)
		qui su `cum_old``i''' if `group'==`g'
		local n2_old=r(sum)
		qui su `Inf_old``i''' if `group'==`g'
		local d_old=r(sum)
		local chi2_old=`chi2_old'+(`n1_old'-`n2_old')^2/(`d_old')
		local chi2_old_``i''=`chi2_old_``i'''+(`n_old')/(`d_old')
		local chi2_old_g`g'=`chi2_old_g`g''+(`n_old')/(`d_old')
	}
	*di "Item ``i'' Chi2``i''=`chi2_``i''' et chi2=`chi2'  Chi2_old=`chi2_old_``i''' et chi2_old=`chi2_old' "
	*su `z``i'''
	label variable `z``i''' "Standardized residuals associated to ``i''"
	label variable `latent' "Latent trait"
	*set trace on
	if  "`graphs'"!=""&"`graphitems'"=="" {
		if "`filesave'"!="" {
			local fs saving("`dirsave'//residuals_``i''",replace)
		}
		qui graph twoway scatter `z``i''' `latent', name(residuals``i'',replace) title("Standardized residuals associated to ``i''") `fs'
	}
	*set trace off
	qui gen `z2``i'''=(`z``i''')^2
	qui su `z2``i'''
	local OUTFIT``i''=`r(mean)'
	qui matrix `fit'[`i',1]=`OUTFIT``i'''
	local OUTFITs``i''=((`r(mean)')^(1/3)-1)*(3/sqrt(`q2o``i'''))+sqrt(`q2o``i''')/3
	qui matrix `fit'[`i',3]=`OUTFITs``i'''
	qui su `Inf``i''' if ``i''!=.
	local sumw``i''=r(sum)
	qui gen `i``i'''=`Inf``i'''*`z2``i''' 
	qui su `i``i''' if ``i''!=.
	local INFIT``i'' = `=`r(sum)'/`sumw``i''''
	qui matrix `fit'[`i',2]=`INFIT``i'''
	local INFITs``i''=(`=`r(sum)'/`sumw``i''''^(1/3)-1)*(3/sqrt(`q2i``i'''))+sqrt(`q2i``i''')/3
	qui matrix `fit'[`i',4]=`INFITs``i'''
	if "`postpce'"=="" {
		di abbrev("``i''",19) _col(35) %5.3f `OUTFIT``i''' _col(50) %5.3f `INFIT``i''' _col(64) %6.3f `OUTFITs``i''' _col(79) %6.3f `INFITs``i''' 
	}
}
if "`postpce'"=="" {
	di as text "{hline 90}"
	di as text "*: As suggested by Wright (Smith, 1998)
	di as text "**: As suggested by Bond and Fox (2007)
}
if "`geninf'"!="" {
   gen `geninf'=`TInf'
}

*set trace off
/*************************************************************************************************************
ESTIMATION OF THE WEIGHTED ML ESTIMATORS
**************************************************************************************************************/
*set trace on
*di "estimation `wmliterate'"
if "`postpce'"!="" {
    local conv=10
	local it=`wmliterate'
	di "Iteration : `it'"
	while(`conv'>=1) {
		di "Itération `it' : conv=`conv'"
		tempvar   sinf
		qui gen `sinf'=sqrt(TInf_`=`it'-1')
		`qui' pcm `varlist' [iweight=`sinf'],diff(loulou) wmliterate(`it') geninf(TInf_`it') genlt(lt_`it') 
		tempvar  ecart_`it' 
		qui gen `ecart_`it''=abs(lt_`it'-lt_`=`it'-1')
		qui su `ecart_`it''
		local conv =r(mean)
		local ++it
	}
    exit	
}


/*************************************************************************************************************
Categories/Items/Test Characteristics Curves and Information graphs
*************************************************************************************************************/

if "`graphs'"!="" {

	tempfile savefile
	qui save `savefile'

	qui clear
	qui set obs 2000
	qui gen u=(_n-1000)/250
	qui gen Tcum=0
	qui gen TInf=0
	forvalues i=1/`nbitems' {
	   local scatteri`i' 
	   forvalues g=1/`nbgroups' {
		  local x=`groups'[`g',`=`nbitems'+1']
		  local y=`groups'[`g',`i']
		  local s1=`groups'[`g',`=`nbitems'+2']
		  local seuil=30
		  local s vtiny
		  *set trace on
		  foreach lab in  tiny vsmall small medsmall medium medlarge  large   vlarge  huge vhuge /*ehuge*/ {
		      if `s1'>`seuil' {
			     local s `lab'
			  }
			  local seuil=`seuil'+10
		  }
		  local scatteri`i' `scatteri`i'' || scatteri `y' `x' , mcolor(black) msize(`s') legend(off)
		*set trace off
		}
		local d=1
		qui gen cum``i''=0
		*set trace on
		if "`rsm'"=="" {
			local mm=`modamax``i'''
		}
		else {
			local mm `modamax'
		}	
		forvalues k=1/`mm' {
			local d `d'+exp(`k'*u-`diffmat2'[`i',`k'])
		}
		qui gen c0_``i''=1/(`d')
		label variable c0_``i'' "Pr(``i''=0)"
		forvalues k=1/`mm' {
			qui gen c`k'_``i''=exp(`k'*u-`diffmat2'[`i',`k'])/(`d')
			qui replace cum``i''=cum``i''+c`k'_``i''*`k'
			label variable c`k'_``i'' "Pr(``i''=`k')"
		}
		qui gen Inf``i''=0
		forvalues k=1/`mm' {
			qui replace Inf``i''=Inf``i''+(`k'-cum``i'')^2*c`k'_``i''
		}
		if "`graphitems'"=="" {
			if "`filesave'"!="" {
				local fsc saving("`dirsave'//CCC_``i''",replace)
				local fsi saving("`dirsave'//ICC_``i''",replace)
			}
		    qui graph twoway line c*_``i'' u , name(CCC``i'', replace) title(Categories Characteristic Curve (CCC) of ``i'') ytitle("Probability") xtitle("Latent trait") `fsc'
		    qui graph twoway line cum``i'' u, name(ICC``i'',replace) title("Item Characteristic Curve (ICC) of ``i''") ytitle("Score to the item") xtitle("Latent trait") `scatteri`i'' `fsi'
		}
		qui replace Tcum=Tcum+cum``i''
		qui replace TInf=TInf+Inf``i''	
		label variable Inf``i'' "``i''"
	}
	if "`filesave'"!="" {
		local fst saving("`dirsave'//TCC",replace)
		local fsteo saving("`dirsave'//TCCeo",replace)
		local fsi saving("`dirsave'//ICC",replace)
		local fsti saving("`dirsave'//TIC",replace)
		local fsm saving("`dirsave'//map",replace)
	}
	qui graph twoway line Tcum u, name(TCC,replace) title("Test Characteristic Curve (TCC)") ytitle("Score to the test") xtitle("Latent trait") `fst'
	qui graph twoway line Inf* u, name(IIC,replace) title("Item Information Curves") ytitle("Information") xtitle("Latent trait")  `fsi'
	qui graph twoway line TInf u, name(TIC,replace) title("Test Information Curve") ytitle("Information") xtitle("Latent trait")  `fsti'

	local scatteri
	forvalues g=1/`nbgroups' {
		local x=`groups'[`g',`=`nbitems'+1']
		local y=`groups'[`g',`=`nbitems'+3']
		  local s1=`groups'[`g',`=`nbitems'+2']
		  local seuil=30
		  local s vtiny
		  *set trace on
		  foreach lab in  tiny vsmall small medsmall medium medlarge  large   vlarge  huge vhuge /*ehuge*/ {
		      if `s1'>`seuil' {
			     local s `lab'
			  }
			  local seuil=`seuil'+10
		  }
		local scatteri `scatteri' || scatteri `y' `x' , mcolor(black) msize(`s') legend(off)
	}
	qui graph twoway line Tcum u , name(TCCeo,replace) title("Test Characteristic Curve (TCC)") ytitle("Score to the test") xtitle("Latent trait") `scatteri' `fsteo'
	
	
	
	
	
/*************************************************************************************************************
MAP
*************************************************************************************************************/
*set trace on
	gen eff=0
	local effmax=0
	forvalues g=1/`nbgroups' {
	    local eff=`groups'[`g',`=`nbitems'+2']
		if `groups'[`g',`=`nbitems'+2']>`effmax' {
		   local effmax=`groups'[`g',`=`nbitems'+2']
		}
	    local lat=round(`groups'[`g',`=`nbitems'+1'],0.004)
	    *di "replace eff=`eff' if round(u,0.004)==`lat'"
	    qui replace eff=`eff' if round(u,0.004)==`lat'
    }
	gen density=normalden(u)*sqrt(`covariates'[1,1])
	label variable eff "Frequencies"
	label variable u "Latent trait"
	label variable TInf "Information curve"
	label variable density "Density function of the latent trait"
	local scatteri
	qui su u if eff!=0
	*set trace on
	local floor=floor(`r(min)')
	local ceil=ceil(`r(max)')
	forvalues i=1/`nbitems' {
	   local color`i':word `i' of `color'
	   local y=-`i'*`effmax'/`nbitems'
	   forvalues l=1/`modamax' {
		   local x=`diffmat'[`i',`l']
		   local scatteri `scatteri' || scatteri `y' `x' "`l'" ,mcolor(black) mlabcolor(black)
		   if `x'<`floor' {
		      local floor=floor(`x')
		   }
		   if `x'>`ceil'&`x'!=. {
		      local ceil=ceil(`x')
		   }
	   }
	   local scatteri `scatteri' || scatteri `y' `floor' "``i''",mcolor(black) mlabcolor(black) msize(vtiny)
	}
	qui su eff
	local maxe=ceil(`=(floor(`r(max)'/10)+1)*10')
	qui su TInf
	local maxi=ceil(`r(max)')
	qui su density
    local maxd=ceil(`r(max)')
	qui drop if u<`floor'|u>`ceil'
	qui graph twoway (bar eff u, barwidth(.2) yaxis(1) legend(off) xlabel(`floor'(1)`ceil')) (line TInf u,yaxis(2)) (line density u,yaxis(3))    `scatteri'  , name(map,replace) ytitle("Frequencies")  ylabel(-`maxi'(`=`maxi'/5')`maxi' ,axis(2)) ylabel(-`maxd'(`=`maxd'/5')`maxd' ,axis(3)) ylabel(-`maxe'(`=`maxe'/5')`maxe' ,axis(1)) title("Individuals/items representations (Map)") xsize(12) ysize(9) note("Red line: Information curve - Green line : Density of the latent trait") xtitle("Latent trait") `fsm'


	qui clear
	qui use `savefile'

}




/*************************************************************************************************************
RESULTS BY GROUP
*************************************************************************************************************/

di
di as text "{hline 57}"
di _col(31) "Latent Variable" _col(50) "Expected"
di "Group" _col(10) "Score" _col(20) "Freq" _col(32) "Mean" _col(42) "s.e." _col(53) "Score"
di as text "{hline 57}"
*set trace on
forvalues g=1/`nbgroups' {
    qui count if `group'==`g' 
	local eff`g'=r(N)
	qui count if `score'!=.&`group'==`g'
	local n=r(N)
	di as text "`g' (n=" as result `eff`g'' as text ")" _c
	if `n'>0 {
		qui su `score' if `group'==`g'
		local scoremin`g'=`r(min)'
		local scoremax`g'=`r(max)'
		forvalues s=`scoremin`g''/`scoremax`g'' {
			qui count if `group'==`g'&`score'==`s'
			local eff=r(N)
			qui su `latent' if `group'==`g'&`score'==`s'
			local mean=r(mean)
			qui su `selatent' if `group'==`g'&`score'==`s'
			local se=r(mean)
			qui su `Tcum' if `group'==`g'&`score'==`s'
			local exp=r(mean)
			if `eff'>0 {
			   di as text _col(10) %5.0f `s' as result _col(20) %4.0f `eff' _col(30) %6.3f `mean' _col(40) %6.3f `se' _col(53) %5.2f `exp'
			}
		}
	}
	qui count if `group'==`g'&`score'==.
	local eff=r(N)
	qui su `latent' if `group'==`g'&`score'==.
	local mean=r(mean)
	qui su `selatent' if `group'==`g'&`score'==.
	local se=r(mean)
	qui su `Tcum' if `group'==`g'&`score'==.
	local exp=r(mean)
	if `eff'>0 {
		di  as text _col(10) "    ." as result _col(20) %4.0f `eff' _col(30) %6.3f `mean' _col(40) %6.3f `se' _col(53) %5.2f `exp'
	}
    di as text "{hline 57}"
}
	



/*************************************************************************************************************
CREATION DU DOCX
*************************************************************************************************************/

if "`docx'"!="" {
    putdocx clear
    putdocx begin
	putdocx paragraph
	putdocx text ("General informations") , bold underline font(,14) smallcaps
	putdocx paragraph
	putdocx text ("Number of individuals: `nbobs'")
	putdocx paragraph
	putdocx text ("Number of complete individuals: `nbobsssmd'")
	putdocx paragraph
    putdocx text ("Number of items: `nbitems'")
	putdocx paragraph
    putdocx text ("List of items: `varlist'")
	putdocx paragraph
    putdocx text ("Date: $S_DATE, $S_TIME")
	putdocx paragraph
	local model Partial Credit Model (PCM)
	if "`rsm'"!="" {
	   local model Rating Scale Model (RSM)
	}
	putdocx text ("Model: `model'")
	putdocx paragraph
	putdocx text ("Marginal log-likelihood: `ll'")

	putdocx paragraph
	putdocx text ("Estimation of the parameters") , bold underline font(,14) smallcaps
	putdocx table tablename = matrix(`diff') , nformat(%9.3f) rownames colnames border(start, nil) border(insideH, nil) border(insideV, nil) border(end, nil)   
	qui putdocx table tablename = matrix(`covariates') , nformat(%9.3f) rownames colnames border(start, nil) border(insideH, nil) border(insideV, nil) border(end, nil)   
	putdocx paragraph
	putdocx text ("Fit indexes for items") , bold underline font(,14) smallcaps
	qui putdocx table tablename = matrix(`fit') , nformat(%9.3f) rownames colnames border(start, nil) border(insideH, nil) border(insideV, nil) border(end, nil)   
	local extension png
}

/*************************************************************************************************************
SAUVEGARDE DES GRAPHIQUES
*************************************************************************************************************/

*set trace on
if "`filesave'"!="" {
    if "`graphs'"!="" {
		if "`docx'"!="" {
		    putdocx pagebreak
		    putdocx paragraph
	        putdocx text ("General graphs") , bold underline font(,14) smallcaps
		}
		foreach i in TCC TCCeo TIC IIC map {
			if "`extension'"!="" {
			    qui graph export "`dirsave'//`i'.`extension'", replace name(`i')     
            }
			*graph display `i' 
			*qui graph save "`dirsave'//`i'", replace    
			if "`docx'"!="" {
			    putdocx paragraph
			    putdocx image "`dirsave'//`i'.png", height(10cm)
			}
		}
	    *discard
		if "`graphitems'"=="" {
			forvalues i=1/`nbitems' {
				if "`docx'"!="" {
				    putdocx paragraph
				    putdocx text ("Graphs for ``i''") , bold underline font(,14) smallcaps
				}
				foreach j in CCC ICC residuals {
					*graph display `j'``i'' 
					*qui graph save "`dirsave'//`j'_``i''", replace    

	 			    if "`extension'"!="" {
					    qui graph export "`dirsave'//`j'_``i''.`extension'", replace name(`j'``i'') 
					}
					if "`docx'"!="" {
						putdocx paragraph
						putdocx image "`dirsave'//`j'_``i''.png" , height(10cm)
					}
				}
			}
		}
	}
}
if "`docx'"!="" {
    putdocx save "`dirsave'//`docx'.docx", replace
}


/*************************************************************************************************************
RETURNS
*************************************************************************************************************/


matrix colnames `diff'=Estimate "s.e." z p lb ul
matrix colnames `covariates'=Estimate "s.e." z p lb ul
matrix rownames `diff'=`diffname'
matrix rownames `covariates'=Variance `continuous' `catname'
return matrix difficulties=`diff'
return matrix covariates=`covariates'
capture restore, not
end