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*! Version 1.2 June 3, 2013
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************************************************************************************************************
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* Stata program : raschres
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* Analysis of the residuals of the Rasch model
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* Version 1 : June 16, 2010
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* Version 1.1 : July 15, 2011
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* Version 1.2 : June 3, 2013 /*formatting outputs*/
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*
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*
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* Jean-benoit Hardouin, phD, Assistant Professor
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* EA4275 - SPHERE
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* Team of Biostatistics, Pharmacoepidemiology and Subjective Measures in Health Sciences
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* University of Nantes - Faculty of Pharmaceutical Sciences
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* France
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* jean-benoit.hardouin@univ-nantes.fr
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*
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* News about this program : http://www.anaqol.org
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*
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* Copyright 2010-2013 Jean-Benoit Hardouin
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 2 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
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************************************************************************************************************/
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program define raschres,rclass
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syntax varlist [if] [in] , diff(string) theta(varname) [genres(string) genfit(string) vargroup(varname) PCAres DETails]
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tempfile saveraschres
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if "`if'"!=""|"`in'"!="" {
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*keep `if' `in'
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}
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*qui save `saveraschres',replace
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tempname res
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qui count
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local ntotal=r(N)
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tokenize `varlist'
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local nbitems: word count `varlist'
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qui tempname score lt
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qui genscore `varlist',score(`score')
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qui gen `lt'=`theta'
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forvalues i=1/`nbitems' {
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local z2`i'=0
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}
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forvalues i=1/`nbitems'{
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qui tempname p`i' res`i'
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qui gen `p`i''=exp(`lt'-`diff'[1,`i'])/(1+exp(`lt'-`diff'[1,`i']))
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qui gen `res'`i'=(1-`p`i'')/sqrt(`p`i''*(1-`p`i'')) if ``i''==1
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qui replace `res'`i'=(0-`p`i'')/sqrt(`p`i''*(1-`p`i'')) if ``i''==0
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}
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su
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local chi2=0
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forvalues i=1/`nbitems' {
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qui tempname res2
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qui gen `res2'`i'=`res'`i'^2
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qui su `res2'`i'
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local chi2=`chi2'+`r(sum)'
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label variable `res'`i' "``i''"
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}
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su
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tempname cor Ev
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matrix `cor'=J(`nbitems',`nbitems',.)
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local list
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forvalues i=1/`nbitems' {
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forvalues j=1/`nbitems' {
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qui corr `res'`i' `res'`j'
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matrix `cor'[`i',`j']=r(rho)
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}
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local list "`list' ``i''"
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}
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matrix colname `cor'=`list'
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matrix rowname `cor'=`list'
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qui pca `res'*
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matrix `Ev'=e(Ev)
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tempname lt2 ltcl group df nbmiss rep total
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qui egen `nbmiss'=rowmiss(`varlist')
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qui gen `rep'=`nbitems'-`nbmiss'
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qui gen `lt2'=`lt' if `score'!=0&`score'!=`rep'
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if "`vargroup'"=="" {
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qui gengroup `lt2', newvar(`group') cont det minsize(33)
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}
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else {
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qui `group'=`vargroup'
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}
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qui su `group'
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local maxgroup=r(max)
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if "`details'"!="" {
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di "{hline 42}"
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di _col(12) "Min" _col(29) "Max"
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di "{dup 42:-}"
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di "" _col(8) "" _col(14) "Latent" _col(28) "" _col(31) "Latent" _col(53) ""
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di "Group" _col(8) "Score" _col(15) "trait" _col(25) "Score" _col(32) "trait" _col(42) "n"
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di "{hline 42}"
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forvalues i=1/`maxgroup' {
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qui count if `group'==`i'
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local n`i'=r(N)
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qui su `score' if `group'==`i'
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local scoremin`i'=r(min)
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local scoremax`i'=r(max)
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qui su `lt' if `group'==`i'
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local ltmin`i'=r(min)
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local ltmax`i'=r(max)
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di "`i'" _col(9) %4.0f `scoremin`i'' _col(14) %6.3f `ltmin`i'' _col(26) %4.0f `scoremax`i'' _col(31) %6.3f `ltmax`i'' _col(39) %4.0f `n`i''
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}
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di "{hline 42}"
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}
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local nj=0
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forvalues i=1/`nbitems' {
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qui count if ``i''!=.
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local nj=`nj'+r(N)
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}
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qui gen `df'=(`nj'-(`ntotal' + `nbitems' - 1 ))/`nj'*`rep'
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qui gen `total' =`score'
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local mult=(`nj'-(`ntotal' + `nbitems' - 1 ))/`nj'
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forvalues i=1/`nbitems' {
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qui count if (`total'!=0&`total'!=`rep')&``i''!=.
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local mult`i'=r(N)
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local df`i'=`mult'*`mult`i''
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tempname res2`i'
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qui gen `res2`i''=(`res'`i')^2
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qui su `res2`i'' if `total'!=0&`total'!=`rep'
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local sumsq`i'=r(sum)
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local fit`i'=(`sumsq`i''-`df`i'')/sqrt(2*`df`i'')
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}
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qui gen `ltcl'=.
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forvalues g=1/`maxgroup' {
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qui su `lt' if `group'==`g'
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local ltgroup`g'=r(mean)
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local N`g'=r(N)
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qui replace `ltcl'=`ltgroup`g'' if `group'==`g'
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}
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forvalues i=1/`nbitems' {
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local chi`i'=0
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forvalues g=1/`maxgroup' {
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qui su ``i'' if `group'==`g'
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local po`i'_`g'=r(mean)
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local pe`i'_`g'=exp(`ltgroup`g''-`diff'[1,`i'])/(1+exp(`ltgroup`g''-`diff'[1,`i']))
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local std`i'_`g'=2*`N`g''*(`po`i'_`g''-`pe`i'_`g'')^2/sqrt(.5*(`po`i'_`g''+`pe`i'_`g'')*(1-.5*(`po`i'_`g''+`pe`i'_`g'')))
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local chi`i'=`chi`i''+`std`i'_`g''
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}
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di "chi item ``i'' = `chi`i''"
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}
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local chisq=0
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tempname y2 vy2
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qui gen `y2'=0
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qui gen `vy2'=0
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forvalues i=1/`nbitems' {
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qui replace `y2'=`y2'+`res'`i'^2 if ``i''!=.
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qui replace `vy2'=`vy2'+2*tanh((`lt2'-`diff'[1,`i'])/2)*sinh(`lt2'-`diff'[1,`i']) if ``i''!=.
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tempname y2`i' vy2`i'
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qui gen `y2`i''=`res'`i'^2
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qui su `y2`i'' if `total'!=0&`total'!=`rep'&``i''!=.
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local sumy2`i'=r(sum)
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qui tab `ltcl'
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qui gen `vy2`i''=2*tanh((`lt2'-`diff'[1,`i'])/2)*sinh(`lt2'-`diff'[1,`i'])
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di "item ``i''"
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su `vy2`i'' if `total'!=0&`total'!=`rep'&``i''!=.
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local sumvy2`i'=r(sum)
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local fit`i'=(`sumy2`i''-`df`i'')/sqrt(`sumvy2`i'')
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local fit2`i'=`df`i''*(ln(`sumy2`i'')-ln(`df`i''))/sqrt(`sumvy2`i'')
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local chisq`i'=0
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forvalues g=1/`maxgroup' {
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qui su `y2`i'' if `group'==`g'&``i''!=.
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local sumy2`i'_g`g'=r(sum)
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local n`i'g`g'=r(N)
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qui su `vy2`i'' if `group'==`g'&``i''!=.
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local sumvy2`i'_g`g'=r(sum)
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local fit`i'_g`g'=(`sumy2`i'_g`g''-`n`i'g`g'')/sqrt(`sumvy2`i'_g`g'')
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local chisq`i'=`chisq`i''+(`fit`i'_g`g'')^2
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}
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local chisq=`chisq'+`chisq`i''
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/*fit2 est l'<27>quivalent de FitResid et chisq est correct*/
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}
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local RMSEA=sqrt(`chisq'/((`nbitems'*(`maxgroup'-1)-1)*(`ntotal'-1)))
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di in gr "{hline 55}"
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di in gr "Items" _col(18) "FitResid" _col(31) "ChiSq" _col(42) "df" _col(55) "p"
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di in gr "{hline 55}"
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forvalues i=1/`nbitems' {
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di in ye abbrev("``i''",18) _col(19) %7.3f `fit2`i'' _col(30) %6.2f `chisq`i'' _col(40) %4.0f `=`maxgroup'-1' _col(50) %6.4f 1-chi2(`=`maxgroup'-1',`chisq`i'')
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}
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di in gr "{dup 55:-}"
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di in ye "Total" _col(30) %6.2f `chisq' _col(40) %4.0f `=(`maxgroup'-1)*`nbitems'' _col(50) %6.4f 1-chi2(`=(`maxgroup'-1)*`nbitems'',`chisq`i'')
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di in ye "RMSEA" _col(30) %6.4f `RMSEA'
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di in gr "{hline 55}"
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di
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if "`pcares'"!="" {
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di "{hline 36}"
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di "Correlation matrix between residuals"
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di "{hline 36}"
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matrix list `cor',noheader format(%5.3f)
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di
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di "{hline 28}"
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di "Eigenvalues of the residuals"
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di "{hline 28}"
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matrix rowname `Ev'=Eigenvalues
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tempname Evp E
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matrix `Evp'=`Ev'/`nbitems'
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matrix `E'=`Ev' \ `Evp'
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matrix rowname `E'=Eigenvalues Proportion
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matrix list `E',noheader format(%5.3f)
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}
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*use `saveraschres', clear
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local dfind=`df'/`ntotal'*`nbitems'
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if "`genfit'"!="" {
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qui gen `genfit'=`df'*(ln(`y2')-log(`df'))/sqrt(`vy2') `if' `in'
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}
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if "`genres'"!="" {
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forvalues i=1/`nbitems' {
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qui gen `genres'`i'=`res'`i' `if' `in'
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}
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}
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end
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