Computed theoretical power for N=100 and N=200 scenarios

Modules/ado/personal/r/raschres.ado

@@ -0,0 +1,235 @@
+*! Version 1.2 June 3, 2013
+************************************************************************************************************
+* Stata program : raschres
+* Analysis of the residuals of the Rasch model
+* Version 1 : June 16, 2010
+* Version 1.1 : July 15, 2011
+* Version 1.2 : June 3, 2013 /*formatting outputs*/
+*
+*
+* Jean-benoit Hardouin, phD, Assistant Professor
+* EA4275 - SPHERE
+* Team of Biostatistics, Pharmacoepidemiology and Subjective Measures in Health Sciences
+* University of Nantes - Faculty of Pharmaceutical Sciences
+* France
+* jean-benoit.hardouin@univ-nantes.fr
+*
+* News about this program : http://www.anaqol.org
+*
+* Copyright 2010-2013 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 raschres,rclass
+syntax varlist [if] [in] , diff(string) theta(varname) [genres(string) genfit(string)  vargroup(varname) PCAres DETails]
+tempfile saveraschres
+if "`if'"!=""|"`in'"!="" {
+   *keep `if' `in'
+}
+*qui save `saveraschres',replace
+
+tempname res
+
+qui count
+local ntotal=r(N)
+tokenize `varlist'
+local nbitems: word count `varlist'
+qui tempname score  lt
+qui genscore `varlist',score(`score')
+qui gen `lt'=`theta'
+forvalues i=1/`nbitems' {
+   local z2`i'=0
+}
+
+forvalues i=1/`nbitems'{
+   qui tempname p`i' res`i'
+   qui gen `p`i''=exp(`lt'-`diff'[1,`i'])/(1+exp(`lt'-`diff'[1,`i']))
+   qui gen `res'`i'=(1-`p`i'')/sqrt(`p`i''*(1-`p`i'')) if ``i''==1
+   qui replace `res'`i'=(0-`p`i'')/sqrt(`p`i''*(1-`p`i'')) if ``i''==0
+}
+su
+local chi2=0
+forvalues i=1/`nbitems' {
+    qui tempname res2
+    qui gen `res2'`i'=`res'`i'^2
+    qui su `res2'`i'
+    local chi2=`chi2'+`r(sum)'
+    label variable `res'`i' "``i''"
+}
+su
+tempname cor  Ev
+matrix `cor'=J(`nbitems',`nbitems',.)
+local list
+forvalues i=1/`nbitems' {
+   forvalues j=1/`nbitems' {
+      qui corr `res'`i' `res'`j'
+      matrix `cor'[`i',`j']=r(rho)
+   }
+   local list "`list' ``i''"
+}
+matrix colname `cor'=`list'
+matrix rowname `cor'=`list'
+qui pca `res'*
+matrix `Ev'=e(Ev)
+
+tempname lt2 ltcl group  df nbmiss rep total
+qui egen `nbmiss'=rowmiss(`varlist')
+qui gen `rep'=`nbitems'-`nbmiss'
+qui gen `lt2'=`lt' if `score'!=0&`score'!=`rep'
+if "`vargroup'"=="" {
+   qui gengroup `lt2', newvar(`group') cont      det  minsize(33)
+}
+else {
+   qui `group'=`vargroup'
+}
+qui su `group'
+local maxgroup=r(max)
+
+if "`details'"!="" {
+    di "{hline 42}"
+    di _col(12) "Min" _col(29) "Max"
+    di "{dup 42:-}"
+    di "" _col(8) "" _col(14) "Latent" _col(28) "" _col(31) "Latent"  _col(53)  ""
+    di "Group" _col(8) "Score" _col(15) "trait" _col(25) "Score" _col(32) "trait"  _col(42)  "n"
+    di "{hline 42}"
+    forvalues i=1/`maxgroup' {
+       qui count if `group'==`i'
+       local n`i'=r(N)
+       qui su `score' if `group'==`i'
+       local scoremin`i'=r(min)
+       local scoremax`i'=r(max)
+       qui su `lt' if `group'==`i'
+       local ltmin`i'=r(min)
+       local ltmax`i'=r(max)
+       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''
+    }
+    di "{hline 42}"
+}
+
+local nj=0
+forvalues i=1/`nbitems' {
+   qui count if ``i''!=.
+   local nj=`nj'+r(N)
+}
+qui gen `df'=(`nj'-(`ntotal' + `nbitems' - 1 ))/`nj'*`rep'
+qui gen `total' =`score'
+local mult=(`nj'-(`ntotal' + `nbitems' - 1 ))/`nj'
+
+
+forvalues i=1/`nbitems' {
+   qui count if (`total'!=0&`total'!=`rep')&``i''!=.
+   local mult`i'=r(N)
+   local df`i'=`mult'*`mult`i''
+   tempname res2`i'
+   qui gen `res2`i''=(`res'`i')^2
+   qui su `res2`i''   if `total'!=0&`total'!=`rep'
+   local sumsq`i'=r(sum)
+   local fit`i'=(`sumsq`i''-`df`i'')/sqrt(2*`df`i'')
+}
+
+qui gen `ltcl'=.
+forvalues g=1/`maxgroup' {
+   qui su `lt' if `group'==`g'
+   local ltgroup`g'=r(mean)
+   local N`g'=r(N)
+   qui replace `ltcl'=`ltgroup`g'' if `group'==`g'
+}
+forvalues i=1/`nbitems' {
+   local chi`i'=0
+   forvalues g=1/`maxgroup' {
+      qui su ``i'' if `group'==`g'
+      local po`i'_`g'=r(mean)
+      local pe`i'_`g'=exp(`ltgroup`g''-`diff'[1,`i'])/(1+exp(`ltgroup`g''-`diff'[1,`i']))
+      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'')))
+      local chi`i'=`chi`i''+`std`i'_`g''
+   }
+   di "chi item ``i'' = `chi`i''"
+}
+
+local chisq=0
+tempname y2 vy2
+qui gen `y2'=0
+qui gen `vy2'=0
+forvalues i=1/`nbitems' {
+   qui replace `y2'=`y2'+`res'`i'^2  if ``i''!=.
+   qui replace `vy2'=`vy2'+2*tanh((`lt2'-`diff'[1,`i'])/2)*sinh(`lt2'-`diff'[1,`i']) if ``i''!=.
+   tempname y2`i' vy2`i'
+   qui gen `y2`i''=`res'`i'^2
+   qui su `y2`i'' if `total'!=0&`total'!=`rep'&``i''!=.
+   local sumy2`i'=r(sum)
+   qui tab `ltcl'
+   qui gen `vy2`i''=2*tanh((`lt2'-`diff'[1,`i'])/2)*sinh(`lt2'-`diff'[1,`i'])
+   di "item ``i''"
+    su `vy2`i'' if `total'!=0&`total'!=`rep'&``i''!=.
+   local sumvy2`i'=r(sum)
+   local fit`i'=(`sumy2`i''-`df`i'')/sqrt(`sumvy2`i'')
+   local fit2`i'=`df`i''*(ln(`sumy2`i'')-ln(`df`i''))/sqrt(`sumvy2`i'')
+   local chisq`i'=0
+   forvalues g=1/`maxgroup' {
+      qui su `y2`i'' if `group'==`g'&``i''!=.
+      local sumy2`i'_g`g'=r(sum)
+      local n`i'g`g'=r(N)
+      qui su `vy2`i'' if `group'==`g'&``i''!=.
+      local sumvy2`i'_g`g'=r(sum)
+      local fit`i'_g`g'=(`sumy2`i'_g`g''-`n`i'g`g'')/sqrt(`sumvy2`i'_g`g'')
+      local chisq`i'=`chisq`i''+(`fit`i'_g`g'')^2
+   }
+   local chisq=`chisq'+`chisq`i''
+   /*fit2 est l'<27>quivalent de FitResid et chisq est correct*/
+}
+local RMSEA=sqrt(`chisq'/((`nbitems'*(`maxgroup'-1)-1)*(`ntotal'-1)))
+
+di in gr "{hline 55}"
+di in gr "Items" _col(18) "FitResid" _col(31) "ChiSq" _col(42) "df" _col(55) "p"
+di in gr "{hline 55}"
+forvalues i=1/`nbitems' {
+   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'')
+}
+di in gr "{dup 55:-}"
+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'')
+di in ye "RMSEA"  _col(30) %6.4f `RMSEA'
+di in gr "{hline 55}"
+di
+
+if "`pcares'"!="" {
+    di "{hline 36}"
+    di "Correlation matrix between residuals"
+    di "{hline 36}"
+    matrix list `cor',noheader format(%5.3f)
+    di
+    di "{hline 28}"
+    di "Eigenvalues of the residuals"
+    di "{hline 28}"
+    matrix rowname `Ev'=Eigenvalues
+    tempname Evp E
+    matrix `Evp'=`Ev'/`nbitems'
+    matrix `E'=`Ev' \ `Evp'
+    matrix rowname `E'=Eigenvalues Proportion
+matrix list `E',noheader format(%5.3f)
+}
+
+*use `saveraschres', clear
+local dfind=`df'/`ntotal'*`nbitems'
+if "`genfit'"!="" {
+   qui gen `genfit'=`df'*(ln(`y2')-log(`df'))/sqrt(`vy2') `if' `in'
+}
+if "`genres'"!="" {
+   forvalues i=1/`nbitems' {
+      qui gen `genres'`i'=`res'`i'  `if' `in'
+   }
+}
+
+end