You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
284 lines
9.0 KiB
Plaintext
284 lines
9.0 KiB
Plaintext
7 months ago
|
*! Version 2.3 10april2014
|
||
|
|
************************************************************************************************************
|
||
|
|
* Stata program : pcm
|
||
|
|
* Estimate the parameters of the Partial Credit Model
|
||
|
|
* Version 1 : December 17, 2007
|
||
|
|
* Version 2 : July 15, 2011
|
||
|
|
* Version 2.1 : October 18th, 2011 : -fixedvar- option, new presentation
|
||
|
|
* Version 2.2 : October 23rd, 2013 : correction of -fixedvar- option
|
||
|
|
* Version 2.3 : April 10th, 2014 : correction of -fixedvar- option
|
||
|
|
*
|
||
|
|
* Jean-benoit Hardouin, EA4275 Biostatistics, Clinical Research and Subjective Measures in Health Sciences
|
||
|
|
* Faculties of Pharmaceutical Sciences & Medicine - University of Nantes - France
|
||
|
|
* jean-benoit.hardouin@univ-nantes.fr
|
||
|
|
*
|
||
|
|
* News about this program : http://www.anaqol.org
|
||
|
|
* FreeIRT Project : http://www.freeirt.org
|
||
|
|
*
|
||
|
|
* Copyright 2007-2014 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 pcmold,eclass
|
||
|
|
version 8.0
|
||
|
|
syntax varlist(min=3 numeric) [if] [in] [,rsm fixed(string) fixedvar(real -1) fixedmu short COVariates(varname) fixedvargroupc(string) vargroupc]
|
||
|
|
preserve
|
||
|
|
tempfile pcmfile
|
||
|
|
qui save `pcmfile',replace
|
||
|
|
|
||
|
|
if "`fixedmu'"!=""&`fixedvar'!=-1&"`covariates'"=="" {
|
||
|
|
di in red "You cannot fix in the same time the mean (fixedmu option) and the variance (fixedvar option) of the latent trait without covariables"
|
||
|
|
error 184
|
||
|
|
}
|
||
|
|
if "`fixed'"!=""&"`fixedmu'"==""&`fixedvar'!=-1&"`covariates'"=="" {
|
||
|
|
di in red "You cannot fix in the same time the difficulties (fixed option) and the variance (fixedvar option) of the latent trait without covariables"
|
||
|
|
error 184
|
||
|
|
}
|
||
|
|
|
||
|
|
/*******************************************************************************
|
||
|
|
ESTIMATION OF THE PARAMETERS
|
||
|
|
********************************************************************************/
|
||
|
|
|
||
|
|
marksample touse
|
||
|
|
qui keep if `touse'
|
||
|
|
qui count
|
||
|
|
local N=r(N)
|
||
|
|
tokenize `varlist'
|
||
|
|
local nbitems : word count `varlist'
|
||
|
|
|
||
|
|
if "`rsm'"=="" {
|
||
|
|
di in gr "Model: " in ye "Partial Credit Model"
|
||
|
|
}
|
||
|
|
else {
|
||
|
|
di in gr "Model: " in ye "Rating Scale Model"
|
||
|
|
}
|
||
|
|
|
||
|
|
tempname one var w id item it obs x chosen d score
|
||
|
|
qui gen `one'=1
|
||
|
|
qui gen `id'=_n
|
||
|
|
local modamax=0
|
||
|
|
forvalues i=1/`nbitems' {
|
||
|
|
qui rename ``i'' `var'`i'
|
||
|
|
qui su `var'`i'
|
||
|
|
local moda`i'=`r(max)'
|
||
|
|
if `modamax'<`r(max)' {
|
||
|
|
local modamax=r(max)
|
||
|
|
}
|
||
|
|
}
|
||
|
|
qui genscore `var'1-`var'`nbitems' ,score(`score')
|
||
|
|
qui collapse (sum) `w'=`one',by(`var'1-`var'`nbitems' `covariates')
|
||
|
|
qui gen `id'=_n
|
||
|
|
qui reshape long `var',i(`id') j(`item')
|
||
|
|
qui drop if `var'==.
|
||
|
|
qui gen `obs'=_n
|
||
|
|
qui expand `=`modamax'+1'
|
||
|
|
qui sort `id' `item' `obs'
|
||
|
|
by `obs', sort: gen `x'=_n-1
|
||
|
|
|
||
|
|
qui gen `chosen'=`var'==`x'
|
||
|
|
qui tab `item', gen(`it')
|
||
|
|
forvalues i=1/`nbitems' {
|
||
|
|
forvalues g=1/`modamax' {
|
||
|
|
qui gen `d'`i'_`g'=-1*`it'`i'*(`x'>=`g')
|
||
|
|
}
|
||
|
|
}
|
||
|
|
qui rename `w' `w'2
|
||
|
|
bysort `id':egen score=sum(`x'*`chosen')
|
||
|
|
qui su score
|
||
|
|
local maxscore=r(max)
|
||
|
|
|
||
|
|
|
||
|
|
if "`covariates'"!="" {
|
||
|
|
qui gen covw=`covariates'*`x'
|
||
|
|
local listcov covw
|
||
|
|
}
|
||
|
|
else {
|
||
|
|
local listcov
|
||
|
|
}
|
||
|
|
if `fixedvar'!=-1 {
|
||
|
|
local tmp=sqrt(`fixedvar')
|
||
|
|
constraint 1 `x'=`tmp'
|
||
|
|
local listconstr "constraints(1)"
|
||
|
|
local eq "eqs(slope) nrf(1)"
|
||
|
|
}
|
||
|
|
local eq "eqs(slope) nrf(1)"
|
||
|
|
*set trace on
|
||
|
|
if "`rsm'"=="" { /*PARTIAL CREDIT MODEL*/
|
||
|
|
*di "cas 1"
|
||
|
|
if "`fixed'"!="" { /*FIXED ITEMS DIFFICULTIES*/
|
||
|
|
*di "cas 2"
|
||
|
|
qui gen offset=0
|
||
|
|
local l=1
|
||
|
|
forvalues i=1/`nbitems' {
|
||
|
|
forvalues mi=1/`moda`i'' {
|
||
|
|
qui replace offset=offset+`fixed'[1,`l']*`d'`i'_`mi'
|
||
|
|
local ++l
|
||
|
|
}
|
||
|
|
}
|
||
|
|
if "`fixedmu'"!="" {
|
||
|
|
local mu
|
||
|
|
}
|
||
|
|
else {
|
||
|
|
local mu "`x'"
|
||
|
|
}
|
||
|
|
*set trace on
|
||
|
|
if "`fixedvargroupc'"!=""|"`vargroupc'"!="" {/*INEQUAL VARIANCES*/
|
||
|
|
local var0: word 1 of `fixedvargroupc'
|
||
|
|
local var1: word 2 of `fixedvargroupc'
|
||
|
|
tempvar G0 G1
|
||
|
|
qui gen `G0'=groupc<0
|
||
|
|
qui gen `G1'=groupc>0
|
||
|
|
qui replace `G0'=`G0'*`x'
|
||
|
|
qui replace `G1'=`G1'*`x'
|
||
|
|
qui eq B0: `G0'
|
||
|
|
qui eq B1: `G1'
|
||
|
|
constraint 1 _cons=0
|
||
|
|
if "`fixedvargroupc'"!="" {/*FIXED INEQUAL VARIANCES*/
|
||
|
|
constraint 2 `G0'=`=sqrt(`var0')'
|
||
|
|
constraint 3 `G1'=`=sqrt(`var1')'
|
||
|
|
local listconstr "constraints(1 2 3)"
|
||
|
|
}
|
||
|
|
else { /*FREE INEQUAL VARIANCE*/
|
||
|
|
local listconstr "constraints(1)"
|
||
|
|
}
|
||
|
|
local eq "eqs(B0 B1) nrf(2)"
|
||
|
|
}
|
||
|
|
eq slope:`x'
|
||
|
|
su
|
||
|
|
tab covw
|
||
|
|
di "ICI*******************jb"
|
||
|
|
di "`x' : x"
|
||
|
|
di "`listcov' : listcov"
|
||
|
|
di "`mu' : mu"
|
||
|
|
noi di "gllamm `x' `listcov' `mu',offset(offset) `listconstr' nocons i(`id') link(mlogit) expand(`obs' `chosen' o) weight(`w') adapt trace `eq'"
|
||
|
|
*set trace on
|
||
|
|
noi gllamm `x' `listcov' `mu' ,offset(offset) `listconstr' nocons i(`id') link(mlogit) expand(`obs' `chosen' o) weight(`w') adapt trace `eq' iterate(100)
|
||
|
|
}
|
||
|
|
else if "`short'"!="" {
|
||
|
|
*di "cas 3"
|
||
|
|
eq slope:`x'
|
||
|
|
qui gllamm `x' `d'1_1-`d'`nbitems'_`modamax',i(`id') eqs(slope) link(mlogit) expand(`obs' `chosen' o) weight(`w') adapt trace nocons init iterate(100)
|
||
|
|
tempname bsave Vsave
|
||
|
|
matrix `bsave'=e(b)
|
||
|
|
matrix `Vsave'=e(V)
|
||
|
|
restore
|
||
|
|
qui pcm `varlist' , fixed(`bsave')
|
||
|
|
}
|
||
|
|
else {
|
||
|
|
*di "cas 4"
|
||
|
|
di "no short"
|
||
|
|
eq slope:`x'
|
||
|
|
qui gen i=`id'
|
||
|
|
constraint 1 `x'=1
|
||
|
|
gllamm `x' `d'1_1-`d'`nbitems'_`modamax' `listcov',i(i) `listconstr' eqs(slope) link(mlogit) expand(`obs' `chosen' o) weight(`w') adapt trace nocons iterate(100)
|
||
|
|
}
|
||
|
|
}
|
||
|
|
else {
|
||
|
|
*di "cas 5"
|
||
|
|
|
||
|
|
tempname step n
|
||
|
|
forvalues i=2/`modamax' {
|
||
|
|
qui gen `step'`i'=-1*(`x'>=`i')
|
||
|
|
}
|
||
|
|
forvalues i=1/`nbitems' {
|
||
|
|
qui gen `n'`var'`i'=(-1)*(`it'`i')*(`x')
|
||
|
|
}
|
||
|
|
qui sort `id' `item' `x'
|
||
|
|
eq slope:`x'
|
||
|
|
gllamm `x' `n'`var'1-`n'`var'`nbitems' `step'2-`step'`modamax' `listcov', i(`id') `listconstr' eqs(slope) link(mlogit) expand(`obs' `chosen' o) weight(`w') adapt trace nocons iterate(100)
|
||
|
|
}
|
||
|
|
|
||
|
|
tempname b V chol
|
||
|
|
matrix b=e(b)
|
||
|
|
matrix V=e(V)
|
||
|
|
local ll=e(ll)
|
||
|
|
matrix chol=e(chol)
|
||
|
|
|
||
|
|
|
||
|
|
if "`rsm'"=="" {
|
||
|
|
di
|
||
|
|
di in gr "Number of observations: " in ye `N'
|
||
|
|
di in gr "Number of items: " in ye `nbitems'
|
||
|
|
di in gr "Number of parameters: " in ye `=`nbitems'*`modamax'+1'
|
||
|
|
di in gr "Log-likelihood: " in ye `ll'
|
||
|
|
di
|
||
|
|
di
|
||
|
|
di in gr "{hline 100}"
|
||
|
|
di in gr "Item" _col(10) "Modality" _col(20) "Parameter" _col(30) "Std Error"
|
||
|
|
di in gr "{hline 100}"
|
||
|
|
if "`fixed'"=="" {
|
||
|
|
forvalues i=1/`nbitems' {
|
||
|
|
forvalues j=1/`modamax' {
|
||
|
|
if `j'==1 {
|
||
|
|
di in ye "``i''" _cont
|
||
|
|
}
|
||
|
|
local k=(`i'-1)*`modamax'+`j'
|
||
|
|
if "`short'"!="" {
|
||
|
|
di in ye _col(17) `j' _col(20) %9.6f `bsave'[1,`k'] in ye _col(30) %9.6f (`Vsave'[`k',`k'])^.5
|
||
|
|
}
|
||
|
|
else {
|
||
|
|
di in ye _col(17) `j' _col(20) %9.6f b[1,`k'] in ye _col(30) %9.6f (V[`k',`k'])^.5
|
||
|
|
}
|
||
|
|
}
|
||
|
|
di in gr "{dup 100:-}"
|
||
|
|
}
|
||
|
|
}
|
||
|
|
else {
|
||
|
|
forvalues i=1/`nbitems' {
|
||
|
|
forvalues j=1/`modamax' {
|
||
|
|
if `j'==1 {
|
||
|
|
di in ye "``i''" _cont
|
||
|
|
}
|
||
|
|
local k=(`i'-1)*`modamax'+`j'
|
||
|
|
di in ye _col(17) `j' _col(20) %9.6f `fixed'[1,`k'] in ye _col(32) "(fixed)"
|
||
|
|
}
|
||
|
|
di in gr "{dup 100:-}"
|
||
|
|
}
|
||
|
|
}
|
||
|
|
if "`fixed'"==""&"`short'"=="" {
|
||
|
|
local k=`nbitems'*`modamax'+1
|
||
|
|
}
|
||
|
|
else if "`fixed'"!=""&"`fixedmu'"=="" {
|
||
|
|
di in ye "Mu" in ye _col(20) %9.6f b[1,1] _col(29) %10.6f (V[1,1])^.5
|
||
|
|
local k=2
|
||
|
|
}
|
||
|
|
else if "`fixed'"!=""&"`fixedmu'"!="" {
|
||
|
|
di in ye "Mu" in ye _col(20) %9.6f 0 _col(32) %10.6f "(fixed)"
|
||
|
|
local k=1
|
||
|
|
}
|
||
|
|
else {
|
||
|
|
local k=1
|
||
|
|
}
|
||
|
|
if "`covariates'"!="" {
|
||
|
|
di in ye "`covariates'" in ye _col(20) %9.6f b[1,`k'] _col(29) %10.6f (V[`k',`k'])^.5
|
||
|
|
local k=`k'+1
|
||
|
|
}
|
||
|
|
if `fixedvar'==-1 {
|
||
|
|
di in ye "Sigma" in ye _col(20) %9.6f b[1,`k'] _col(29) %10.6f (V[`k',`k'])^.5
|
||
|
|
di in ye "Variance" in ye _col(20) %9.6f b[1,`k']^2 _col(29) %10.6f 2*(V[`k',`k'])^.5*b[1,`k']
|
||
|
|
}
|
||
|
|
else {
|
||
|
|
di in ye "Sigma" in ye _col(20) %9.6f `fixedvar'^.5 _col(32) %10.6f "(fixed)"
|
||
|
|
di in ye "Variance" in ye _col(20) %9.6f `fixedvar' _col(32) %10.6f "(fixed)"
|
||
|
|
}
|
||
|
|
di in gr "{hline 100}"
|
||
|
|
di
|
||
|
|
di
|
||
|
|
}
|
||
|
|
|
||
|
|
end
|