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557 lines
17 KiB
Plaintext
557 lines
17 KiB
Plaintext
*! version 1.1 8december2005
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*! Jean-Benoit Hardouin
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************************************************************************************************************
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* Simirt: Simulation of dichotomous data following an IRT model (Rasch model,
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* OPLM, Birnbaum model, 3-PLM, 4-PLM, 5-PAM
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*
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* Version 1 : May 9, 2005 (Jean-Benoit Hardouin)
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* Version 1.1 : December 8, 2005 (Jean-Benoit Hardouin) /*group and deltagroup options*/
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*
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* Jean-benoit Hardouin, Regional Health Observatory of Orléans - France
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* jean-benoit.hardouin@orscentre.org
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*
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* News about this program : http://anaqol.free.fr
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* FreeIRT Project : http://freeirt.free.fr
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*
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* Copyright 2005 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 simirt , rclass
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version 8.0
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syntax [, NBObs(integer 2000) Dim(string) MU(string) COV(string) DISc(string) DIFf(string) PMIN(string) PMAX(string) ACC(string) clear STOre(string) REPlace PREFix(string) DRAW GRoup(real 0) DELtagroup(real 0)]
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/********************************************************************************
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TESTS
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********************************************************************************/
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if `group'<0|`group'>1 {
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di in red "{p}The {hi:group} option defines a probability. The values defined by this option must be greater (or equal) to 0 and lesser (or equal) to 1.{p_end}"
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error 198
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exit
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}
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if "`clear'"==""&"`store'"=="" {
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di in red "You must use at least one of these two options: clear and/or store."
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error 198
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exit
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}
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if "`dim'"!="" {
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local nbdim:word count `dim'
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if `nbdim'>2 {
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di in red "You can simulate data with one or two dimensions, and you have indicated `nbdim' dimensions in the {hi:dim} option. Please correct it."
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error 198
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exit
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}
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if `nbdim'==1 {
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local dim1=`dim'
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local nbitems=`dim1'
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local dim=1
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}
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else if `nbdim'==2 {
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local dim1:word 1 of `dim'
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local dim2:word 2 of `dim'
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local nbitems=`dim1'+`dim2'
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local dim=2
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}
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else {
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di in red "Your {hi:dim} option is uncorrect, please correct it. This option must indicate one or two integer(s)."
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error 198
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exit
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}
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if "`diff'"!="" {
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local nbdiff:word count `diff'
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if (`nbdiff'==3&`dim'==1)|(`nbdiff'==5&`dim'==2)|`nbdiff'==1 {
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local typediff:word 1 of `diff'
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if "`typediff'"!="gauss"&"`typediff'"!="uniform" {
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local typediff values
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}
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}
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if "`typediff'"=="values"&`nbdiff'!=`nbitems' {
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di in red "You have indicated a number of difficulty parameters ({hi:diff} option) different of the number of items to simulate ({hi:dim} option). Please correct these options."
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error 198
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exit
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}
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}
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if "`diff'"=="" {
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if `dim'==1 {
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local diff gauss 0 1
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}
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else if `dim'==2 {
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local diff gauss 0 1 0 1
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}
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local typediff gauss
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local nbdiff:word count `diff'
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}
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}
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else if "`dim'"==""{
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if "`diff'"=="" {
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di in red "You must indicate the number of items to simulate with the {hi:dim} or the {hi:diff} option(s)."
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error 198
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exit
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}
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else {
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local nbdiff:word count `diff'
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if `nbdiff'!=`nbitems' {
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di in red "You have indicated a number of difficulty parameters ({hi:diff} option) different of the number of items to simulate ({hi:dim} option). Please correct these options."
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error 198
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exit
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}
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}
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}
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if "`draw'"!=""&`dim'!=1 {
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di in red "The {hi:draw} option is available only with unidimensional simulated data."
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error 198
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exit
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}
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if (`group'!=0|`deltagroup'!=0)&`dim'!=1 {
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di in red "The {hi:group} and the {hi:deltagroup} options are available only with unidimensional simulated data."
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error 198
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exit
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}
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if "`prefix'"=="" {
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local prefix item
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}
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local nbprefix:word count `prefix'
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local prefix1:word 1 of `prefix'
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if `dim'==2&`nbprefix'>=2 {
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local prefix2:word 2 of `prefix'
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}
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else if `dim'==2 {
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local prefix2:word 1 of `prefix'
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}
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if `dim'==2&"`prefix1'"=="`prefix2'" {
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local prefix1 `prefix1'A
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local prefix2 `prefix2'B
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}
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*di in ye "dim : `dim' ; diff : `diff' ; nbdiff : `nbdiff'"
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local nbcov:word count `cov'
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if `dim'==1&`nbcov'>1 {
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di in red "You simulate one dimension. You must indicate only the variance of the simulated latent trait in the {hi:cov} option."
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error 198
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exit
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}
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else if `dim'==2&`nbcov'!=3&`nbcov'>0 {
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di in red "You simulate two dimensions. You must indicate exactly 3 values in the {hi:cov} option (Variance of the first simulated latent trait, Variance of the second simulated latent trait, Covariance between the two simulated latent traits)."
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error 198
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exit
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}
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else if `nbcov'==0 {
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if `dim'==1 {
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local cov "1"
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}
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else if `dim'==2 {
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local cov "1 1 0"
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}
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local nbcov:word count `cov'
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}
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if `nbcov'==1 {
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if `cov'<0 {
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di in red "The variance of your latent trait can not be negative. Please correct your {hi:cov} option."
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error 198
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}
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}
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else if `nbcov'==3 {
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local cov1:word 1 of `cov'
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local cov2:word 2 of `cov'
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local cov3:word 3 of `cov'
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local rho=`cov3'/sqrt(`cov1'*`cov2')
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if `cov1'<0|`cov2'<0|`rho'<-1|`rho'>1 {
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di in red "Your covariance matrix defined by the {hi:cov} option is not correct. Please correct it."
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error 198
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exit
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}
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}
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local nbmu:word count `mu'
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if `nbmu'!=`dim'&`nbmu'!=0 {
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di in red "You must indicate as many values in the {hi:mu} option as the number of dimension(s) (`dim')"
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error 198
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exit
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}
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local nbdisc:word count `disc'
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if `nbdisc'!=`nbitems'&`nbdisc'!=0 {
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di in red "You must indicate as many values in the {hi:disc} option as items defined by the {hi:dim} and the {hi:diff} options (`nbitems')"
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error 198
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exit
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}
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local nbpmin:word count `pmin'
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if `nbpmin'!=`nbitems'&`nbpmin'!=0 {
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di in red "You must indicate as many values in the {hi:pmin} option as items defined by the {hi:dim} and the {hi:diff} options (`nbitems')"
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error 198
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exit
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}
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local nbpmax:word count `pmax'
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if `nbpmax'!=`nbitems'&`nbpmax'!=0 {
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di in red "You must indicate as many values in the {hi:pmax} option as items defined by the {hi:dim} and the {hi:diff} options (`nbitems')"
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error 198
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exit
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}
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local nbacc:word count `acc'
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if `nbacc'!=`nbitems'&`nbacc'!=0 {
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di in red "You must indicate as many values in the {hi:acc} option as items defined by the {hi:dim} and the {hi:diff} options (`nbitems')"
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error 198
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exit
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}
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preserve
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tempfile saveraschbin
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capture qui save `saveraschbin'
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/********************************************************************************
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PARAMETERS
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********************************************************************************/
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/*
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scalar define hour=real(substr("$S_TIME",1,2))
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scalar define min=real(substr("$S_TIME",4,2))
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scalar define sec=real(substr("$S_TIME",7,2))
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scalar define jour=real(substr("$S_DATE",1,2))
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*/
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local hour=real(substr("$S_TIME",1,2))
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local min=real(substr("$S_TIME",4,2))
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local sec=real(substr("$S_TIME",7,2))
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local jour=real(substr("$S_DATE",1,2))
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if "$seed"!="" {
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global seed2=int($seed)
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}
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else {
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global seed2=0
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}
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global seed=$seed2+256484+`sec'*1000000+`min'*10000+`hour'*100+`jour'
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if $seed>2^31-1 {
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global seed=int($seed/10)
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}
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qui set seed $seed
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if "`typediff'"=="uniform" {
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if `dim'==1 {
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if `nbdiff'==3 {
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local min:word 2 of `diff'
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local max:word 3 of `diff'
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}
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else if `nbdiff'==1 {
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local min=-2
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local max=2
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}
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else {
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di in red "Your {hi:diff} option is uncorrect. Please correct it."
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}
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local diff
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forvalues i=1/`nbitems' {
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local diff `diff' `=`min'+(`max'-`min')*`i'/(`nbitems'+1)'
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}
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}
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if `dim'==2 {
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if `nbdiff'==5 {
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local min1:word 2 of `diff'
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local max1:word 3 of `diff'
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local min2:word 4 of `diff'
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local max2:word 5 of `diff'
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}
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else if `nbdiff'==1 {
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local min1=-2
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local max1=2
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local min2=-2
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local max2=2
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}
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else {
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di in red "Your {hi:diff} option is uncorrect. Please correct it."
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exit
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}
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local diff
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forvalues i=1/`dim1' {
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local diff `diff' `=`min1'+(`max1'-`min1')*`i'/(`dim1'+1)'
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}
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forvalues i=1/`dim2' {
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local diff `diff' `=`min2'+(`max2'-`min2')*`i'/(`dim2'+1)'
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}
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}
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}
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if "`typediff'"=="gauss" {
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if `dim'==1 {
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if `nbdiff'==3 {
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local mean:word 2 of `diff'
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local var:word 3 of `diff'
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}
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else if `nbdiff'==1 {
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local mean=0
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local var=1
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}
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else {
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di in red "Your {hi:diff} option is uncorrect. Please correct it."
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error 198
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exit
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}
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local diff
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forvalues i=1/`nbitems' {
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local tmp=invnorm(`i'/(`nbitems'+1))*sqrt(`var')+`mean'
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local diff `diff' `tmp'
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}
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}
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if `dim'==2 {
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if `nbdiff'==5 {
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local mean1:word 2 of `diff'
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local var1:word 3 of `diff'
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local mean2:word 4 of `diff'
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local var2:word 5 of `diff'
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}
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else if `nbdiff'==1 {
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local mean1=0
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local var1=1
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local mean2=0
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local var2=1
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}
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else {
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di in red "Your {hi:diff} option is uncorrect. Please correct it."
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error 198
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exit
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}
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local diff
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forvalues i=1/`dim1' {
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local tmp=invnorm(`i'/(`dim1'+1))*sqrt(`var1')+`mean1'
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local diff `diff' `tmp'
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}
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forvalues i=1/`dim2' {
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local tmp=invnorm(`i'/(`dim2'+1))*sqrt(`var2')+`mean2'
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local diff `diff' `tmp'
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}
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}
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}
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tempname matmu matcov matdiff matdisc matpmin matpmax matacc
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matrix define `matdiff'=J(`nbitems',1,0)
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matrix define `matdisc'=J(`nbitems',1,0)
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matrix define `matpmin'=J(`nbitems',1,0)
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matrix define `matpmax'=J(`nbitems',1,0)
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matrix define `matacc'=J(`nbitems',1,0)
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matrix define `matmu'=J(`dim',1,0)
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matrix define `matcov'=J(`=(`dim'+1)*`dim'/2',1,0)
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forvalues i=1/`nbitems' {
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local tmp:word `i' of `diff'
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matrix `matdiff'[`i',1]=`tmp'
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if `nbdisc'!=0 {
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local tmp:word `i' of `disc'
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matrix `matdisc'[`i',1]=`tmp'
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}
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else {
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matrix `matdisc'[`i',1]=1
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}
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if `nbpmin'!=0 {
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local tmp:word `i' of `pmin'
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matrix `matpmin'[`i',1]=`tmp'
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}
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else {
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matrix `matpmin'[`i',1]=0
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}
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if `nbpmax'!=0 {
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local tmp:word `i' of `pmax'
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matrix `matpmax'[`i',1]=`tmp'
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}
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else {
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matrix `matpmax'[`i',1]=1
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}
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if `nbacc'!=0 {
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local tmp:word `i' of `acc'
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matrix `matacc'[`i',1]=`tmp'
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}
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else {
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matrix `matacc'[`i',1]=1
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}
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}
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if `nbcov'==3|`nbcov'==1 {
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local tmp:word 1 of `cov'
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matrix `matcov'[1,1]=`tmp'
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if `nbcov'==3&`dim'==2 {
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local tmp:word 2 of `cov'
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matrix `matcov'[2,1]=`tmp'
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local tmp:word 3 of `cov'
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matrix `matcov'[3,1]=`tmp'
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}
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}
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else {
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matrix `matcov'[1,1]=1
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if `dim'==2 {
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matrix `matcov'[2,1]=1
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matrix `matcov'[3,1]=0
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}
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}
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if (`nbmu'==`dim') {
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local tmp:word 1 of `mu'
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matrix `matmu'[1,1]=`tmp'
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if `dim'==2 {
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local tmp:word 2 of `mu'
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matrix `matmu'[2,1]=`tmp'
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}
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}
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if `dim'==2 {
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local corr=`matcov'[3,1]/sqrt(`matcov'[1,1]*`matcov'[2,1])
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}
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/********************************************************************************
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ITEMS CHARACTERISTIC CURVES
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********************************************************************************/
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if "`draw'"!="" {
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*set trace on
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drop _all
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qui set obs 2001
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qui gen lt1=_n
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qui replace lt1=(lt1-1001)/1000*4*sqrt(`cov')+`matmu'[1,1]
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label variable lt1 "Latent trait"
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local dess
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forvalues i=1/`dim1' {
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qui gen `prefix1'`i'=`matpmin'[`i',1]+(`matpmax'[`i',1]-`matpmin'[`i',1])*(1/(1+exp(-`matdisc'[`i',1]*(lt1-`matdiff'[`i',1]))))^(`matacc'[`i',1])
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local dess `dess' (line `prefix'`i' lt1)
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}
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graph twoway `dess' , ylabel(0(.25)1) legend(off) ytitle("Probability of a positive response")
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}
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/********************************************************************************
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SIMULATION
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********************************************************************************/
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drop _all
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qui set obs `nbobs'
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qui gen lt1=invnorm(uniform())
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if `dim'==2 {
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qui gen lt2=invnorm(uniform())
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qui replace lt2=`corr'*lt1+sqrt(1-(`corr')^2)*lt2
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qui replace lt2=lt2*sqrt(`matcov'[2,1])+`matmu'[2,1]
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}
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qui replace lt1=lt1*sqrt(`matcov'[1,1])+`matmu'[1,1]
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if `dim'==1&`group'!=0 {
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qui gen group=uniform()<`group'
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qui replace lt1=lt1+`deltagroup'*(1-`group') if group==1
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qui replace lt1=lt1-`deltagroup'*`group' if group==0
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}
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di in gr "{hline 75}"
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di _col(1) in gr "Items" _col(18) "Difficulty" _col(34) "Discr." _col(45) "Pmin" _col(58) "Pmax" _col(73) "Acc"
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di in gr "{hline 75}"
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forvalues i=1/`dim1' {
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qui gen `prefix1'`i'=`matpmin'[`i',1]+(`matpmax'[`i',1]-`matpmin'[`i',1])*(1/(1+exp(-`matdisc'[`i',1]*(lt1-`matdiff'[`i',1]))))^(`matacc'[`i',1])
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qui replace `prefix1'`i'=uniform()<=`prefix1'`i'
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di _col(1) in gr "`prefix1'`i'" _col(20) in ye %8.4f `matdiff'[`i',1] _col(32) %8.4f `matdisc'[`i',1] _col(44) %6.4f `matpmin'[`i',1] _col(56) %6.4f `matpmax'[`i',1] _col(68) %8.4f `matacc'[`i',1]
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}
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if `dim'==2 {
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di in gr "{hline 75}"
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forvalues i=`=`dim1'+1'/`=`dim1'+`dim2'' {
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qui gen `prefix2'`=`i'-`dim1''=`matpmin'[`i',1]+(`matpmax'[`i',1]-`matpmin'[`i',1])*(1/(1+exp(-`matdisc'[`i',1]*(lt2-`matdiff'[`i',1]))))^(`matacc'[`i',1])
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qui replace `prefix2'`=`i'-`dim1''=uniform()<=`prefix2'`=`i'-`dim1''
|
|
di _col(1) in gr "`prefix2'`=`i'-`dim1''" _col(20) in ye %8.4f `matdiff'[`i',1] _col(32) %8.4f `matdisc'[`i',1] _col(44) %6.4f `matpmin'[`i',1] _col(56) %6.4f `matpmax'[`i',1] _col(68) %8.4f `matacc'[`i',1]
|
|
}
|
|
}
|
|
di in gr "{hline 75}"
|
|
di
|
|
|
|
|
|
|
|
qui corr lt*,cov
|
|
local var_1=r(Var_1)
|
|
return scalar var_1=r(Var_1)
|
|
if `dim'==2 {
|
|
local cov_12=r(cov_12)
|
|
local var_2=r(Var_2)
|
|
return scalar cov_12=r(cov_12)
|
|
return scalar var_2=r(Var_2)
|
|
qui corr lt*
|
|
local rho=r(rho)
|
|
return scalar rho=r(rho)
|
|
}
|
|
qui su lt1
|
|
local mean1=r(mean)
|
|
return scalar mean_1=r(mean)
|
|
if `dim'==2 {
|
|
qui su lt2
|
|
local mean2=r(mean)
|
|
return scalar mean_2=r(mean)
|
|
}
|
|
if `dim'==1&`group'!=0 {
|
|
qui su lt1 if group==0
|
|
local mean_0=r(mean)
|
|
qui su lt1 if group==1
|
|
local mean_1=r(mean)
|
|
local delta=`mean_1'-`mean_0'
|
|
}
|
|
|
|
return scalar nbobs=`nbobs'
|
|
|
|
di in gr "{hline 50}"
|
|
di _col(1) in gr "Latent trait" _c
|
|
if `dim'==2 {
|
|
di in gr "s"_c
|
|
}
|
|
di in gr _col(29) "Theorical" _col(42) "Observed"
|
|
di in gr "{hline 50}"
|
|
forvalues i=1/`dim' {
|
|
di _col(1) in gr "Mean(lt`i')" _col(30) in ye %8.4f `matmu'[`i',1] _col(42) %8.4f `mean`i''
|
|
di _col(1) in gr "Variance(lt`i')" _col(30) in ye %8.4f `matcov'[`i',1] _col(42) %8.4f `var_`i''
|
|
}
|
|
if `dim'==1&`group'!=0 {
|
|
di _col(1) in gr "Mean(lt1) group 0" _col(30) in ye %8.4f `matmu'[1,1]-`deltagroup'*`group' _col(42) %8.4f `mean_0'
|
|
di _col(1) in gr "Mean(lt1) group 1" _col(30) in ye %8.4f `matmu'[1,1]+`deltagroup'*(1-`group') _col(42) %8.4f `mean_1'
|
|
qui count if group==1
|
|
local prop=r(N)/`nbobs'
|
|
di _col(1) in gr "Proportion group 1" _col(30) in ye %8.4f `group' _col(42) %8.4f `prop'
|
|
}
|
|
if `dim'==2 {
|
|
di _col(1) in gr "Covariance" _col(30) in ye %8.4f `matcov'[3,1] _col(42) %8.4f `cov_12'
|
|
di _col(1) in gr "Correlation" _col(31) in ye %7.4f `corr' _col(43) %7.4f `rho'
|
|
}
|
|
di in gr "{hline 50}"
|
|
|
|
/********************************************************************************
|
|
CLEAR AND/OR STORE
|
|
********************************************************************************/
|
|
|
|
|
|
if "`clear'"!="" {
|
|
restore, not
|
|
preserve
|
|
}
|
|
if "`store'"!="" {
|
|
save "`store'",`replace'
|
|
}
|
|
if "`clear'"=="" {
|
|
use "`saveraschbin'",replace
|
|
}
|
|
end
|