Computed theoretical power for N=100 and N=200 scenarios
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297
Modules/ado/plus/b/brant.ado
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297
Modules/ado/plus/b/brant.ado
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*! version 1.6.0 3/29/01
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capture program drop brant
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program define brant, rclass
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version 6
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tempvar touse
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tempname bout d pvals ivchi ivout step1 step2 ologit
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tempname XpWmmX iXpWmmX XpWmlX XpWllX iXpWllX DB DBp iDvBDp
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syntax [, detail]
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if "`e(cmd)'"!="ologit" {
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di in r "brant can only be used after ologit"
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exit
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}
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*to make output stata 6 or stata 7 compatible
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cap version 7
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if _rc!=0 {
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local vers7 "no"
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local smcl ""
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local dash "-"
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local vline "|"
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local plussgn "+"
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local topt "-"
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local bottomt "-"
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}
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else { local vers7 "yes"
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local smcl "in smcl "
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local dash "{c -}"
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local vline "{c |}"
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local plussgn "{c +}"
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local topt "{c TT}"
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local bottomt "{c BT}"
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}
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version 6.0
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local ocmd "`e(cmd)'"
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if "`ocmd'"=="ologit" { local bcmd "logit" }
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local depvar "`e(depvar)'"
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gen `touse' = e(sample)
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local wtis ""
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if "`e(wtype)'"!="" {
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di in r "-brant- does not work with ologit models with weights"
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error 999
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}
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_perhs
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local rhsnms "`r(rhsnms)'"
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local nrhs "`r(nrhs)'"
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_pecats
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local numcats = `r(numcats)'
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local catvals "`r(catvals)'"
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local catnms "`r(catnms)'"
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local catnms8 "`r(catnms8)'"
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estimates hold `ologit'
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*** estimate series of binary logits
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local i = 1
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while `i' <= `numcats'-1 {
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local splitat : word `i' of `catvals'
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tempvar dummy
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quietly gen `dummy' = 0 if `depvar' <= `splitat' & `touse'==1
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quietly replace `dummy' = 1 if `depvar' > `splitat' & `touse'==1
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quietly `bcmd' `dummy' `rhsnms' `wtis' if `touse' == 1
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_perhs
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local binnrhs = "`r(nrhs)'"
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if `nrhs' != `binnrhs' {
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di in r "not all independent variables can be retained in all binary logits"
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di in r "brant test cannot be computed"
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exit 999
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}
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tempvar prob`i'
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quietly predict `prob`i''
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tempname b`i' V`i' bc`i'
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mat `b`i'' = e(b)
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mat `b`i'' = `b`i''[1, 1..`nrhs']
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mat `V`i'' = e(V)
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mat `V`i'' = `V`i''[1..`nrhs', 1..`nrhs']
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mat `bc`i'' = e(b) /* with constant--for detail output only */
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mat `bc`i'' = `bc`i'''
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local outname "y>`splitat'"
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local outname = substr("`outname'", 1, 8)
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mat colnames `bc`i'' = "`outname'"
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mat `bout' = nullmat(`bout'), `bc`i''
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local i = `i' + 1
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}
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*** make variables for W(ml) matrices
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local i = 1
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while `i' <= `numcats'-1 {
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local i2 = `i'
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while `i2' <= `numcats'- 1 {
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tempvar w`i'_`i2'
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quietly gen `w`i'_`i2'' = `prob`i2'' - (`prob`i''*`prob`i2'')
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local i2 = `i2' + 1
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}
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local i = `i' + 1
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}
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*** calculate variance Bm, Bl
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local i = 1
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while `i' <= `numcats'-1 {
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local i2 = `i'
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while `i2' <= `numcats'- 1 {
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quietly {
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* inverse(X'W(mm)X)
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matrix accum `XpWmmX' = `rhsnms' [iw=`w`i'_`i''] if `touse'==1
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matrix `iXpWmmX' = inv(`XpWmmX')
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* X'W(ml)X
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matrix accum `XpWmlX' = `rhsnms' [iw=`w`i'_`i2''] if `touse'==1
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* inverse(X'W(ll)X)
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matrix accum `XpWllX' = `rhsnms' [iw=`w`i2'_`i2''] if `touse'==1
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matrix `iXpWllX' = inv(`XpWllX')
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* product of three matrices
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matrix `step1' = `iXpWmmX' * `XpWmlX'
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tempname vb`i'_`i2'
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matrix `vb`i'_`i2'' = `step1' * `iXpWllX'
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}
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mat `vb`i'_`i2''= `vb`i'_`i2''[1..`nrhs',1..`nrhs']
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local i2 = `i2' + 1
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}
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local i = `i' + 1
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}
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* define var(B) matrix
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local i = 1
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while `i' <= `numcats'-1 {
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tempname row`i'
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local i2 = 1
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while `i2' <= `numcats'- 1 {
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quietly {
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if `i'==`i2' { mat `row`i'' = nullmat(`row`i''), `V`i'' }
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if `i'<`i2' { mat `row`i'' = nullmat(`row`i'') , `vb`i'_`i2'' }
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if `i'>`i2' { mat `row`i'' = nullmat(`row`i'') , `vb`i2'_`i''' }
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}
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local i2 = `i2' + 1
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}
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local i = `i' + 1
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}
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* combine matrices
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tempname varb
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local i = 1
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while `i' <= `numcats'-1 {
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mat `varb' = nullmat(`varb') \ `row`i''
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local i = `i' + 1
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}
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* make beta vector
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tempname bstar
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local i = 1
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while `i' <= `numcats'-1 {
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mat `bstar' = nullmat(`bstar') , `b`i''
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local i = `i' + 1
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}
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mat `bstar' = `bstar''
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* create design matrix for wald test; make I, -I, and 0 matrices
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tempname id negid zero
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local dim = `nrhs'
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mat `id' = I(`dim')
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mat rownames `id' = `rhsnms'
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mat colnames `id' = `rhsnms'
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mat `negid' = -1*`id'
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mat rownames `negid' = `rhsnms'
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mat colnames `negid' = `rhsnms'
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mat `zero' = J(`dim', `dim', 0)
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mat rownames `zero' = `rhsnms'
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mat colnames `zero' = `rhsnms'
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* dummy matrix
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local i = 1
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while `i' <= `numcats'-2 {
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tempname drow`i'
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local i2 = 1
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while `i2' <= `numcats'- 1 {
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quietly {
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tempname feed
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if `i2'==1 { mat `feed' = `id' }
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else if `i2'-`i'==1 { mat `feed' = `negid' }
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else { mat `feed' = `zero' }
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mat `drow`i'' = nullmat(`drow`i'') , `feed'
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}
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local i2 = `i2' + 1
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}
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local i = `i' + 1
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}
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* combine matrices
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local i = 1
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while `i' <= `numcats'-2 {
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mat `d' = nullmat(`d') \ `drow`i''
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local i = `i' + 1
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}
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* terms of wald test
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mat `DB' = `d' * `bstar'
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mat `DBp' = `DB''
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mat `step1' = `d'*`varb'
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mat `step2' = `step1' * (`d'')
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mat `iDvBDp' = inv(`step2')
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*** calculate wald stat
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tempname step1 wald waldout pout dfout
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mat `step1' = `DBp' * `iDvBDp'
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mat `wald' = `step1' * `DB'
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sca `waldout' = `wald'[1,1]
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sca `dfout' = `nrhs'*(`numcats'-2)
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sca `pout' = chiprob(`dfout', `waldout')
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tempname dtemp vbtemp bstemp
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local i = 1
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while `i' <= `nrhs' {
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tempname d`i' vb`i' bstar`i'
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local i2 = 1
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while `i2' <= `numcats'-1 {
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local row = ((`nrhs')*(`i2'-1)) + (`i')
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tempname drow vbrow
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local i3 = 1
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while `i3' <= `numcats'-1 {
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local column = ((`nrhs')*(`i3'-1)) + (`i')
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if (`i2'<`numcats'-1) {
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mat `dtemp' = `d'[`row',`column']
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mat `drow' = nullmat(`drow') , `dtemp'
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}
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mat `vbtemp' = `varb'[`row',`column']
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mat `vbrow' = nullmat(`vbrow') , `vbtemp'
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local i3 = `i3' + 1
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}
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if (`i2'<`numcats'-1) { mat `d`i'' = nullmat(`d`i'') \ `drow' }
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mat `vb`i'' = nullmat(`vb`i'') \ `vbrow'
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mat `bstemp' = `bstar'[`row', 1]
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mat `bstar`i'' = nullmat(`bstar`i'') \ `bstemp'
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local i2 = `i2' + 1
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}
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local i = `i' + 1
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}
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*** wald test for each independent variable
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tempname waldiv
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local i = 1
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while `i' <= `nrhs' {
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tempname DB DBp iDvBDp step1 step2
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mat `DB' = `d`i'' * `bstar`i''
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mat `DBp' = `DB''
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mat `step1' = `d`i''*`vb`i''
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mat `step2' = `step1' * (`d`i''')
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mat `iDvBDp' = inv(`step2')
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tempname step1 wald`i'
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mat `step1' = `DBp' * `iDvBDp'
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mat `wald`i'' = `step1' * `DB'
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mat `waldiv' = nullmat(`waldiv') \ `wald`i''
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local i = `i' + 1
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}
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if "`detail'"!="" {
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di _n in gr "Estimated coefficients from j-1 binary regressions"
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mat list `bout', noheader
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}
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di _n in g "Brant Test of Parallel Regression Assumption"
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di _n `smcl' in g " Variable `vline' chi2 p>chi2 df"
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di `smcl' _dup(13) in g "`dash'" "`plussgn'" _dup(26) in g "`dash'"
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di `smcl' in g " All `vline'" in y /*
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*/ %10.2f `waldout' %9.3f `pout' %6.0f `dfout'
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di `smcl' _dup(13) in g "`dash'" "`plussgn'" _dup(26) in g "`dash'"
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* calculate p for individual wald tests
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mat `pvals' = J(`nrhs', 1, 0)
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local i = 1
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local df = `numcats'-2
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while `i' <= `nrhs' {
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sca `ivchi' = `waldiv'[`i',1]
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if `ivchi' >= 0 {
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mat `pvals'[`i',1] = chiprob(`df',`ivchi')
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}
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if `ivchi' < 0 {
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mat `pvals'[`i',1] = -999
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}
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local vnm : word `i' of `rhsnms'
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*added for stata 7 compatibility
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local printnm "`vnm'"
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if "`vers7'"=="yes" { local printnm = abbrev("`printnm'", 12) }
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di `smcl' in g %12s "`printnm'" _col(14) "`vline'" in y /*
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*/ %10.2f `ivchi' %9.3f `pvals'[`i',1] %6.0f `df'
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local i = `i' + 1
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}
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di `smcl' _dup(13) in g "`dash'" "`bottomt'" _dup(26) in g "`dash'"
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di _n in g /*
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*/ "A significant test statistic provides evidence that the parallel"
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di in g "regression assumption has been violated."
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mat `ivout' = `waldiv', `pvals'
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mat rownames `ivout' = `rhsnms'
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mat colnames `ivout' = chi2 p>chi2
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estimates unhold `ologit'
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return scalar chi2 = `waldout'
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return scalar p = `pout'
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return scalar df = `dfout'
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return matrix ivtests `ivout'
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end
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