*! v.2.0.2 Confirmatory factor analysis, by Stas Kolenikov, skolenik at gmail dot com, 08 Sep 2009 program define confa, eclass properties( svyr svyb svyj ) sortpreserve version 10.0 if replay() { if ("`e(cmd)'" != "confa") error 301 Replay `0' } else { Estimate `0' } end program define Estimate, eclass properties( svyr svyb svyj ) syntax anything [if] [in] [aw pw iw/ ], [ /// UNITvar(str) /// provides the list of factors where unit variance identification is used FREE /// estimate all parameters as free -- the user provides identification through constraints CONSTRaint(numlist) /// see the previous one FROM(str) /// starting values, compliant with -ml init- syntax LEVel(int $S_level) ROBust VCE(string) CLUster(passthru) /// standard errors and inference LOGLEVel(int 1) /// logging level CORRelated(string) /// correlated measurement errors SUBtractone /// subtract one from the sample size in places USENames /// MISSing /// allow for special treatment of missing data SVY * ] * preliminary work global CONFA_loglevel = `loglevel' cap bothlist a \ b, global( CONFA_t ) if _rc==199 { * listutil not installed di as err "listutil not found, trying to install from SSC..." ssc install listutil } if "`subtractone'"~="" local subtractone -1 *** MISSING tempvar touse marksample touse, zeroweight global CONFA_touse `touse' if $CONFA_loglevel > 2 tab $CONFA_touse * weights? if "`weight'" ~= "" { global CONFA_wgt [`weight'=`exp'] global CONFA_wgti [iw=`exp'] } * initial values? if "`from'"~="" { if "`from'" == "iv" | "`from'" == "IV" | "`from'" == "ivreg" | "`from'" == "2SLS" { if "`unitvar'" ~= "" { di as err "cannot specify from(`from') and unitvar at the same time" CleanIt exit 198 } else global CONFA_init IV } else if "`from'" == "ones" global CONFA_init ones else if "`from'" == "smart" global CONFA_init smart else { gettoken isitmat isitnot : from , parse(",") cap confirm matrix `isitmat' if _rc { di "{err}Warning: matrix `isitmat' not found" * do something sensible instead global CONFA_init smart } else { * do nothing --- let the hell break loose global CONFA_init } } } * vce? if "`vce'" ~= "" { gettoken vce1 rest : vce, parse(" ,") CheckVCE , `vce1' local lvce = length("`vce'") if `"`vce'"' != substr("sbentler", 1, max(2, `lvce')) /// & `"`vce'"' != substr("satorrabentler", 1, max(3, `lvce')) { local vceopt vce(`vce') } } if $CONFA_loglevel > 2 di as text "Parsing..." cap noi Parse `anything' if _rc { CleanIt exit 198 } * copy everything down -- -ivreg- cleans -sreturn- local obsvar=s(obsvar) global CONFA_obsvar `obsvar' local nobsvar : word count `obsvar' local nfactors = s(nfactors) forvalues k=1/`nfactors' { local indicators`k' = s(indicators`k') local name`k' = s(name`k') local factorlist `factorlist' `name`k'' } * begin collecting the equations, starting values, bounds, and model structure if $CONFA_loglevel > 2 di as text "Setting the structure up..." Structure, unitvar(`unitvar') correlated(`correlated') `usenames' local nicecorr $CONFA_t * produces a bunch of globals * did we need all this starting values business at all? gettoken isitmat isitnot : from , parse(",") cap confirm matrix `isitmat' if ~_rc | strpos("`from'",",") { * the user has provided the starting values global CONFA_start `from' } else { * not a matrix, no comma: use our ugly computations global CONFA_start $CONFA_start, copy } * if "$CONFA_bounds" ~= "" global CONFA_bounds bounds($CONFA_bounds) if $CONFA_loglevel > 3 di `" ml model lf confa_lf $CONFA_toML $CONFA_wgt, constraint($CONFA_constr `constraint') `svy' `robust' `cluster' init($CONFA_start) bounds($CONFA_bounds) `options' maximize"' tempvar misspat touse1 global CONFA_miss `misspat' qui gen byte `touse1' = 1-$CONFA_touse if "`missing'" != "" { if $CONFA_loglevel > 1 di "{txt}Working on missing values..." * cycle over the observed variables, create missing indicators forvalues k=1/`nobsvar' { local thisvar : word `k' of `obsvar' tempvar miss`k' qui gen byte `miss`k'' = mi( `thisvar' ) if $CONFA_touse local misslist `misslist' `miss`k'' } * sort by pattern: relevant observations first * when $CONFA_touse==0 `misslist' will be missing qui { bysort `touse1' `misslist' : gen long $CONFA_miss = (_n==1) replace $CONFA_miss = sum( $CONFA_miss ) replace $CONFA_miss = . if mi( $CONFA_touse ) } cap assert $CONFA_miss == 1 if $CONFA_touse local anymissing = _rc if !`anymissing' { di "{txt}Option missing specified, but no missing data found" } else { qui tab $CONFA_miss di _n "{txt}Note: {res}" r(r) "{txt} patterns of missing data found" } if $CONFA_loglevel > 3 li $CONFA_miss `misslist' } * if "`anymissing'"=="0" | "`missing'" == "" { else { * -missing- option is omitted if $CONFA_loglevel > 1 di "{err}NOT {txt}working on missing values" markout $CONFA_touse `obsvar' qui gen byte $CONFA_miss = 1 if $CONFA_touse if $CONFA_loglevel > 2 { sum `obsvar' if $CONFA_touse tab $CONFA_miss, missing } } cap noi ml model lf confa_lfm $CONFA_toML $CONFA_wgt if $CONFA_touse, /// constraint($CONFA_constr `constraint') `svy' `robust' `cluster' `vceopt' /// init($CONFA_start) bounds($CONFA_bounds) `options' `missing' /// maximize local mlrc = _rc if `mlrc' { CleanIt error `mlrc' } * parametric matrices tempname bb mat `bb' = e(b) global CONFA_loglevel -1 * to indicate to CONFA_StrucToSigma() that the matrices should be posted to Stata qui mata : CONFA_StrucToSigma(st_matrix("`bb'")) global CONFA_loglevel `loglevel' * now, post all those matrices to ereturn mat rownames CONFA_Sigma = `obsvar' mat colnames CONFA_Sigma = `obsvar' mat rownames CONFA_Lambda = `obsvar' mat colnames CONFA_Lambda = `factorlist' mat rownames CONFA_Phi = `factorlist' mat colnames CONFA_Phi = `factorlist' mat colnames CONFA_Theta = `obsvar' mat rownames CONFA_Theta = `obsvar' ereturn matrix Sigma = CONFA_Sigma, copy ereturn matrix Lambda = CONFA_Lambda, copy ereturn matrix Phi = CONFA_Phi, copy ereturn matrix Theta = CONFA_Theta, copy if "`missing'"!= "" ereturn local missing missing eret local observed `obsvar' eret local factors `factorlist' if "`unitvar'" ~= "" { * need to unwrap the contents of `unitvar'... * or change its defintion from passthru to string if "`unitvar'" == "_all" eret local unitvar `factorlist' else eret local unitvar `unitvar' } forvalues k=1/`nfactors' { eret local factor`k' `name`k'' : `indicators`k'' } if "`correlated'"!="" eret local correlated `nicecorr' if "`svy'`cluster'`exp'`robust'" == "" & "`vce'"!="robust" & substr("`vce'",1,2)!="cl" & "`missing'"=="" { * if the data are not i.i.d., LRT is not applicable * don't know what to do with missing data tempname S Sindep trind qui mat accum `S' = `obsvar' $CONFA_wgti if $CONFA_touse, dev nocons mat `S' = `S' / ( e(N) `subtractone' ) mat `Sindep' = diag(vecdiag(`S')) * degrees of freedom local nconstr = `: word count $CONFA_constr' + `: word count `constraint'' local pstar = `nobsvar' * (`nobsvar' + 1) / 2 local df_m = rowsof(CONFA_Struc) - `nobsvar' - `nconstr' ereturn scalar pstar = `pstar' * test against independence mat `trind' = trace( syminv(`Sindep') * `S' ) local trind = `trind'[1,1] ereturn scalar ll_indep = -0.5 * `nobsvar' * e(N) * ln(2*_pi) - 0.5 * e(N) * ln(det(`Sindep')) - 0.5 * e(N) * `trind' ereturn scalar lr_indep = 2*(e(ll)-e(ll_indep)) ereturn scalar df_indep = `pstar' - `nobsvar' ereturn scalar p_indep = chi2tail(e(df_indep),e(lr_indep)) * goodness of fit test ereturn scalar ll_0 = -0.5 * `nobsvar' * e(N) * ln(2*_pi) - 0.5 * e(N) * ln(det(`S')) - 0.5 * `nobsvar' * e(N) ereturn scalar df_u = `pstar' - `df_m' ereturn scalar lr_u = cond(e(df_u)==0,0,-2*(e(ll)-e(ll_0))) ereturn scalar p_u = chi2tail(e(df_u),e(lr_u)) * make the g.o.f. test the default test ereturn scalar df_m = `df_m' ereturn local chi2type LR ereturn scalar chi2 = e(lr_u) ereturn scalar p = e(p_u) * other crap ereturn matrix S = `S' if `"`vce'"'==substr("satorrabentler",1,max(3, length("`vce'"))) /// | "`vce'" ==substr("sbentler",1,max(4, length("`vce'"))) { * repost Satorra-Bentler covariance matrix * not defined for complex survey data, cap noi SatorraBentler, constraint(`constraint') `missing' if _rc { di as err "Satorra-Bentler standard errors are not supported; revert to vce(oim)" } else { tempname SBVar SBV Delta Gamma VV U trUG2 Tdf mat `SBVar' = r(SBVar) mat `Delta' = r(Delta) mat `Gamma' = r(Gamma) mat `SBV' = r(SBV) mat `VV' = e(V) mat `SBVar' = ( `VV'[1..`nobsvar',1..`nobsvar'], `VV'[1..`nobsvar',`nobsvar'+1 ...] /// \ `VV'[`nobsvar'+1...,1..`nobsvar'], `SBVar'[`nobsvar'+1...,`nobsvar'+1...] ) ereturn repost V = `SBVar' ereturn matrix SBGamma = `Gamma', copy ereturn matrix SBDelta = `Delta', copy ereturn matrix SBV = `SBV', copy ereturn local vce SatorraBentler ereturn local vcetype "Satorra-Bentler" * compute the corrected tests, too * only takes care of the covariance structure * Satorra-Bentler 1994 mat `U' = `SBV' - `SBV'*`Delta'*syminv(`Delta''*`SBV'*`Delta')*`Delta''*`SBV' ereturn matrix SBU = `U' mat `U' = trace( e(SBU)*e(SBGamma) ) ereturn scalar SBc = `U'[1,1]/e(df_u) ereturn scalar Tsc = e(lr_u)/e(SBc) * (e(N) `subtractone' ) / e(N) ereturn scalar p_Tsc = chi2tail( e(df_u), e(Tsc) ) mat `trUG2' = trace( e(SBU)*`Gamma'*e(SBU)*`Gamma') ereturn scalar SBd = `U'[1,1]*`U'[1,1]/`trUG2'[1,1] ereturn scalar Tadj = ( e(SBd)/`U'[1,1]) * e(lr_u) * (e(N) `subtractone' ) / e(N) ereturn scalar p_Tadj = chi2tail( e(SBd), e(Tadj) ) * saddlepoint approximation comes here!!! * Yuan-Bentler 1997 ereturn scalar T2 = e(lr_u)/(1+e(lr_u)/e(N) ) ereturn scalar p_T2 = chi2tail( e(df_u), e(T2) ) } } } * are we done yet? ereturn matrix CONFA_Struc = CONFA_Struc ereturn local predict confa_p ereturn local estat_cmd confa_estat ereturn local cmd confa Replay CleanIt end program define CleanIt * just in case return clear * release the constraints constr drop $CONFA_constr * clear the globals if $CONFA_loglevel < 3 { global CONFA_constr global CONFA_init global CONFA_loglevel global CONFA_toML global CONFA_start global CONFA_bounds global CONFA_args global CONFA_constr global CONFA_obsvar global CONFA_t global CONFA_wgt global CONFA_wgti } end program define Parse, sclass * number of factors? local input `0' mata: st_local("nfactors",strofreal(CONFA_NF(`"`input'"'))) if `nfactors' == 0 { * something terrible happened di as err "incorrect factor specification" exit 198 } sreturn local nfactors = `nfactors' tokenize `input', parse("()") local k = 0 while "`1'"~="" { * right now, `1' should contain an opening bracket if "`1'"~="(" { * the first character is not a "(" di as err "incorrect factor specification" exit 198 } else { * the first character IS a "(" mac shift * right now, `1' should contain a factor-type statement local ++k local factor`k' `1' mac shift * right now, `1' should contain a closing bracket if "`1'"~=")" { * the first character is not a ")" di as err "incorrect factor specification" exit 198 } else mac shift * it may contain a space, I guess * then -mac shift- it again if trim("`1'")=="" mac shift } } forvalues k=1/`nfactors' { * now, parse each factor statement tokenize `factor`k'', parse(":") sreturn local name`k' `1' * `2' is the colon unab indicators : `3' sreturn local indicators`k' `indicators' local obsvar `obsvar' `indicators' } cap uniqlist `obsvar' if _rc == 199 { * uniqlist not found di as err "uniqlist not found, trying to install from SSC..." ssc install listutil uniqlist `obsvar' } local obsvar = r(list) * mata: st_local("obsvar",CONFA_UL(`"`obsvar'"')) sreturn local obsvar `obsvar' sreturn local nobsvar = `: word count `obsvar'' end program define Structure syntax , [unitvar(str) correlated(str) usenames] * implement usenames: * the parameters go along with the factor and variable names * rather than matrix indices * utilize all the sreturn results if $CONFA_loglevel > 3 sreturn list * copy everything down -- -ivreg- cleans -sreturn- local obsvar=s(obsvar) local nobsvar : word count `obsvar' local nfactors = s(nfactors) forvalues k=1/`nfactors' { local indicators`k' = s(indicators`k') local name`k' = s(name`k') local factorlist `factorlist' `name`k'' } if "`unitvar'" == "_all" { local unitvar `factorlist' } * set up the labeling system if "`usenames'" != "" { * give the parameters varname labels forvalues k=1/`nobsvar' { local o`k' : word `k' of `obsvar' } forvalues k=1/`nfactors' { local f`k' `name`k'' } } else { * give the parameters numberic lables forvalues k=1/`nobsvar' { local o`k' `k' } forvalues k=1/`nfactors' { local f`k' `k' } } * returns: * - ML equations * - ML bounds * - the structure matrix * - ML statement for the likelihood evaluator * initialize everything local eqno = 0 global CONFA_toML global CONFA_start global CONFA_args global CONFA_constr global CONFA_bounds mata : CONFA_Struc = J(0,4,.) * process the means first tokenize `obsvar' forvalues j=1/`nobsvar' { * 1. equations to ML local ++eqno global CONFA_toML $CONFA_toML (mean_`o`j'':) * 2. starting values sum ``j'', mean global CONFA_start $CONFA_start `r(mean)' * 3. confa_lf arguments global CONFA_args $CONFA_args mean_`o`j'' * 4. CONFA structure mata : CONFA_Struc = CONFA_Struc \ (1, `eqno', `j', 0) } * next, process lambda's forvalues k=1/`nfactors' { * determine if unitvar is needed here bothlist `name`k'' \ `unitvar', global(CONFA_t) if "$CONFA_t" ~= "" { * identification by unit variance, no scaling variables local scalevar } else { * identification by the scaling variable: the 1st one on the list local scalevar : word 1 of `indicators`k'' } forvalues j=1/`nobsvar' { * determine whether `k'-th factor loads on `j'-th variable if strpos( "`indicators`k''", "``j''") { * 1. equations to ML local ++eqno global CONFA_toML $CONFA_toML (lambda_`o`j''_`f`k'':) * 2. starting values local r2_`j' = 0.5 if "``j''" == "`scalevar'" { * the current one is the scaling variable * set up the constraints, initialize to 1 global CONFA_start $CONFA_start 1 constraint free local nconstr = r(free) constraint `nconstr' [lambda_`o`j''_`f`k'']_cons = 1 global CONFA_constr $CONFA_constr `nconstr' } else if "$CONFA_init" == "IV" { * initialize by a simple version of instrumental variables * use the remaining indicators of this factor as instruments dellist `indicators`k'', delete(`scalevar' ``j'') local ivlist = r(list) if "`ivlist'" == "." { di as err "Warning: no instruments available for ``j''" local ivl = 1 } else { qui ivreg ``j'' (`scalevar' = `ivlist') local ivl = _b[`scalevar'] } global CONFA_start $CONFA_start `ivl' if !mi(e(r2)) local r2_`j' = e(r2) } else if "$CONFA_init" == "ones" { global CONFA_start $CONFA_start 1 } else { * no init options global CONFA_start $CONFA_start 0 } global CONFA_bounds $CONFA_bounds /lambda_`o`j''_`f`k'' -100 100 * 3. confa_lf arguments global CONFA_args $CONFA_args lambda_`o`j''_`f`k'' * 4. CONFA structure mata : CONFA_Struc = CONFA_Struc \ (2, `eqno', `j', `k') } } } * next, process Phi matrix forvalues k=1/`nfactors' { local scalevar1 : word 1 of `indicators`k'' foreach kk of numlist `k'/1 { * 1. equations to ML local ++eqno global CONFA_toML $CONFA_toML (phi_`f`kk''_`f`k'':) * 2. starting values if `k' == `kk' { * diagonal entry bothlist `name`k'' \ `unitvar', global(CONFA_t) if "$CONFA_t" ~= "" { * identification by unit variance constraint free local nconstr = r(free) constraint `nconstr' [phi_`f`k''_`f`k'']_cons = 1 global CONFA_constr $CONFA_constr `nconstr' local v`k' = 1 } else { * identification by the scaling variable if "$CONFA_init" == "smart" | "$CONFA_init" == "IV" { qui sum `scalevar1' local v`k' = r(Var)*0.5 } else if "$CONFA_init" == "ones" local v`k' = 1 else local v`k' = 0 } global CONFA_start $CONFA_start `v`k'' global CONFA_bounds $CONFA_bounds /phi_`f`k''_`f`kk'' 0 1000 } else { * off-diagonal entry if "$CONFA_init" == "smart" | "$CONFA_init" == "IV" { local scalevar2 : word 1 of `indicators`kk'' qui corr `scalevar1' `scalevar2' local v = 0.5*r(rho)*sqrt(`v`k''*`v`kk'') } else if "$CONFA_init" == "ones" local v = 0.5 else local v = 0 local vv = 1.5*abs(`v') + 0.01 global CONFA_start $CONFA_start `v' global CONFA_bounds $CONFA_bounds /phi_`f`kk''_`f`k'' -`vv' `vv' } * 3. confa_lf arguments global CONFA_args $CONFA_args phi_`f`kk''_`f`k'' * 4. CONFA structure mata : CONFA_Struc = CONFA_Struc \ (3, `eqno', `kk', `k') } } * residual variances forvalues j=1/`nobsvar' { * 1. equations to ML local ++eqno global CONFA_toML $CONFA_toML (theta_`o`j'':) * 2. starting values if "$CONFA_init" == "ones" { local v_`j' = 1 } else if "$CONFA_init" == "IV" | "$CONFA_init" == "smart" { qui sum ``j'' local v_`j' = r(Var)*(1-`r2_`j'') } else local v_`j' = 0.01 global CONFA_start $CONFA_start `v_`j'' global CONFA_bounds $CONFA_bounds /theta_`o`j'' 0 1000 * 3. confa_lf arguments global CONFA_args $CONFA_args theta_`o`j'' * 4. CONFA structure mata : CONFA_Struc = CONFA_Struc \ (4, `eqno', `j', 0) } * the error correlations while "`correlated'" != "" { gettoken corrpair correlated : correlated , match(m) gettoken corr1 corrpair : corrpair, parse(":") unab corr1 : `corr1' gettoken sc corr2 : corrpair, parse(":") unab corr2 : `corr2' * make sure both are present in the list of observed variables poslist `obsvar' \ `corr1', global(CONFA_t) local k1 = $CONFA_t if `k1' == 0 { di as err "`corr1' is not among the observed variables" CleanIt exit 198 } poslist `obsvar' \ `corr2', global(CONFA_t) local k2 = $CONFA_t if `k2' == 0 { di as err "`corr2' is not among the observed variables" CleanIt exit 198 } * will be empty @ the first call local nicecorr `nicecorr' (`corr1':`corr2') * 1. equations to ML local ++eqno global CONFA_toML $CONFA_toML (theta_`o`k1''_`o`k2'':) * 2. starting values global CONFA_start $CONFA_start 0 local vv = sqrt(`v_`k1''*`v_`k2'') global CONFA_bounds $CONFA_bounds /theta_`o`k1''_`o`k2'' -`vv' `vv' * 3. confa_lf arguments global CONFA_args $CONFA_args theta_`o`k1''_`o`k2'' * 4. CONFA structure mata : CONFA_Struc = CONFA_Struc \ (5, `eqno', `k1', `k2') } if "`nicecorr'"!="" global CONFA_t `nicecorr' if $CONFA_loglevel > 3 { di as text "ML input (" as res `: word count $CONFA_toML' as text "): " as res "$CONFA_toML" di as text "Starting values (" as res `: word count $CONFA_start' as text "): " as res "$CONFA_start" di as text "Likelihood evaluator (" as res `: word count $CONFA_args' as text"): " as res "$CONFA_args" di as text "Constraints (" as res `nfactors' as text "): " as res "$CONFA_constr" di as text "Correlated errors: " as res "`nicecorr'" constraint dir $CONFA_constr mata : CONFA_Struc } mata : st_matrix("CONFA_Struc",CONFA_Struc) end program define Replay syntax, [posvar llu(str) level(passthru)] * get the implied matrix tempname bb Sigma mat `bb' = e(b) * mata : st_matrix("Sigma",CONFA_StrucToSigma(st_matrix("`bb'"))) mat `Sigma' = e(Sigma) mat CONFA_Struc = e(CONFA_Struc) * determine what kind of labeling has been used * RATHER FRAGILE: checking for mean_1 rather than trying to find * whether option usenames was specified cap local whatis = [mean_1]_cons if _rc { * mean_1 not found => labeling by names forvalues k=1/`: word count `e(observed)' ' { local o`k' : word `k' of `e(observed)' } forvalues k=1/`: word count `e(factors)' ' { local f`k' : word `k' of `e(factors)' } } else { * mean_1 was found => labeling by numbers forvalues k=1/`: word count `e(observed)' ' { local o`k' `k' } forvalues k=1/`: word count `e(factors)' ' { local f`k' `k' } } * header di _n as text "`e(crittype)' = " as res e(ll) _col(59) as text "Number of obs = " as res e(N) di as text "{hline 13}{c TT}{hline 64}" if "`e(vcetype)'" ~= "" { di as text " {c |} {center 15:`e(vcetype)'}" } di as text " {c |} Coef. Std. Err. z P>|z| [$S_level% Conf. Interval]" di as text "{hline 13}{c +}{hline 64}" tokenize `e(observed)' local nobsvar : word count `e(observed)' * let's go equation by equation local eqno = 0 * Means _diparm __lab__, label("Means") eqlabel forvalues j = 1/`nobsvar' { local ++eqno _diparm mean_`o`j'' , label("``j''") prob `level' } * Loadings _diparm __lab__, label("Loadings") eqlabel local ++eqno // to point to the next line forvalues k=1/`: word count `e(factors)' ' { _diparm __lab__ , label("`: word `k' of `e(factors)' '") while CONFA_Struc[`eqno',1]<=2 & CONFA_Struc[`eqno',4]==`k' { local j = CONFA_Struc[`eqno',3] _diparm lambda_`o`j''_`f`k'', label("``j''") prob `level' local ++eqno } } * Factor covariance _diparm __lab__, label("Factor cov.") eqlabel forvalues k=1/`: word count `e(factors)'' { foreach kk of numlist `k'/1 { _diparm phi_`f`kk''_`f`k'', label("`: word `kk' of `e(factors)''-`: word `k' of `e(factors)''") prob `level' local ++eqno } } * Error variances _diparm __lab__, label("Var[error]") eqlabel forvalues j= 1/`nobsvar' { _diparm theta_`o`j'' , label("``j''") prob `level' local ++eqno } * Error correlations if `eqno' <= rowsof(CONFA_Struc) & CONFA_Struc[`eqno',1] == 5 { _diparm __lab__, label("Cov[error]") eqlabel while (`eqno' <= rowsof(CONFA_Struc) & CONFA_Struc[`eqno',1] == 5) { local k1 = CONFA_Struc[`eqno',3] local k2 = CONFA_Struc[`eqno',4] _diparm theta_`o`k1''_`o`k2'', label("``k1''-``k2''") prob `level' * range check: what am I supposed to check here? Hm... local ++eqno } } if "`e(vcetype)'"~="Robust" & "`e(missing)'"=="" { di as text "{hline 13}{c +}{hline 64}" di as text "R2{col 14}{c |}" forvalues j = 1/`nobsvar' { qui sum ``j'' if e(sample) local r2 = (`Sigma'[`j',`j']-_b[theta_`o`j'':_cons])/r(Var) di as text %12s "``j''" "{col 14}{c |}{col 20}" as res %6.4f `r2' } } di as text "{hline 13}{c BT}{hline 64}" if e(df_u)>0 { di as text _n "Goodness of fit test: LR = " as res %6.3f e(lr_u) /// as text _col(40) "; Prob[chi2(" as res %2.0f e(df_u) as text ") > LR] = " as res %6.4f e(p_u) } else { di as text "No degrees of freedom to perform the goodness of fit test" } di as text "Test vs independence: LR = " as res %6.3f e(lr_indep) /// as text _col(40) "; Prob[chi2(" as res %2.0f e(df_indep) as text ") > LR] = " as res %6.4f e(p_indep) if "`e(vce)'" == "SatorraBentler" & e(df_u)>0 { * need to report all those corrected statistics di as text _n "Satorra-Bentler Tsc" _col(26) "= " as res %6.3f e(Tsc) /// as text _col(40) "; Prob[chi2(" as res %2.0f e(df_u) as text ") > Tsc ] = " as res %6.4f e(p_Tsc) di as text "Satorra-Bentler Tadj" _col(26) "= " as res %6.3f e(Tadj) /// as text _col(40) "; Prob[chi2(" as res %4.1f e(SBd) as text ") > Tadj] = " as res %6.4f e(p_Tadj) di as text "Yuan-Bentler T2" _col(26) "= " as res %6.3f e(T2) /// as text _col(40) "; Prob[chi2(" as res %2.0f e(df_u) as text ") > T2 ] = " as res %6.4f e(p_T2) } if "`e(vce)'" == "BollenStine" { * need to report Bollen-Stine measures di as text _n "Bollen-Stine simulated Prob[ LR > " as res %6.4f e(lr_u) as text " ] = " as res %6.4f e(p_u_BS) /// as text _n "Based on " as res e(B_BS) as text " replications. " /// as text "The bootstrap 90% interval: (" as res %6.3f e(T_BS_05) as text "," /// as res %6.3f e(T_BS_95) as text ")" } mat drop CONFA_Struc end **************************** Satorra-Bentler covariance matrix code program SatorraBentler, rclass syntax [, noisily constraint(numlist) missing] if "`missing'"!="" { di "{err}cannot specify Satorra-Bentler standard errors with missing data" exit 198 } * assume the maximization completed, the results are in memory as -ereturn data- * we shall just return the resulting matrix * assume sample is restricted to e(sample) * preserve * keep if e(sample) * get the variable names tempname VV bb mat `bb' = e(b) mat `VV' = e(V) local p : word count $CONFA_obsvar qui count if $CONFA_touse local NN = r(N) * compute the implied covariance matrix tempname Lambda Theta Phi Sigma mata : st_matrix("`Sigma'",CONFA_StrucToSigma(st_matrix("`bb'"))) * compute the empirical cov matrix tempname SampleCov qui mat accum `SampleCov' = $CONFA_obsvar $CONFA_wgti if $CONFA_touse , nocons dev * divide by sum of weights instead??? mat `SampleCov' = `SampleCov' / (`NN'-1) * compute the matrix Gamma (fourth moments) if $CONFA_loglevel > 4 { di as text "Computing the Gamma matrix of fourth moments..." } tempname Gamma SBGamma $CONFA_obsvar if $CONFA_touse mat `Gamma' = r(Gamma) return add * compute the V matrix, the normal theory weight if $CONFA_loglevel > 4 { di as text "Computing the V matrix..." } SBV `SampleCov' `noisily' if !mi(r(needmatsize)) { di as err "matsize too small; need at least " r(needmatsize) exit 908 } tempname V mat `V' = r(SBV) return add * compute the Delta matrix if $CONFA_loglevel > 4 { di as text "Computing the Delta matrix..." } tempname Delta DeltaId noi mata : SBStrucToDelta("`Delta'") *** put the pieces together now * enact the constraints! SBconstr `bb', constraint(`constraint') * zero out the rows of Delta that correspond to fixed parameters mat `DeltaId' = `Delta' * diag( r(Fixed) ) local dcnames : colfullnames `bb' local drnames : rownames `Gamma' mat colnames `DeltaId' = `dcnames' mat rownames `DeltaId' = `drnames' return matrix Delta = `DeltaId', copy tempname VVV mat `VVV' = ( `DeltaId'' * `V' * `DeltaId' ) mat `VVV' = syminv(`VVV') mat `VVV' = `VVV' * ( `DeltaId'' * `V' * `Gamma' * `V' * `DeltaId' ) * `VVV'/`NN' * add the covariance matrix for the means, which is just Sigma/_N * weights! * third moments! return matrix SBVar = `VVV' end * of satorrabentler * Compute Gamma: the fourth moments matrix -- check! program define SBGamma, rclass syntax varlist [if] [in] unab varlist : `varlist' tokenize `varlist' marksample touse local p: word count `varlist' forvalues k=1/`p' { * make up the deviations; weights are used in a weird way *** MISSING: change r(mean) to _b[whatever] ? qui sum ``k'' $CONFA_wgti if `touse', meanonly tempvar d`k' qui g double `d`k'' = ``k'' - r(mean) if `touse' local dlist `dlist' `d`k'' } local pstar = `p'*(`p'+1)/2 forvalues k=1/`pstar' { tempvar b`k' qui g double `b`k'' = . local blist `blist' `b`k'' } * convert into vech (z_i-bar z)(z_i-bar z)' mata : SBvechZZtoB("`dlist'","`blist'") * blist now should contain the moments around the sample means * we need to get their covariance matrix tempname Gamma qui mat accum `Gamma' = `blist' $CONFA_wgti if `touse', dev nocons mat `Gamma' = `Gamma'/(r(N)-1) mata : Gamma = st_matrix( "`Gamma'" ) * make nice row and column names forvalues i=1/`p' { forvalues j=`i'/`p' { local namelist `namelist' ``i''_X_``j'' } } mat colnames `Gamma' = `namelist' mat rownames `Gamma' = `namelist' return matrix Gamma = `Gamma' end * of computing Gamma * compute V = 1/2 D' (Sigma \otimes Sigma) D * normal theory weight matrix, see Satorra (1992), eq (24) -- check! program define SBV, rclass args A noisily tempname D Ainv V local p = rowsof(`A') if $CONFA_loglevel > 3 di as text "Computing the duplication matrix..." mata : Dupl(`p',"`D'") mat `Ainv' = syminv(`A') cap mat `V' = .5*`D''* (`Ainv' # `Ainv') * `D' if _rc == 908 { * need a larger matrix return scalar needmatsize = rowsof(`A')*rowsof(`A') } else { return matrix SBV = `V' } end * of computing V program define SBconstr, rclass * need to figure out whether a constraint has the form [parameter]_cons = value, * and to nullify the corresponding column syntax anything, [constraint(numlist)] local bb `anything' * that's the name of the parameter vector, a copy of e(b) tempname Iq mat `Iq' = J(1,colsof(`bb'),1) tokenize $CONFA_constr `constraint' while "`1'" ~= "" { constraint get `1' local constr `r(contents)' gettoken param value : constr, parse("=") * is the RHS indeed a number? local value = substr("`value'",2,.) confirm number `value' * parse the square brackets and turn them into colon * replace the opening brackets with nothing, and closing brackets, with colon * that way, we will get "parameter:_cons", which is the format of e(b) labels local param = subinstr("`param'","["," ",1) local param = subinstr("`param'","]",":",1) local param = trim("`param'") local coln = colnumb(`bb',"`param'" ) mat `Iq'[1,`coln']=0 mac shift } return matrix Fixed = `Iq' end program define CheckVCE syntax [anything] , [ROBust CLuster oim opg SBentler SATorrabentler BOOTstrap JACKknife] if "`bootstrap'" ~= "" { di "{err}vce(bootstrap) not allowed, but you can run {inp}bootstrap ... : confa ... {err}instead." CleanIt exit 198 } if "`jackknife'" ~= "" { di "{err}vce(jackknife) not allowed, but you can run {inp}jackknife ... : confa ... {err}instead." CleanIt exit 198 } end exit if "$SOCST" == "c:\-socialstat" { // at home, run the Mata file do C:\-Mizzou\CONFA\confa.mata } else { // for public release, add Mata code mata : mata mlib index } Globals used: CONFA_init -- initialization type CONFA_loglevel -- detail level CONFA_toML -- model statement for -ml model- CONFA_start -- default starting values CONFA_bounds -- ml search bounds CONFA_args -- the list of parameters, to appear in -confa_lf- CONFA_constr -- the list of constraints CONFA_obsvar -- the list of observed variables CONFA_wgt -- weight specification CONFA_wgti -- iweight CONFA_t -- temporary global for -listutil- Structure matrix: CONFA_Struc -- the model structure: (parameter type, equation number, index1, index2) History: v.1.0 -- Jan 09, 2008 -- basic formulation without -cluster-, -robust-, -weights-, -svy- v.1.1 -- Mar 21, 2008 -- Satorra-Bentler? v.1.2 -- Sep 16, 2008 -- Ken Higbee comments v.1.5 -- usenames -- Mata moved to lconfa.mlib -- survey-compatible v.1.6 -- listwise deletion for missing data -- what kind of idiot should Stas be to not pay attention to this??? -- informative message about matsize in Satorra-Bentler calculations v.2.0 -- FIML missing data -- prepared for revision in SJ v.2.0.1 -- fixed -if- in Satorra-Bentler calculations v.2.0.2 -- fixed reporting of correlations with -unitvar-: confa.ado, confa_estat.ado v.2.1 -- someday? -- Bartlett correction: (N - 1 - (2p+4m+5)/6) -- F-statistic in place of chi-square, both normal theory and S-B