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504 lines
15 KiB
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504 lines
15 KiB
Plaintext
7 months ago
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*! Mata definitions for confa package; 3 March 2009; v.2.0
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set matalnum on
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mata:
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mata set matastrict on
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mata clear
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//////////////////////////////////////////////
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// needed by confa.ado
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real CONFA_NF( string input ) {
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real scalar nopenpar, nclosepar, ncolon;
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// opening and closing parentheses
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nopenpar = length(tokens(input, ")" ))
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nclosepar = length(tokens(input, "(" ))
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// n*par will be 2*nf
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ncolon = length(tokens(input, ":" ))
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// ncolon will be 2*nf + 1
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if ( (nopenpar == nclosepar) & (nopenpar == ncolon-1 ) ) {
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if (mod(nopenpar,2) == 0) {
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return( nopenpar/2 )
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}
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}
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// if everything was OK, should've exited by now
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// if something's wrong, return zero
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return(0)
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}
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matrix CONFA_StrucToSigma(real vector parms) {
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real scalar CONFA_loglevel, nobsvar, nfactors, eqno;
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real matrix Lambda, Phi, Theta, Sigma, CONFA_Struc;
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// loglevel
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CONFA_loglevel = strtoreal( st_global("CONFA_loglevel"))
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CONFA_Struc = st_matrix("CONFA_Struc")
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if (CONFA_loglevel>4) CONFA_Struc
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if (CONFA_loglevel>4) {
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printf("{txt}Current parameter values:\n")
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parms
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}
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// the length should coinicde with the # pars from CONFA_Struc
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if ( cols(parms) ~= rows(CONFA_Struc) ) {
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// something's wrong, let's just drop out with an empty matrix
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if (CONFA_loglevel>4) {
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printf("{txt}Expected parameters: {res}%3.0f{txt}; received parameters: {res}%3.0f\n",
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rows(CONFA_Struc),cols(parms))
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}
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return(J(0,0,0))
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}
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// # observed variables: max entry in the number of means
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nobsvar = colmax( select(CONFA_Struc[,3], !(CONFA_Struc[,1]-J(rows(CONFA_Struc),1,1)) ) )
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if (CONFA_loglevel>4) printf("{txt}No. of observed variables: {res}%3.0f\n",nobsvar)
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// # observed factors: max entry in the phi indices
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nfactors = colmax( select(CONFA_Struc[,3], !(CONFA_Struc[,1]-J(rows(CONFA_Struc),1,3)) ) )
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if (CONFA_loglevel>4) printf("{txt}No. of latent factors: {res}%3.0f\n",nfactors)
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// set up the matrices
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Lambda = J(nobsvar,nfactors,0)
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Phi = J(nfactors,nfactors,0)
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Theta = J(nobsvar,nobsvar,0)
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// fill the stuff in
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for(eqno=nobsvar+1;eqno<=rows(CONFA_Struc);eqno++) {
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if (CONFA_Struc[eqno,1] == 2) {
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// a lambda-type entry
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Lambda[ CONFA_Struc[eqno,3], CONFA_Struc[eqno,4] ] = parms[eqno]
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}
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if (CONFA_Struc[eqno,1] == 3) {
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// a phi-type entry
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Phi[ CONFA_Struc[eqno,3], CONFA_Struc[eqno,4] ] = parms[eqno]
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Phi[ CONFA_Struc[eqno,4], CONFA_Struc[eqno,3] ] = parms[eqno]
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}
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if (CONFA_Struc[eqno,1] == 4) {
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// a theta-type entry
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Theta[ CONFA_Struc[eqno,3], CONFA_Struc[eqno,3] ] = parms[eqno]
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}
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if (CONFA_Struc[eqno,1] == 5) {
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// a theta-type correlated errors entry
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Theta[ CONFA_Struc[eqno,3], CONFA_Struc[eqno, 4] ] = parms[eqno]
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Theta[ CONFA_Struc[eqno,4], CONFA_Struc[eqno, 3] ] = parms[eqno]
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}
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}
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if (CONFA_loglevel > 4) {
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printf("{txt}Loadings:\n")
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Lambda
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printf("{txt}Factor covariances:\n")
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Phi
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printf("{txt}Residual variances:\n")
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Theta
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}
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Sigma = Lambda*Phi*Lambda' + Theta
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if (CONFA_loglevel > 4) {
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printf("{txt}Implied moments:\n")
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Sigma
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}
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if (CONFA_loglevel == -1) {
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// post matrices to Stata
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st_matrix("CONFA_Lambda",Lambda)
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st_matrix("CONFA_Phi",Phi)
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st_matrix("CONFA_Theta",Theta)
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st_matrix("CONFA_Sigma",Sigma)
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}
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// done with model structure, compute and return implied matrix
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return( Sigma )
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}
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// vech covariance matrix, for Satorra-Bentler
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void SBvechZZtoB(string dlist, string blist) {
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real matrix data, moments, B;
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real scalar i;
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// view the deviation variables
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st_view(data=.,.,tokens(dlist))
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// view the moment variables
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// blist=st_local("blist")
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st_view(moments=.,.,tokens(blist))
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// vectorize!
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for(i=1; i<=rows(data); i++) {
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B = data[i,.]'*data[i,.]
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moments[i,.] = vech(B)'
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}
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}
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// duplication matrix, for Satorra-Bentler
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void Dupl(scalar p, string Dname) {
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real scalar pstar, k;
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real matrix Ipstar, D;
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pstar = p*(p+1)/2
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Ipstar = I(pstar)
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D = J(p*p,0,.)
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for(k=1;k<=pstar;k++) {
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D = (D, vec(invvech(Ipstar[.,k])))
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}
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st_matrix(Dname,D)
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}
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// Satorra-Bentler Delta matrix
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// Delta = \frac \partial{\partial \theta} vech \Sigma(\theta)
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void SBStrucToDelta(string DeltaName) {
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real scalar CONFA_loglevel, p, t, varno, facno, i, j, k, fac1, fac2, k1, k2;
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// log level, # obs vars, # parameters, current var, current factor, cycle indices, temp indices
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real matrix Lambda, Phi, Theta, Sigma, CONFA_Struc, Delta, DeltaRow;
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// must be self-explanatory
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real matrix U, E;
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// identity matrices of the size #factors and #obs vars
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// loglevel
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CONFA_loglevel = strtoreal( st_global("CONFA_loglevel"))
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// need the CONFA matrices
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CONFA_Struc = st_matrix("CONFA_Struc")
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Sigma = st_matrix("CONFA_Sigma")
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Lambda = st_matrix("CONFA_Lambda")
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Phi = st_matrix("CONFA_Phi")
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// Theta = st_matrix("CONFA_Theta")
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if (CONFA_loglevel>4) CONFA_Struc
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// # parameters in the model
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t = rows(CONFA_Struc)
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// cols(Delta) = t = # pars
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// rows(Delta) = pstar = p*(p+1)/2 = length( vech( Sigma ) )
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// but that should be accumulated one by one...
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Delta = J(0,t,.)
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// sources of u and e vectors
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p = rows( Sigma )
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U = I( p )
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E = I( rows(Phi) )
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for(i=1;i<=p;i++) {
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for(j=i;j<=p;j++) {
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if (CONFA_loglevel > 4) printf("{txt}Working with pair ({res}%2.0f{txt},{res}%2.0f{txt})\n",i,j)
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DeltaRow = J(1,t,0)
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// parse Struc matrix and see how each parameter affects Cov(X_i,X_j)
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for(k=1;k<=t;k++) {
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if (CONFA_Struc[k,1] == 1) {
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// a mean-type entry
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// for the moment, assume it does not affect anything
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}
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if (CONFA_Struc[k,1] == 2) {
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// a lambda-type entry
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// CONFA_Struc[k,.] = (2, equation #, variable #, factor #)
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varno = CONFA_Struc[k,3]
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facno = CONFA_Struc[k,4]
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DeltaRow[1,k] = U[i,.] * U[.,varno] * E[facno,.] * Phi * Lambda' * U[.,j] +
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U[i,.] * Lambda * Phi * E[.,facno] * U[varno,.] * U[.,j]
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}
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if (CONFA_Struc[k,1] == 3) {
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// a phi-type entry
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// CONFA_Struc[k,.] = (3, equation #, `factor`kk'', `factor`k'')
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fac1 = CONFA_Struc[k,3]
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fac2 = CONFA_Struc[k,4]
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DeltaRow[1,k] = U[i,.] * Lambda * E[.,fac1] * E[fac2,.] * Lambda' * U[.,j]
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}
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if (CONFA_Struc[k,1] == 4) {
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// a theta-type entry
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// CONFA_Struc[k,.] = (4, equation #, variable #, 0)
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varno = CONFA_Struc[k,3]
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DeltaRow[1,k] = (i==j) & (i==varno)
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}
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if (CONFA_Struc[k,1] == 5) {
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// a theta_{jk}-type entry
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// CONFA_Struc[k,.] = (5, equation #, variable k1, variable k2)
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k1 = CONFA_Struc[k,3]
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k2 = CONFA_Struc[k,4]
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DeltaRow[1,k] = ((i==k1) & (j==k2) ) | ((i==k2) & (j==k1))
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}
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}
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Delta = Delta \ DeltaRow
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}
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}
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st_matrix(DeltaName,Delta)
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}
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///////////////////////////////////////////
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// needed by confa_p.ado
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void CONFA_P_EB(string Fnames, string ObsVarNames, string ToUseName) {
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real matrix ff, xx;
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// views
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real matrix bb, Sigma, Lambda, Theta, Phi;
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// substantive matrices
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real scalar p
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// view on the newly generated factors
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st_view(ff=.,.,tokens(Fnames),ToUseName)
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// view on the observed variables
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st_view(xx=.,.,tokens(ObsVarNames),ToUseName)
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// get the estimated matrices
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bb = st_matrix("e(b)")
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Sigma = st_matrix("e(Sigma)")
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Theta = st_matrix("e(Theta)")
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Lambda = st_matrix("e(Lambda)")
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Phi = st_matrix("e(Phi)")
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// # observed vars
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p = rows(Sigma)
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// prediction
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ff[,] = (xx-J(rows(xx),1,1)*bb[1..p]) * invsym(Sigma) * Lambda * Phi
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}
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void CONFA_P_MLE(string Fnames, string ObsVarNames, string ToUseName) {
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real matrix ff, xx;
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// views
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real matrix bb, Sigma, Lambda, Theta, Phi, ThetaInv;
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// substantive matrices
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real scalar p
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// view on the newly generated factors
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st_view(ff=.,.,tokens(Fnames),ToUseName)
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// view on the observed variables
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st_view(xx=.,.,tokens(ObsVarNames),ToUseName)
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// get the estimated matrices
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bb = st_matrix("e(b)")
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Sigma = st_matrix("e(Sigma)")
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Theta = st_matrix("e(Theta)")
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Lambda = st_matrix("e(Lambda)")
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Phi = st_matrix("e(Phi)")
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// # observed vars
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p = rows(Sigma)
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// Theta is the vector of diagonal elements,
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// so the inverse is easy!
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ThetaInv = diag( 1:/Theta )
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// prediction
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ff[,] = (xx-J(rows(xx),1,1)*bb[1..p]) * ThetaInv * Lambda * invsym(Lambda' * ThetaInv * Lambda)
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}
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//////////////////////////////////
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// needed by confa_lf.ado
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void CONFA_NormalLKHDr( string ParsName, string lnfname) {
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// ParsName are the parameters
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// lnfname is the name of the likelihood variable
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// the observed variables are in $CONFA_obsvar
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real scalar CONFA_loglevel, nobsvar, ldetWS, i;
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// log level, # obs vars, log determinant, cycle index
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real matrix Sigma, means, SS, InvWorkSigma;
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// intermediate computations
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string scalar obsvar, touse;
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// list of observed variables
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real matrix data, lnl, parms;
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// views
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CONFA_loglevel = strtoreal( st_global("CONFA_loglevel"))
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obsvar = st_global("CONFA_obsvar")
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nobsvar = length(tokens(obsvar))
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touse = st_global("CONFA_touse")
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st_view(data=., ., tokens(obsvar), touse )
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st_view(lnl=., ., tokens(lnfname), touse)
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st_view(parms=., ., tokens(ParsName), touse)
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// using the set up where the means are the first nobsvar entries of the parameter vector,
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means = parms[1,1..nobsvar]
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Sigma = CONFA_StrucToSigma(parms[1,.])
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if (CONFA_loglevel > 2) {
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parms[1,.]
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means
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Sigma
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}
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// do some equilibration??
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SS = cholesky(Sigma)
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InvWorkSigma = solvelower(SS,I(rows(SS)))
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InvWorkSigma = solveupper(SS',InvWorkSigma)
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ldetWS = 2*ln(dettriangular(SS))
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for( i=1; i<=rows(data); i++ ) {
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lnl[i,1] = -.5*(data[i,.]-means)*InvWorkSigma*(data[i,.]-means)' - .5*ldetWS - .5*nobsvar*ln(2*pi())
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}
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if (CONFA_loglevel>2) {
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sum(lnl)
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}
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}
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// normal likelihood with missing data
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void CONFA_NormalLKHDrMiss( string ParsName, string lnfname) {
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// ParsName are the parameters
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// lnfname is the name of the likelihood variable
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// the observed variables are in $CONFA_obsvar
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real scalar CONFA_loglevel, nobsvar, thisldetWS, i, j;
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// log level, # obs vars, log determinant, cycle index
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real matrix Sigma, means, thisSigma, thisSS, thisInvSigma, thispattern, parms;
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// intermediate computations
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string scalar obsvar, misspat, touse;
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// list of observed variables; the names of the missing patterns and touse tempvars
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real matrix data, lnl, parmview, pattern, mdata, mlnl, info;
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// views
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CONFA_loglevel = strtoreal( st_global("CONFA_loglevel"))
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obsvar = st_global("CONFA_obsvar")
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nobsvar = length(tokens(obsvar))
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misspat = st_global("CONFA_miss")
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touse = st_global("CONFA_touse")
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st_view(pattern=., ., misspat, touse )
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st_view(data=., ., tokens(obsvar), touse )
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st_view(lnl=., ., lnfname, touse )
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// STILL USING THE FIRST OBSERVATIONS TO GET THE PARAMETERS!!!
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st_view(parmview=., ., tokens(ParsName), touse )
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parms = parmview[1,1..cols(parmview)]
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if (CONFA_loglevel>2) {
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obsvar
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parms
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}
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// using the set up where the means are the first nobsvar entries of the parameter vector,
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means = parms[1..nobsvar]
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Sigma = CONFA_StrucToSigma(parms)
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// utilize an existing set up of the missing data patterns
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// data assumed to be sorted by the patterns of missing data
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info = panelsetup( pattern, 1 )
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for (i=1; i<=rows(info); i++) {
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panelsubview(mdata=., data, i, info)
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panelsubview(mlnl=., lnl, i, info)
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// mdata should contain the portion of the data with the same missing data pattern
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// mlnl will be conforming to mdata
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// OK, now need to figure out that pattern
|
||
|
thispattern = J(1, cols(data), 1) - colmissing( mdata[1,] )
|
||
|
if (CONFA_loglevel > 2) {
|
||
|
printf("{txt}Pattern #{res}%5.0f{txt} :", i)
|
||
|
thispattern
|
||
|
};
|
||
|
|
||
|
// modify the matrices
|
||
|
|
||
|
thisSigma = select( select( Sigma, thispattern), thispattern' )
|
||
|
thisSS = cholesky(thisSigma)
|
||
|
thisInvSigma = solvelower(thisSS,I(rows(thisSS)))
|
||
|
thisInvSigma = solveupper(thisSS',thisInvSigma)
|
||
|
thisldetWS = 2*ln(dettriangular(thisSS))
|
||
|
|
||
|
if (CONFA_loglevel > 3) {
|
||
|
thisSigma
|
||
|
thisInvSigma
|
||
|
};
|
||
|
|
||
|
for( j=1; j<=rows(mdata); j++ ) {
|
||
|
// this is actually a single line broken by arithmetic operator signs
|
||
|
// that's bad style but it works
|
||
|
mlnl[j,1] = -.5*(select(data[j,.],thispattern)-select(means,thispattern)) *
|
||
|
thisInvSigma *
|
||
|
(select(data[j,.],thispattern)-select(means,thispattern))' -
|
||
|
.5*thisldetWS - .5*sum(thispattern)*ln(2*pi())
|
||
|
}
|
||
|
|
||
|
if (CONFA_loglevel>3) {
|
||
|
mlnl
|
||
|
};
|
||
|
|
||
|
}
|
||
|
|
||
|
|
||
|
}
|
||
|
|
||
|
// Bollen-Stine bootstrap rotation
|
||
|
void CONFA_BSrotate(
|
||
|
string SigmaName, // the parameter matrix name
|
||
|
string varnames // the variable names
|
||
|
) {
|
||
|
|
||
|
// declarations
|
||
|
real matrix data // views of the data
|
||
|
real matrix Sigma, SS, S2, SS2 // the covariance matrices and temp matrices
|
||
|
real matrix means // the means -- need modifications for weighted data!!!
|
||
|
real scalar n // dimension, no. obs
|
||
|
|
||
|
// get the data in
|
||
|
st_view(data=., ., tokens(varnames) )
|
||
|
n=rows(data)
|
||
|
|
||
|
Sigma = st_matrix(SigmaName)
|
||
|
|
||
|
// probability weights!!!
|
||
|
means = colsum(data)/n
|
||
|
SS = (cross(data,data)-n*means'*means)/(n-1)
|
||
|
|
||
|
S2 = cholesky(Sigma)
|
||
|
SS2 = cholesky(SS)
|
||
|
SS2 = solveupper(SS2',I(rows(SS)))
|
||
|
|
||
|
data[,] = data*SS2*S2'
|
||
|
|
||
|
}
|
||
|
|
||
|
|
||
|
// build a library
|
||
|
mata mlib create lconfa, replace
|
||
|
mata mlib add lconfa *()
|
||
|
mata mlib index
|
||
|
|
||
|
end
|
||
|
// of mata
|
||
|
|
||
|
exit
|
||
|
|
||
|
// don't need this:
|
||
|
|
||
|
string scalar CONFA_UL( string input ) {
|
||
|
|
||
|
string rowvector s;
|
||
|
real scalar i,j,n;
|
||
|
|
||
|
// tokenize input into a string vector
|
||
|
s = tokens( input )
|
||
|
n = cols( s )
|
||
|
for(i=1;i<=n;i++) {
|
||
|
// as I go over the elements, compare to the previous ones
|
||
|
for(j=1;j<i;j++) {
|
||
|
if ( s[i] == s[j] ) {
|
||
|
s[i] = ""
|
||
|
continue
|
||
|
}
|
||
|
}
|
||
|
}
|
||
|
// assemble back into a string scalar
|
||
|
return( stritrim(invtokens( s ) ) )
|
||
|
}
|