Options nocenter linesize=81 pagesize=66; /* THIS PROGRAM PERFORMS A PARTIAL PROPORTIONAL ODDS REGRESSION ANALYSIS */ /* FOR ORDINAL RESPONSE VARIABLES AS DISCUSSED BY */ /* PATERSON & HARRELL (1990) APPLIED STATISTICS 2:205-217 */ /* THE PROBIT FORMULATION IS ALSO ALLOWED GIVING MODELS AS DESCRIBED BY */ /* TERZA (1985) COMMUNICATIONS IN STATISTICAL THEORY AND METHODS 14:1-11*/ /* NOTE: */ /* THE TWO FILES THRESHM1 AND THRESHM2 ARE DIFFERENT IN THE FOLLOWING WAY */ /* THRESHM1 assumes that there are two sets of explanatory variables */ /* setA: variables following the proportional odds assumption */ /* setB: variables relaxing the proportional odds assumption */ /* (this set includes the intercept) */ /* THRESHM2 only allows setB variables */ /* Thus, use THRESHM1 to fit proportional or partial proportional odds */ /* models, and THRESHM2 to fit a strictly non-proportional odds model */ /* */ /* */ /* FOR THE ANALYSIS OF STAGES OF CHANGE DATA */ /* THIS MODEL HAS BEEN DUBBED THE THRESHOLDS OF CHANGE MODEL: */ /* HEDEKER, MERMELSTEIN, & WEEKS (1999) */ /* THE THRESOLDS OF CHANGE MODEL: */ /* AN APPROACH TO ANALYZING STAGES OF CHANGE DATA */ /* ANNALS OF BEHAVIORAL MEDICINE, 21(1):61-70 */ /* (we're hoping this name will really catch on!!) */ /* */ /* ANY COMMENTS OR QUESTIONS CAN BE DIRECTED TO DON HEDEKER hedeker@uic.edu */ /* PLEASE FEEL FREE TO REDISTRIBUTE THIS MACRO */ /* */ /* NOTE THAT IN THE PROGRAM BELOW - THE DATA AND SAS COMMANDS ARE */ /* INCLUDED AS 1 FILE - THIS IS ONLY FOR CONVENIENCE IN DISTRIBUTION */ /* THE DATA CAN BE EXTRACTED INTO A SEPARATE FILE AND THEN READ IN */ /* BY THE PROGRAM FILE - SEE THE SAS MANUAL FOR INSTRUCTIONS ON THIS */ /* */ /* THE DATA USED BELOW ARE LONGITUDINAL ORDINAL RESPONSES */ /* BUT FOR THIS EXAMPLE ARE TREATED AS INDEPENDENT RESPONSES */ /* FOR A MIXED-EFFECTS PARTIAL PROPORTIONAL ODDS MODEL SEE THE MIXOR */ /* PROGRAM (also available at this website) AND THE PAPER */ /* HEDEKER & MERMELSTEIN (1998) */ /* A MULTILEVEL THRESHOLDS OF CHANGE MODEL */ /* FOR ANALYSIS OF STAGES OF CHANGE DATA */ /* MULTIVARIATE BEHAVIORAL RESEARCH, 33(4):427-455 */ /* */ /* THIS SAS MACRO PROGRAM IS SOMEWHAT SLOW IN EXECUTING */ /* FOR A FASTER PROGRAM TRY MIXOR */ /* A STAND-ALONE FREEWARE PROGRAM (also available at this website) */ /* MIXOR DOES THE SAME KIND OF MODELS, BUT CAN ADDITIONALLY INCLUDE RANDOM */ /* EFFECTS IN THE MODEL AS WELL AS SOME OTHER ADVANCED FEATURES */ TITLE1 'THRESHOLDS OF CHANGE - ORDINAL REGRESSION MODEL'; TITLE2 'ANALYSIS OF AGRESTI & LANG DATA (Biometrika, 1993)'; DATA one; input ID RESPONSE ONE ITEM2 ITEM3; LABEL RESPONSE = 'Opinions about Sex' Item2 = 'Premarital vs Teen' Item3 = 'Extramarital vs Teen'; cards; 10001 1 1 0 0 10001 1 1 1 0 10001 1 1 0 1 10002 1 1 0 0 10002 1 1 1 0 10002 1 1 0 1 10003 1 1 0 0 10003 1 1 1 0 10003 1 1 0 1 10004 1 1 0 0 10004 1 1 1 0 10004 1 1 0 1 10005 1 1 0 0 10005 1 1 1 0 10005 1 1 0 1 10006 1 1 0 0 10006 1 1 1 0 10006 1 1 0 1 10007 1 1 0 0 10007 1 1 1 0 10007 1 1 0 1 10008 1 1 0 0 10008 1 1 1 0 10008 1 1 0 1 10009 1 1 0 0 10009 1 1 1 0 10009 1 1 0 1 10010 1 1 0 0 10010 1 1 1 0 10010 1 1 0 1 10011 1 1 0 0 10011 1 1 1 0 10011 1 1 0 1 10012 1 1 0 0 10012 1 1 1 0 10012 1 1 0 1 10013 1 1 0 0 10013 1 1 1 0 10013 1 1 0 1 10014 1 1 0 0 10014 1 1 1 0 10014 1 1 0 1 10015 1 1 0 0 10015 1 1 1 0 10015 1 1 0 1 10016 1 1 0 0 10016 1 1 1 0 10016 1 1 0 1 10017 1 1 0 0 10017 1 1 1 0 10017 1 1 0 1 10018 1 1 0 0 10018 1 1 1 0 10018 1 1 0 1 10019 1 1 0 0 10019 1 1 1 0 10019 1 1 0 1 10020 1 1 0 0 10020 1 1 1 0 10020 1 1 0 1 10021 1 1 0 0 10021 1 1 1 0 10021 1 1 0 1 10022 1 1 0 0 10022 1 1 1 0 10022 1 1 0 1 10023 1 1 0 0 10023 1 1 1 0 10023 1 1 0 1 10024 1 1 0 0 10024 1 1 1 0 10024 1 1 0 1 10025 1 1 0 0 10025 1 1 1 0 10025 1 1 0 1 10026 1 1 0 0 10026 1 1 1 0 10026 1 1 0 1 10027 1 1 0 0 10027 1 1 1 0 10027 1 1 0 1 10028 1 1 0 0 10028 1 1 1 0 10028 1 1 0 1 10029 1 1 0 0 10029 1 1 1 0 10029 1 1 0 1 10030 1 1 0 0 10030 1 1 1 0 10030 1 1 0 1 10031 1 1 0 0 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0 0 190004 3 1 1 0 190004 2 1 0 1 190005 2 1 0 0 190005 3 1 1 0 190005 2 1 0 1 190006 2 1 0 0 190006 3 1 1 0 190006 2 1 0 1 190007 2 1 0 0 190007 3 1 1 0 190007 2 1 0 1 190008 2 1 0 0 190008 3 1 1 0 190008 2 1 0 1 200001 2 1 0 0 200001 4 1 1 0 200001 1 1 0 1 200002 2 1 0 0 200002 4 1 1 0 200002 1 1 0 1 200003 2 1 0 0 200003 4 1 1 0 200003 1 1 0 1 200004 2 1 0 0 200004 4 1 1 0 200004 1 1 0 1 200005 2 1 0 0 200005 4 1 1 0 200005 1 1 0 1 200006 2 1 0 0 200006 4 1 1 0 200006 1 1 0 1 200007 2 1 0 0 200007 4 1 1 0 200007 1 1 0 1 200008 2 1 0 0 200008 4 1 1 0 200008 1 1 0 1 200009 2 1 0 0 200009 4 1 1 0 200009 1 1 0 1 200010 2 1 0 0 200010 4 1 1 0 200010 1 1 0 1 200011 2 1 0 0 200011 4 1 1 0 200011 1 1 0 1 200012 2 1 0 0 200012 4 1 1 0 200012 1 1 0 1 200013 2 1 0 0 200013 4 1 1 0 200013 1 1 0 1 200014 2 1 0 0 200014 4 1 1 0 200014 1 1 0 1 200015 2 1 0 0 200015 4 1 1 0 200015 1 1 0 1 200016 2 1 0 0 200016 4 1 1 0 200016 1 1 0 1 200017 2 1 0 0 200017 4 1 1 0 200017 1 1 0 1 200018 2 1 0 0 200018 4 1 1 0 200018 1 1 0 1 200019 2 1 0 0 200019 4 1 1 0 200019 1 1 0 1 200020 2 1 0 0 200020 4 1 1 0 200020 1 1 0 1 200021 2 1 0 0 200021 4 1 1 0 200021 1 1 0 1 200022 2 1 0 0 200022 4 1 1 0 200022 1 1 0 1 200023 2 1 0 0 200023 4 1 1 0 200023 1 1 0 1 210001 2 1 0 0 210001 4 1 1 0 210001 2 1 0 1 210002 2 1 0 0 210002 4 1 1 0 210002 2 1 0 1 210003 2 1 0 0 210003 4 1 1 0 210003 2 1 0 1 210004 2 1 0 0 210004 4 1 1 0 210004 2 1 0 1 210005 2 1 0 0 210005 4 1 1 0 210005 2 1 0 1 210006 2 1 0 0 210006 4 1 1 0 210006 2 1 0 1 210007 2 1 0 0 210007 4 1 1 0 210007 2 1 0 1 210008 2 1 0 0 210008 4 1 1 0 210008 2 1 0 1 220001 2 1 0 0 220001 4 1 1 0 220001 3 1 0 1 220002 2 1 0 0 220002 4 1 1 0 220002 3 1 0 1 220003 2 1 0 0 220003 4 1 1 0 220003 3 1 0 1 220004 2 1 0 0 220004 4 1 1 0 220004 3 1 0 1 220005 2 1 0 0 220005 4 1 1 0 220005 3 1 0 1 220006 2 1 0 0 220006 4 1 1 0 220006 3 1 0 1 220007 2 1 0 0 220007 4 1 1 0 220007 3 1 0 1 230001 3 1 0 0 230001 1 1 1 0 230001 1 1 0 1 240001 3 1 0 0 240001 3 1 1 0 240001 1 1 0 1 240002 3 1 0 0 240002 3 1 1 0 240002 1 1 0 1 240003 3 1 0 0 240003 3 1 1 0 240003 1 1 0 1 250001 3 1 0 0 250001 3 1 1 0 250001 2 1 0 1 250002 3 1 0 0 250002 3 1 1 0 250002 2 1 0 1 260001 3 1 0 0 260001 3 1 1 0 260001 3 1 0 1 260002 3 1 0 0 260002 3 1 1 0 260002 3 1 0 1 260003 3 1 0 0 260003 3 1 1 0 260003 3 1 0 1 270001 3 1 0 0 270001 3 1 1 0 270001 4 1 0 1 280001 3 1 0 0 280001 4 1 1 0 280001 1 1 0 1 280002 3 1 0 0 280002 4 1 1 0 280002 1 1 0 1 280003 3 1 0 0 280003 4 1 1 0 280003 1 1 0 1 280004 3 1 0 0 280004 4 1 1 0 280004 1 1 0 1 280005 3 1 0 0 280005 4 1 1 0 280005 1 1 0 1 280006 3 1 0 0 280006 4 1 1 0 280006 1 1 0 1 280007 3 1 0 0 280007 4 1 1 0 280007 1 1 0 1 280008 3 1 0 0 280008 4 1 1 0 280008 1 1 0 1 280009 3 1 0 0 280009 4 1 1 0 280009 1 1 0 1 280010 3 1 0 0 280010 4 1 1 0 280010 1 1 0 1 280011 3 1 0 0 280011 4 1 1 0 280011 1 1 0 1 280012 3 1 0 0 280012 4 1 1 0 280012 1 1 0 1 280013 3 1 0 0 280013 4 1 1 0 280013 1 1 0 1 290001 3 1 0 0 290001 4 1 1 0 290001 2 1 0 1 290002 3 1 0 0 290002 4 1 1 0 290002 2 1 0 1 290003 3 1 0 0 290003 4 1 1 0 290003 2 1 0 1 290004 3 1 0 0 290004 4 1 1 0 290004 2 1 0 1 300001 3 1 0 0 300001 4 1 1 0 300001 3 1 0 1 300002 3 1 0 0 300002 4 1 1 0 300002 3 1 0 1 300003 3 1 0 0 300003 4 1 1 0 300003 3 1 0 1 300004 3 1 0 0 300004 4 1 1 0 300004 3 1 0 1 300005 3 1 0 0 300005 4 1 1 0 300005 3 1 0 1 300006 3 1 0 0 300006 4 1 1 0 300006 3 1 0 1 310001 4 1 0 0 310001 3 1 1 0 310001 3 1 0 1 320001 4 1 0 0 320001 4 1 1 0 320001 1 1 0 1 320002 4 1 0 0 320002 4 1 1 0 320002 1 1 0 1 320003 4 1 0 0 320003 4 1 1 0 320003 1 1 0 1 320004 4 1 0 0 320004 4 1 1 0 320004 1 1 0 1 320005 4 1 0 0 320005 4 1 1 0 320005 1 1 0 1 320006 4 1 0 0 320006 4 1 1 0 320006 1 1 0 1 320007 4 1 0 0 320007 4 1 1 0 320007 1 1 0 1 330001 4 1 0 0 330001 4 1 1 0 330001 2 1 0 1 330002 4 1 0 0 330002 4 1 1 0 330002 2 1 0 1 340001 4 1 0 0 340001 4 1 1 0 340001 3 1 0 1 340002 4 1 0 0 340002 4 1 1 0 340002 3 1 0 1 350001 4 1 0 0 350001 4 1 1 0 350001 4 1 0 1 350002 4 1 0 0 350002 4 1 1 0 350002 4 1 0 1 350003 4 1 0 0 350003 4 1 1 0 350003 4 1 0 1 350004 4 1 0 0 350004 4 1 1 0 350004 4 1 0 1 ; proc format; VALUE RESPONSE 1='Always Wrong' 2='Almost Always Wrong' 3='Wrong Sometimes' 4='Not Wrong'; proc means data=one; var RESPONSE ONE item2 item3; /* for the program */ /* subjects with missing data on */ /* the dependent variable */ /* or any of the independent variables */ /* need to be excluded */ data nomiss; set one; MISSVAR = 0; IF ((RESPONSE=.) OR (item2=.) OR (item3=.)) then MISSVAR = 1; IF (MISSVAR = 0) then output; proc means data=nomiss; var RESPONSE ONE item2 item3; /* THESHOLDS OF CHANGE */ /* ORDINAL LOGISTIC OR PROBIT REGRESSION MODEL */ /* */ /* N = NUMBER OF OBSERVATIONS */ /* P = NUMBER OF INDEPENDENT VARIABLES WITH VARYING EFFECTS ON */ /* THRESHOLDS (including the intercept) */ /* ==> these are the variables for which proportional odds */ /* is NOT assumed */ /* Q = NUMBER OF INDEPENDENT VARIABLES WITH NON-VARYING EFFECTS ON */ /* THRESHOLDS */ /* ==> these are the variables for which proportional odds */ /* is assumed */ /* */ /* modify ONLY the following statements below for a given analysis */ /* */ /* x = tcdat[,1:2]; */ /* (list the P independent variables */ /* with varying effects on thresholds, including the intercept) */ /* w = tcdat[,3]; */ /* (list the Q independent variables */ /* with non-varying effects on thresholds) */ /* y = tcdat[,4]; */ /* (list the dependent variable for the analysis) */ /* VARXLB = {'Intercpt' 'Item2'}; */ /* (list 8-character variable names for each independent variable */ /* with varying effects on thresholds, including the intercept) */ /* VARWLAB = {'Item3'}; */ /* (list 8-character variable names for each independent variable */ /* with non-varying effects on thresholds) */ /* DEPNAME = {'SexOpin'}; */ /* (list an 8-character variable name for the dependent variable) */ /* MAXJ = 4; */ /* (list the number of ordered categories for the dependent variable)*/ /* CODE = {1, 2, 3, 4}; */ /* (list the values of the ordered dependent variable) */ /* RESPFN = 1; */ /* (desired response function: 0=probit, 1=logistic) */ /* CONVERGE = 0.0001; */ /* (give the convergence criterion) */ proc iml; reset noname; use nomiss var{one item2 item3 response}; read all into tcdat; x = tcdat[,1:2]; w = tcdat[,3]; y = tcdat[,4]; VARXLAB = {'Intercpt' 'Item2vs1'}; VARWLAB = 'Item3vs1'; DEPNAME = 'SexOpin'; MAXJ = 4; CODE = {1 2 3 4}; CONVERGE = 0.0001; RESPFN = 1; P = NCOL(X); Q = NCOL(W); NPAR = P*(MAXJ-1) + Q; IF (RESPFN = 0) then RESPNAME = {'Probit'}; ELSE RESPNAME = {'Logistic'}; PRINT 'THRESHOLDS OF CHANGE (ordinal regression) MODEL'; PRINT DEPNAME; PRINT ' '; PRINT 'Response Function'; PRINT RESPNAME; /*** FIGURE OUT NUMBER OF OBSERVATIONS ***/ N = NROW(Y); PRINT 'NUMBER OF OBSERVATIONS'; print N; /*** starting values ***/ MEANY = SUM(Y) / N; MEANX = X[+,] / N; MEANW = W[+,] / N; STDY = SQRT(SSQ(Y - MEANY) / (N-1)); XDEV = J(N,P-1,0); DO L = 2 TO P; XDEV[,L-1] = X[,L] - MEANX[L]; END; B = (INV(XDEV` * XDEV)) * (XDEV` * (Y - MEANY[1])) / STDY[1]; XB = MEANX[,2:P] * B; WDEV = J(N,Q,0); DO L = 1 TO Q; WDEV[,L] = W[,L] - MEANW[L]; END; ALPHA = (INV(WDEV` * WDEV)) * (WDEV` * (Y - MEANY[1])) / STDY[1]; WA = MEANW[,1:Q] * ALPHA; FREQY = J(MAXJ,1,0); BETA = J(P,MAXJ-1,0); CUMSUM= 0; DO I = 1 TO N; DO J = 1 TO MAXJ; IF (Y[I] = CODE[J]) THEN DO; FREQY[J] = FREQY[J] + 1; goto find1; END; END; find1: END; DO J = 1 TO MAXJ-1; CUMSUM = CUMSUM + FREQY[J]; CUMODDS= CUMSUM / (N - CUMSUM); LNCUMOD= LOG(CUMODDS); IF (RESPFN = 0) THEN TEMPPAR= 0.625 # (LNCUMOD + XB + WA); ELSE TEMPPAR = LNCUMOD + XB + WA; IF (J = 1) THEN BETA[1,1] = 0 - TEMPPAR; ELSE BETA[1,J] = TEMPPAR + BETA[1,1]; END; DO J = 1 TO MAXJ-1; DO I = 2 TO P; BETA[I,J] = B[I-1]; END; END; PRINT 'CATEGORY FREQUENCIES'; PRINT FREQY; /*** start iterations ***/ IT = 0; DO until (MAXCORR < CONVERGE); IT = IT + 1; PRINT '*************'; PRINT 'ITERATION' IT [format=2.0]; PRINT '*************'; /*** calculate and save the sample log-likelihood value logl. ***/ logl= 0; /*** calculate the derivatives and information matrix ***/ der2 = J(npar,npar,0); der = J(npar,1,0); DO i=1 TO n; derp=J(npar,1,0); WA = 0; DO L=1 TO Q; WA = WA + ALPHA[L] * W[I,L]; END; DO J=1 TO MAXJ; IF (Y[I] = CODE[J]) THEN DO; IF (J=1) THEN DO; XB1 = 0; DO L=1 TO P; XB1 = XB1 + BETA[L,J] * X[I,L]; END; Z1 = XB1 + WA; IF (RESPFN = 0) THEN do; prob=probnorm(z1); IF (Z1 < 10 & Z1 > -10) THEN PDFZ1 = EXP((0-Z1)*Z1/2) / 2.506628275; ELSE PDFZ1 = 0; END; ELSE do; prob=1/(1 + EXP(0-z1)); IF (Z1 < 16 & Z1 > -16) THEN PDFZ1 = EXP(0-Z1) / ((1 + EXP(0-z1))**2); ELSE PDFZ1 = 0; END; probp=0-pdfz1; probp0=0; probp1=pdfz1; end; else if (j>1 & j -10) THEN PDFZ0 = EXP((0-Z0)*Z0/2) / 2.506628275; ELSE PDFZ0 = 0; IF (Z1 < 10 & Z1 > -10) THEN PDFZ1 = EXP((0-Z1)*Z1/2) / 2.506628275; ELSE PDFZ1 = 0; END; ELSE do; prob = (1/(1+ EXP(0-z1)))-(1/(1+ EXP(0-z0))); IF (Z0 < 16 & Z0 > -16) THEN PDFZ0 = EXP(0-Z0) / ((1 + EXP(0-z0))**2); ELSE PDFZ0 = 0; IF (Z1 < 16 & Z1 > -16) then PDFZ1 = EXP(0-Z1) / ((1 + EXP(0-z1))**2); ELSE PDFZ1 = 0; END; probp=pdfz0-pdfz1; probp0=pdfz0; probp1=pdfz1; end; else do; XB0 = 0; do L=1 TO P; XB0 = XB0 + BETA[L,J-1] * X[I,L]; END; Z0 = XB0 + WA; IF (RESPFN = 0) then do; prob=1-probnorm(z0); IF (Z0 < 10 & Z0 > -10) then PDFZ0 = EXP((0-Z0)*Z0/2) / 2.506628275; ELSE PDFZ0 = 0; end; ELSE do; prob = 1 - (1 / (1 + EXP(0-z0))); IF (Z0 < 16 & Z0 > -16) then PDFZ0 = EXP(0-Z0) / ((1 + EXP(0-z0))**2); ELSE PDFZ0 = 0; END; probp=pdfz0; probp0=pdfz0; probp1=0; end; if (prob <= .00000001) then prob = .00000001; DERIV = 0 - (PROBP/PROB); do L=1 TO Q; DERP[L] = DERP[L] + DERIV # W[I,L]; END; DERIV0 = 0 - (PROBP0/PROB); DERIV1 = (PROBP1/PROB); if (j = maxj) then do; IC0 = (J-2)*P + Q; do L=1 TO P; IC0 = IC0 + 1; DERP[IC0] = DERP[IC0] + DERIV0 # X[I,L]; END; end; else if (j>=2 & j