*---------------------------------------------------------------* * A SAS MACRO TO TEST THE SIGNIFICANCE OF DIFFERENCES * * BETWEEN PARAMETER ESTIMATES IN PROC CATMOD * * * * This macro, called DIFFPARM, will compute significance tests * * for the DIFFerence in PARMater estimates that are obtained * * for multinomial logistic regression models using PROC CATMOD. * * * * A description of the DIFFPARM macro is published in * * OAC's Perspective, volume 18(2), 1994, pp. XX-XX and in * * proceedings for the Western Users of SAS Software Conference, * * Santa Monica, CA, October 1993. * * * * The DIFFPARM macro was written in version 6.08 of the * * SAS System running under MVS on an IBM ES/9000 model 900. * * If the macro is ported to another version of SAS or * * to another operating system you should thoroughly test * * the accuracy of the results. * * * * Created 9-9-93, redesigned 10-10-93 * * Linda R. Ferguson * * Mel Widawski * * Office of Academic Computing * * 5628 Math Science Addition * * University of California, Los Angeles * * Los Angeles CA 90024-1557 * * (310) 825-7452 * * consult@mvs.oac.ucla.edu * *---------------------------------------------------------------*; options pagesize=56; %macro diffparm(numcat,numparm,dsn); options nocenter; options linesize=132; /*-------------------------------------------------------------*/ /* The following determines the number of cases in the dataset */ /* output by catmod and tests whether the parameters NUMCAT */ /* and NUMPARM fit the dataset. */ /* */ /* Added: Mel Widawski 10-10-93 */ /*-------------------------------------------------------------*/ %global num ; %if &dsn = %then %do; %let dsn=LOGITEST ; %PUT NOTE: No DSN specified using &DSN ; %end; DATA _NULL_; IF 0 THEN SET &DSN POINT=_N_ NOBS=COUNT; CALL SYMPUT('NUM',LEFT(PUT(COUNT,8.))); STOP; RUN; %let numdf = %eval(&numcat-1); %let t = %eval(&numdf*&numparm) ; %let eval = %eval( &t + 1) ; %IF &eval ^= &num %then %do; /* observations not OK */ %PUT ******************************************************; %PUT **** ERROR: ; %PUT **** Number of lines, &num, in &dsn ; %PUT **** ^= ((Number of Categories -1 = &numdf) ; %PUT **** X (Number of Parameters = &numparm)) + 1; %PUT **** ; %PUT **** Probable error in specifying NUMCAT or NUMPARM ; %PUT ******************************************************; %end; /* end observations not OK */ %else %do; /* observations OK */ *-----------------------------------------------------------* * To test for the significance of parameter * * estimates bi and bj, a z-test can be computed * * using the following formula for variance. * * * * bi - bj * * z= ------------------------------------- * * sqrt{var(bi) + var(bj) - 2cov(bi,bj)} * *-----------------------------------------------------------*; data _null_; set &dsn (DROP=_METHOD_); file print /*log*/ header=newpage; retain rowpoint 0 Bpoint 0; *---------------------------------------------------------------* * Example to help understand levels and parameters. * * * * If the dependent variable has 5 levels, there will be * * 4 response functions, and the last level of the * * dependent variable will be the baseline. * * If there are 6 predictor variables, there will be * * 7 parameter estimates per response function (add one * * for the intercept). * * * * The parameter estimates are numbered as follows: * * B1=intercept for level1 * * B2=intercept for level2 * * B3=intercept for level3 * * B4=intercept for level4 * * B5=var1 for level1 * * B6=var1 for level2 * * B7=var1 for level3 * * B8=var1 for level4 * * B9=var2 for level1 * * B10=var2 for level2 * * etc. * * * * Significance tests are computed for the following differences * * in parameter estimates: * * B1-B2, B1-B3, B1-B4, B2-B3, B2-B4, B3-B4 * * B5-B6, B5-B7, B5-B8, B6-B7, B6-B8, B7-B8 * * B9-B10, B9-B11, B9-B12, B10-B11, B10-B12, B11-B12 * * etc. * *---------------------------------------------------------------*; *------------------------------------------------------------* * Explanation of Macro Variables: * * numcat = number of outcome categories = k. * * numdf = number of response functions = (k-1). * * numparm = number of parameter estimates per response * * function = p. * * t = total number of parameter est = t = p*(k-1). * * num = total number of obs = t+1 = p*(k-1)+1. * * * * Explanation of additional counts: * * number of comparisons per set of parameter estimates = * * c = (k-1)!/(k-3)!2!. * * total number of comparisons for model = p*c. * * * * Explanation of Arrays: * * The following arrays have dimension "t" (total number * * of parameter estimates for the entire model): * * ARRAY B (input array of parameters and covar matrix) * * ARRAY P (array to retain parameters) * * * * The following array has dimensions "(k-1),(k-1)" * * (size of covariance matrix of response functions * * for each model parmeter (predictor variables and * * intercept)): * * ARRAY COV * *------------------------------------------------------------*; /* compute numerator as bi - bj, where j=i+1 */ ARRAY B(&t) ; /* B1-Bt (where t = number of parameters) */ ARRAY P(&t) _TEMPORARY_ ; /* retains parameters */ ARRAY cov(&numdf,&numdf) _TEMPORARY_ ; /*covariance matrix used for computing comparisons*/ if _TYPE_='PARMS' then do; /* Fill the P (parm) array to retain parameters */ DO I = 1 TO &t; P(i) = B(i); end; end; else if _TYPE_='COV' then do; rowpoint=rowpoint+1; DO I = rowpoint TO &numdf; /* fill current covariance matrix */ cov(rowpoint,i) = B(i+Bpoint) ; end; if rowpoint=&numdf then do; /* compute and print */ do i = 1 to &numdf - 1 ; /* do i */ do j = i+1 to &numdf ; /* do j */ k = i + Bpoint ; kk = j + Bpoint ; /* compute test only for relevant comparisons */ /* compute differences */ diff = p(k)-p(kk); /* find demoninator (standard error of difference) */ sediff=SQRT(cov(i,i) + cov(j,j) - 2*cov(i,j)); /* put it all together */ zdiff = diff / sediff; /* find probability level for z-score */ ztemp=abs(zdiff); zprob = 2*(1 - probnorm(ztemp)); /* print the results */ put / @1 k @5 kk @10 p(k) 8.4 @20 p(kk) 8.4 @30 diff 8.4 @40 cov(i,i) 8.4 @50 cov(j,j) 8.4 @60 cov(i,j) 8.4 @70 sediff 8.4 @80 zdiff 8.4 @90 zprob 8.4 ; end; /* do j */ end; /* do i */ Bpoint = Bpoint + &numdf ; rowpoint=0; end; /* compute and print */ end; /* type ='COV' */ return; newpage: put 132*'-' ; /*---------------------------*/ /* create heading for output */ /*---------------------------*/ put / 'Significance test for difference between' ' parameter i and parameter j' ' (with probability level for a two-tailed test).' ; put / ; put "Number of categories for outcome variable is &numcat"; put / ; put "Number of parameter estimates per response function &numparm"; put / @1 'i' @5 'j' @11 'beta(i)' @21 'beta(j)' @31 'diff(i,j)' @41 'var(i)' @51 'var(j)' @61 'cov(i,j)' @71 'se(i,j)' @81 'z(i,j)' @91 'prob' ; put / 132*'-' ; numline=4; return; /* end link to newpage */ run; %end; /*end observations OK */ %mend diffparm;