It turns that the problem is with the data and not the code. Thank you so much. Raphael ... View more

According to the note below the option should be available in SAS® 9.4 TS1M0 or later. 36383 - Randomly assign the observations in a data set to two or more groups ... View more

Modifying the BC function to handle negative values is the approach I took. Since putting a constraint on u1>0 limits the type of transformations we have available. However, I soon realize that this approach has drawbacks as this is a transform both sides model. Meaning we must apply the same transformation to both the response and the regression function to preserve the relationship. I began with wanting to simultaneously estimate c , u1 and u2. That is, mu = BD(BC(xb + c,u1),u2) It turns out that applying the two-parameter Box-Cox transformation to the transform-both-sides (TBS) regression model is not straight forward. The main reason being that the constraint min(xb) + c > 0 is data dependent. This in it self is not an issue until you realize that at each iteration of the algorithm the coefficients can take on positive as well as negative values. Hence I see no way to specify the constraint min(xb) + c > 0 since the sign of xb may change at each iteration. It does seem easier to fix c > -min(x) then estimate u1 and u2. As you rightly suggested some time ago in another discussion, we can fix c such that c > - min(xb). It is well known that as c moves away from - min(xb) the transformation becomes less effective. ... View more

Here is a snippet of the code: I know why the error occurs but why not in NLMIXED also. I don't want to constrain my coefficients. How to solve this issue? SAS/IML error WARNING: Invalid argument resulted in missing value result. count     : number of occurrences is 1000 operation : ## at line 1295 column 5 operands  : y, u y   1000 rows      1 col     (numeric) u      1 row       1 col     (numeric) -0.180567 statement : ASSIGN at line 1295 column 5 traceback : module BC at line 1295 column 5              module OBJFUN at line 1322 column 5 /* Box-Cox transformation */ start BC(y,u);   f = (y##u - 1)/u;          /* <-- line 1295 */   return(f); finish BC; /* Bickle-Doksum transformation */ start BD(y,u);   f = (sign(y)#abs(y)##u - 1)/u;   return(f); finish BD; /* log-likelihood */ start OBJFUN(parm) global(yy, xx);   b = parm[1:2];   u1 = parm[3];   u2 = parm[4];   v = parm[5];   xb = xx*b;   w = BD(BC(yy,u1),u2);   mu = BD(BC(xb,u1),u2);      /* <-- line 1322 */   n = nrow(yy);   f = -n/2*log(v) - 1/2/v*sum((w-mu)##2) + (u2-1)*sum(log(abs(BC(yy,u1)))) + u1*sum(log(yy));   return (f); finish OBJFUN; xx = xx || J(nrow(xx),1); /* add intercept term */   /* b1-b0-u1-u2-v constraint matrix */   con = { .  .  .  1e-6  1e-6,   /* lower bounds */           .  .  .  .  .}; /* upper bounds */   x0 = {1 6.5 0.1 1 1}; /* starting values */   opt = {1 0};   /* maximization - supress results */   call nlpnra(rc, mle, "OBJFUN", x0, opt, con); PROC NLMIXED proc nlmixed data = sample tech = NEWRAP maxit = 1000; parms b1 = 6.5 b2 = 1 v = 1 u1= 0.1 u2= 1 ; xb = b1 + b2 * x ; y0 = (  y ** u1 - 1 )/u1 ; xb0 = (  xb ** u1 - 1 )/u1 ; y_ = (sign(y0)*abs(y0)**u2-1)/u2 ; xb_ = (sign(xb0)*abs(xb0)**u2-1)/u2 ; llik = ( -1/2*log(v) - 1/2/v*( y_ - xb_)**2 + (u2 - 1)*log((abs(y0)) +  u1*log(y); model zzz ~ general(llik); run; ... View more

Thanks Rick! ... View more

Or rather \int_{0}^{1} u^{(a + 1/2) - 1} \exp(-u*b/2) du ... View more

Thank you. The incomplete gamma function I am using is \int_{0}^{1} u^{(a + 1/2) - 1} \exp(-u*b) du and not the usual  \int_{0}^{x} u^{a - 1} \exp(-u) du. ... View more