MATLAB: ROWEXCH function gives a warning – Starting design is rank deficient

Question

The following lines of code give a warning message that the starting design is rank deficient: ERROR: >> nfactors = 6; >> nruns=12; >> dfF = sortrows(rowexch(nfactors,nruns,'l','cat',1:nfactors,'levels',[3 3 3 3 3 2],'tries',100)) In rowexch at 207 In candexch at 122 In smartForReduce at 128 In candexch>loopBody at 250 > In candexch>gen1design at 155 Warning: Starting design is rank deficient

I also got the same warning when I run cordexch function.

Answer 1

The ROWEXCH and CORDEXCH function selects a starting design at random, and uses a row-exchange algorithm to iteratively replace rows of X by rows of C from the candidate set in an attempt to improve the determinant of X'*X. The starting design may be rank deficient sometimes since it is randomly selected, but if the final design matrix X (the second output of ROWEXCH) is full rank, there should be no problem.