Table 1.
Comparison of computing time of different methods for parameter estimation in a single mvLMM, and for performing likelihood ratio tests in GWASs. Results are shown for both HMDP and NFBC1966 data sets. All computation was performed on a single core of an Intel Xeon L5420 2.50GHz CPU. n is the number of individuals, s is the number of SNPs, d is the number of traits, c is the number of covariates (c=1 here), t1 is the number of iterations used in the EM type algorithm and t2 is the number of iterations used in the NR type algorithm. Notice that the computing time for GEMMA is essentially the same for all d, because in GEMMA the computing time is dominated by the initial O(n3) eigen-decomposition step; the following optimization iterations are negligible. The sn2 step in GEMMA could be replaced with an snr step if the relatedness matrix is of rank r.
| Method | Time Complexity | Computation Time | |||||
|---|---|---|---|---|---|---|---|
| HMDP (n=656, s=108,562) | NFBC1966 (n=5255, s=319,111) | ||||||
| d=2 | d=3 | d=4 | d=2 | d=3 | d=4 | ||
| Fitting a single mvLMM | |||||||
| GEMMA | O(n3+n2d+n2c+t1nc2d2+t2nc2d6) | < 1 s | < 1 s | < 1 s | 6.7 min | 6.7 min | 6.7 min |
| WOMBAT | O(t1n3(d + c)3+t2n3d7) | 12.5 s | 39.2 s | 71.0 s | 31.0 min | 127.6 min | 477.3 min |
| GCTA | O(t1n3(d + c)3+t2n3d7) | 11.2 s | -- | -- | 38.2 min | -- | -- |
| Genome-wide applications | |||||||
| GEMMA | O(n3+n2d+n2c+s(n2+t1nc2d2+t2nc2d6)) | 6.2 min | 13.7 min | 28.5 min | 4.4 h | 4.8 h | 5.8 h |
| MTMM | O(t1n3(d + c)3+t2n3d7+sn2d2) | 16.4 min | -- | -- | 58.0 h | -- | -- |