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gemma2 is an implementation in R of the GEMMA v 0.97 EM algorithm that is part of the GEMMA algorithm for REML estimation of multivariate linear mixed effects models of the form:

[vec(Y) = X vec(B) + vec(G) + vec(E)]

where (E) is a n by 2 matrix of random effects that follows the matrix-variate normal distribution

[G MN(0, K, V_g)]

where (K) is a relatedness matrix and (V_g) is a 2 by 2 covariance matrix for the two traits of interest.

Additionally, the random errors matrix (E) follows the distribution:

[E MN(0, I_n, V_e)]

and (G) and (E) are independent.


To install gemma2, use the devtools R package from CRAN. If you haven’t installed devtools, please run this line of code:


Then, run this line of code to install gemma2:



X. Zhou & M. Stephens. Efficient multivariate linear mixed model algorithms for genome-wide association studies. Nature Methods volume 11, pages 407–409 (2014).