Matvec Users’ Guide

10.6. LEAST SQUARES MEANS (LSMEANS) 65
D = Data();
D.input("try.dat","animal\$ herd _skip y");
M = Model();
M.equation("y = intercept herd animal");
M.variance("residual",2);
M.variance("animal",P,1);
M.fitdata(D);
Kp = [0,1,-1];
M.contrast(Kp)
Now, at the Matvec prompt, I type
> input try4
RESULTS FROM CONTRAST(S)
----------------------------------------------------------
Contrast MME_addr K_coef Raw_data_code
---------------------------------------------
1 2 1 herd:1
1 3 -1 herd:2
estimated value (K’b-M) = -1.69 +- 1.3997
Prob(|t| > 1.2074) = 0.227421 (p_value)
----------------------------------------------------------
0.227278
The last two statements in the above Matvec script can be replaced by a single statement:
M.contrast("herd",[1,-1])
Any composite hypothesis tests require multi-row matrix Kp. For instance, the test H0: h1 = h2 = 0
can be accomplished in Matvec as below:
M.contrast("herd",[1,0; 0,1])
10.6 Least Squares Means (lsmeans)
The least-squares means (lsmeans), also called population marginal means, are the expected values of class
or subclass means that you would expect for a balanced design involving the class variable with all covariates
at their mean level. A least-squares mean for a given level of a given model-term may not be estimable.
M.lsmeans("") outputs the least-squares means for each terms in termname-list. Here
is the example saved in a file try5
D = Data();
D.input("try.dat","animal\$ herd _skip y");
P = Pedigree();
P.input("try.ped");
M = Model();
M.equation("y = intercept herd animal");
M.variance("residual",2.0);
M.variance("animal",P,1.0);
M.fitdata(D);
M.lsmeans("herd");