julia> using DataFrames, MixedModels, RData
julia> const dat = convert(Dict{Symbol,DataFrame}, load(Pkg.dir("MixedModels", "test", "dat.rda")));
julia> mm1 = fit!(lmm(@formula(Y ~ 1+S+T+U+V+W+X+Z+(1+S+T+U+V+W+X+Z|G)+(1+S+T+U+V+W+X+Z|H)), dat[:kb07]))
Linear mixed model fit by maximum likelihood
Formula: Y ~ 1 + S + T + U + V + W + X + Z + ((1 + S + T + U + V + W + X + Z) | G) + ((1 + S + T + U + V + W + X + Z) | H)
logLik -2 logLik AIC BIC
-1.42931613×10⁴ 2.85863226×10⁴ 2.87483226×10⁴ 2.91930103×10⁴
Variance components:
Column Variance Std.Dev. Corr.
G (Intercept) 90791.6237 301.316484
S 5187.9402 72.027357 -0.43
T 5552.4111 74.514503 -0.47 0.07
U 7584.6653 87.089984 0.21 -0.20 0.41
V 8841.5313 94.029417 0.20 -0.76 -0.54 -0.20
W 1823.9330 42.707529 0.47 -0.53 -0.11 -0.44 0.29
X 7422.6234 86.154648 -0.10 0.13 -0.05 -0.86 -0.06 0.70
Z 3801.2195 61.654031 -0.48 0.41 -0.38 -0.09 0.18 -0.78 -0.39
H (Intercept) 130031.4034 360.598674
S 1853.0405 43.046957 -0.34
T 62466.7444 249.933480 -0.68 -0.45
U 2941.3214 54.233950 0.20 -0.06 -0.18
V 1037.6157 32.212044 0.57 -0.75 0.02 0.02
W 1619.1082 40.238144 0.28 -0.04 -0.27 0.44 -0.21
X 4706.3361 68.602741 0.08 -0.24 0.21 -0.13 -0.26 0.01
Z 4837.5738 69.552669 0.04 -0.45 0.32 -0.69 0.65 -0.68 -0.10
Residual 399587.7869 632.129565
Number of obs: 1790; levels of grouping factors: 56, 32
Fixed-effects parameters:
Estimate Std.Error z value P(>|z|)
(Intercept) 2180.63 76.8637 28.3701 <1e-99
S -66.9899 19.3343 -3.46482 0.0005
T -333.881 47.6917 -7.00082 <1e-11
U 78.9861 21.2279 3.72087 0.0002
V 22.1509 20.3366 1.08922 0.2761
W -18.9244 17.5052 -1.08107 0.2797
X 5.26196 22.4251 0.234646 0.8145
Z -23.9501 21.0314 -1.13878 0.2548
julia> mm1.optsum
Initial parameter vector: [1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 1.0]
Initial objective value: 30014.36976860626
Optimizer (from NLopt): LN_BOBYQA
Lower bounds: [0.0, -Inf, -Inf, -Inf, -Inf, -Inf, -Inf, -Inf, 0.0, -Inf, -Inf, -Inf, -Inf, -Inf, -Inf, 0.0, -Inf, -Inf, -Inf, -Inf, -Inf, 0.0, -Inf, -Inf, -Inf, -Inf, 0.0, -Inf, -Inf, -Inf, 0.0, -Inf, -Inf, 0.0, -Inf, 0.0, 0.0, -Inf, -Inf, -Inf, -Inf, -Inf, -Inf, -Inf, 0.0, -Inf, -Inf, -Inf, -Inf, -Inf, -Inf, 0.0, -Inf, -Inf, -Inf, -Inf, -Inf, 0.0, -Inf, -Inf, -Inf, -Inf, 0.0, -Inf, -Inf, -Inf, 0.0, -Inf, -Inf, 0.0, -Inf, 0.0]
ftol_rel: 1.0e-12
ftol_abs: 1.0e-8
xtol_rel: 0.0
xtol_abs: [1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10, 1.0e-10]
initial_step: [0.75, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.75, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.75, 1.0, 1.0, 1.0, 1.0, 1.0, 0.75, 1.0, 1.0, 1.0, 1.0, 0.75, 1.0, 1.0, 1.0, 0.75, 1.0, 1.0, 0.75, 1.0, 0.75, 0.75, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.75, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.75, 1.0, 1.0, 1.0, 1.0, 1.0, 0.75, 1.0, 1.0, 1.0, 1.0, 0.75, 1.0, 1.0, 1.0, 0.75, 1.0, 1.0, 0.75, 1.0, 0.75]
maxfeval: -1
Function evaluations: 2150
Final parameter vector: [0.476669, -0.0495603, -0.0559578, 0.0294869, 0.0291771, 0.0319766, -0.0139779, -0.0464195, 0.102601, -0.0172312, -0.0166362, -0.110942, -0.0244482, 0.0126322, 0.0219091, 0.102309, 0.0780709, -0.0945351, 0.00503189, -0.0133206, -0.0649625, 0.108351, 0.00551326, -0.0540187, -0.134323, 0.0515467, 0.0, 0.000989713, 0.00082312, -0.000902588, 0.0, 0.00013651, -0.000244137, 0.0, 6.27183e-9, 0.0, 0.570451, -0.0233509, -0.267494, 0.0174073, 0.0289346, 0.0178525, 0.00842305, 0.00494545, 0.0639696, -0.288241, 0.00128561, -0.0302377, 0.00360149, -0.0252118, -0.050996, 0.0411303, -0.0300041, -0.0137795, -0.0247621, 0.0957016, 0.0127431, 0.07846, -0.0102507, 0.0172816, 0.0193387, -0.0779396, 0.0234571, -0.0529219, -0.0391965, 0.0569404, 0.00277857, -0.00149982, -0.00147603, 0.0, -4.42426e-5, 0.0]
Final objective value: 28586.322643859592
Return code: FTOL_REACHED
julia> mm1.trms[1].Λ
8×8 Array{Float64,2}:
0.476669 0.0 0.0 0.0 0.0 0.0 0.0 0.0
-0.0495603 0.102601 0.0 0.0 0.0 0.0 0.0 0.0
-0.0559578 -0.0172312 0.102309 0.0 0.0 0.0 0.0 0.0
0.0294869 -0.0166362 0.0780709 0.108351 0.0 0.0 0.0 0.0
0.0291771 -0.110942 -0.0945351 0.00551326 0.0 0.0 0.0 0.0
0.0319766 -0.0244482 0.00503189 -0.0540187 0.000989713 0.0 0.0 0.0
-0.0139779 0.0126322 -0.0133206 -0.134323 0.00082312 0.00013651 0.0 0.0
-0.0464195 0.0219091 -0.0649625 0.0515467 -0.000902588 -0.000244137 6.27183e-9 0.0
julia> mm1.trms[2].Λ
8×8 Array{Float64,2}:
0.570451 0.0 0.0 0.0 0.0 0.0 0.0 0.0
-0.0233509 0.0639696 0.0 0.0 0.0 0.0 0.0 0.0
-0.267494 -0.288241 0.0411303 0.0 0.0 0.0 0.0 0.0
0.0174073 0.00128561 -0.0300041 0.07846 0.0 0.0 0.0 0.0
0.0289346 -0.0302377 -0.0137795 -0.0102507 0.0234571 0.0 0.0 0.0
0.0178525 0.00360149 -0.0247621 0.0172816 -0.0529219 0.00277857 0.0 0.0
0.00842305 -0.0252118 0.0957016 0.0193387 -0.0391965 -0.00149982 0.0 0.0
0.00494545 -0.050996 0.0127431 -0.0779396 0.0569404 -0.00147603 -4.42426e-5 0.0