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
-1.4293159×10⁴ 2.8586318×10⁴ 2.8748318×10⁴ 2.91930056×10⁴
Variance components:
Column Variance Std.Dev. Corr.
G (Intercept) 90715.0184 301.189340
S 5180.3901 71.974927 -0.43
T 5543.1348 74.452232 -0.47 0.08
U 7584.8816 87.091226 0.21 -0.20 0.41
V 8832.9843 93.983958 0.20 -0.76 -0.54 -0.20
W 1821.9809 42.684668 0.47 -0.53 -0.11 -0.44 0.28
X 7417.1453 86.122850 -0.10 0.13 -0.05 -0.86 -0.06 0.70
Z 3801.0318 61.652509 -0.47 0.41 -0.39 -0.09 0.18 -0.78 -0.39
H (Intercept) 129690.6871 360.125932
S 1856.9765 43.092650 -0.34
T 62370.7020 249.741270 -0.68 -0.45
U 2950.1553 54.315332 0.20 -0.03 -0.18
V 1042.0598 32.280950 0.57 -0.76 0.02 0.02
W 1620.5108 40.255569 0.28 -0.03 -0.27 0.44 -0.21
X 4703.6870 68.583431 0.08 -0.24 0.21 -0.13 -0.26 0.02
Z 4821.2335 69.435103 0.04 -0.47 0.32 -0.68 0.65 -0.69 -0.10
Residual 399627.0136 632.160592
Number of obs: 1790; levels of grouping factors: 56, 32
Fixed-effects parameters:
Estimate Std.Error z value P(>|z|)
(Intercept) 2180.63 76.7856 28.3989 <1e-99
S -66.99 19.3346 -3.46478 0.0005
T -333.881 47.6587 -7.00566 <1e-11
U 78.987 21.235 3.71967 0.0002
V 22.1518 20.3368 1.08925 0.2760
W -18.9243 17.5061 -1.08101 0.2797
X 5.26182 22.4216 0.234677 0.8145
Z -23.951 21.0197 -1.13946 0.2545
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: 2829
Final parameter vector: [0.476444, -0.0495227, -0.0557742, 0.0295214, 0.0292097, 0.0319541, -0.0139336, -0.0463229, 0.102521, -0.0170701, -0.0165868, -0.110967, -0.0243266, 0.0126983, 0.0218126, 0.102316, 0.0781059, -0.0943707, 0.00505476, -0.0135029, -0.0650083, 0.108318, 0.00550319, -0.0540444, -0.134248, 0.0516112, 0.0, 0.000111037, 9.89607e-5, -0.000120772, 0.0, 0.000144849, -0.000171985, 0.0, 1.49074e-5, 0.0, 0.569675, -0.0234122, -0.266913, 0.0173413, 0.0290032, 0.0178621, 0.00844082, 0.0049074, 0.0640206, -0.288127, 0.00329602, -0.0307006, 0.00437284, -0.0241439, -0.053426, 0.0425733, -0.0139551, -0.0162798, -0.0184925, 0.0991966, -0.00479098, 0.0829213, -0.00678668, 0.0223168, 0.000985977, -0.0775749, 0.0226446, -0.0535127, -0.0355039, 0.0560694, 0.00364195, -0.00381326, -0.00114592, 0.0, -5.49465e-5, 0.0]
Final objective value: 28586.31798310179
Return code: FTOL_REACHED
julia> mm1.trms[1].Λ
8×8 LowerTriangular{Float64,Array{Float64,2}}:
0.476444 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
-0.0495227 0.102521 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
-0.0557742 -0.0170701 0.102316 ⋅ ⋅ ⋅ ⋅ ⋅
0.0295214 -0.0165868 0.0781059 0.108318 ⋅ ⋅ ⋅ ⋅
0.0292097 -0.110967 -0.0943707 0.00550319 0.0 ⋅ ⋅ ⋅
0.0319541 -0.0243266 0.00505476 -0.0540444 0.000111037 0.0 ⋅ ⋅
-0.0139336 0.0126983 -0.0135029 -0.134248 9.89607e-5 0.000144849 0.0 ⋅
-0.0463229 0.0218126 -0.0650083 0.0516112 -0.000120772 -0.000171985 1.49074e-5 0.0
julia> mm1.trms[2].Λ
8×8 LowerTriangular{Float64,Array{Float64,2}}:
0.569675 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
-0.0234122 0.0640206 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
-0.266913 -0.288127 0.0425733 ⋅ ⋅ ⋅ ⋅ ⋅
0.0173413 0.00329602 -0.0139551 0.0829213 ⋅ ⋅ ⋅ ⋅
0.0290032 -0.0307006 -0.0162798 -0.00678668 0.0226446 ⋅ ⋅ ⋅
0.0178621 0.00437284 -0.0184925 0.0223168 -0.0535127 0.00364195 ⋅ ⋅
0.00844082 -0.0241439 0.0991966 0.000985977 -0.0355039 -0.00381326 0.0 ⋅
0.0049074 -0.053426 -0.00479098 -0.0775749 0.0560694 -0.00114592 -5.49465e-5 0.0