Metida
Mixed Models
Metida.jl is a Julia package for fitting mixed-effects models with flexible covariance structure. At this moment package is in early development stage.
Main goal to make reproducible output corresponding to SAS/SPSS.
Now implemented covariance structures:
- Scaled Identity (SI)
- Variance Components / Diagonal (VC)
- Autoregressive (AR)
- Heterogeneous Autoregressive (ARH)
- Heterogeneous Compound Symmetry (CSH)
Usage:
LMM(model, data; subject = nothing, random = nothing, repeated = nothing)
where
model is a fixed-effect model (@formula), example: @formula(var ~ sequence + period + formulation)
random vector of random effects or single random effect. Effect can be declared like this: VarEffect(@covstr(formulation), CSH). @covstr is a effect model: @covstr(formulation). CSH is a CovarianceType structure. Premade constants: SI, VC, AR, ARH, CSH.
repeated is a repeated effect (only single).
subject is a block-diagonal factor.
Examples:
using Metida, StatsBase, StatsModels, CSV, DataFrames
df = CSV.File(dirname(pathof(Metida))*"\\..\\test\\csv\\df0.csv") |> DataFrame
# EXAMPLE 1
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#=
PROC MIXED data=df0;
CLASSES subject sequence period formulation;
MODEL var = sequence period formulation/ DDFM=SATTERTH s;
RANDOM formulation/TYPE=CSH SUB=subject G V;
REPEATED/GRP=formulation SUB=subject R;
RUN;
REML: 10.06523862
=#
lmm = LMM(@formula(var ~ sequence + period + formulation), df;
random = VarEffect(@covstr(formulation), CSH),
repeated = VarEffect(@covstr(formulation), VC),
subject = :subject)
fit!(lmm)
#=
Linear Mixed Model: var ~ sequence + period + formulation
Random 1:
Model: formulation
Type: HeterogeneousCompoundSymmetry (3)
Coefnames: ["formulation: 1", "formulation: 2"]
Repeated:
Model: formulation
Type: VarianceComponents (2)
Coefnames: ["formulation: 1", "formulation: 2"]
Status: converged
-2 logREML: 10.0652
Fixed effects:
Name Estimate SE
(Intercept) 1.57749 0.334543
sequence: 2 -0.170833 0.384381
period: 2 0.195984 0.117228
period: 3 0.145014 0.109171
period: 4 0.157363 0.117228
formulation: 2 -0.0791667 0.0903709
Random effects:
θ vector: [0.455584, 0.367656, 1.0, 0.143682, 0.205657]
Random 1 formulation: 1 var 0.207557
Random 1 formulation: 2 var 0.135171
Random 1 Rho rho 1.0
Repeated formulation: 1 var 0.0206445
Repeated formulation: 2 var 0.0422948
=#
# EXAMPLE 2
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#=
PROC MIXED data=df0;
CLASSES subject sequence period formulation;
MODEL var = sequence period formulation/ DDFM=SATTERTH s;
RANDOM formulation/TYPE=VC SUB=subject G V;
REPEATED/GRP=formulation SUB=subject R;
RUN;
REML: 16.06148160
=#
lmm = LMM(
@formula(var ~ sequence + period + formulation), df;
random = VarEffect(@covstr(formulation), SI),
repeated = VarEffect(@covstr(formulation), VC),
subject = :subject,
)
fit!(lmm)
#=
Linear Mixed Model: var ~ sequence + period + formulation
Random 1:
Model: formulation
Type: ScaledIdentity (1)
Coefnames: ["formulation: 1", "formulation: 2"]
Repeated:
Model: formulation
Type: VarianceComponents (2)
Coefnames: ["formulation: 1", "formulation: 2"]
Status: converged
-2 logREML: 16.0615
Fixed effects:
Name Estimate SE
(Intercept) 1.57212 0.305807
sequence: 2 -0.170833 0.279555
period: 2 0.204087 0.289957
period: 3 0.155769 0.11308
period: 4 0.160015 0.289957
formulation: 2 -0.0791667 0.279555
Random effects:
θ vector: [0.412436, 0.145184, 0.220819]
Random 1 Var var 0.170103
Repeated formulation: 1 var 0.0210784
Repeated formulation: 2 var 0.048761
=#
#EXAMPLE 3
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#=
PROC MIXED data=df0;
CLASSES subject sequence period formulation;
MODEL var = sequence period formulation/ DDFM=SATTERTH s;
RANDOM subject/TYPE=VC G V;
RUN;
REML: 10.86212458
=#
lmm = LMM(@formula(var ~ sequence + period + formulation), df;
random = VarEffect(@covstr(subject), SI)
)
fit!(lmm)
#=
Linear Mixed Model: var ~ sequence + period + formulation
Random 1:
Model: subject
Type: ScaledIdentity (1)
Coefnames: ["subject: 1", "subject: 2", "subject: 3", "subject: 4", "subject: 5"]
Repeated:
Model: nothing
Type: ScaledIdentity (1)
Coefnames: -
Status: converged
-2 logREML: 10.8621
Fixed effects:
Name Estimate SE
(Intercept) 1.61 0.309774
sequence: 2 -0.170833 0.383959
period: 2 0.144167 0.116706
period: 3 0.08 0.115509
period: 4 0.144167 0.116706
formulation: 2 -0.0791667 0.0833617
Random effects:
θ vector: [0.410574, 0.182636]
Random 1 Var var 0.168571
Repeated Var var 0.0333559
=#
#EXAMPLE 4
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#=
PROC MIXED data=df0;
CLASSES subject sequence period formulation;
MODEL var = sequence period formulation/ DDFM=SATTERTH s;
RANDOM period/TYPE=VC G V;
RANDOM formulation/TYPE=VC G V;
RUN;
REML: 25.12948063
=#
lmm = LMM(
@formula(var ~ sequence + period + formulation), df;
random = [VarEffect(@covstr(period), VC), VarEffect(@covstr(formulation), VC)]
)
fit!(lmm)
#=
Linear Mixed Model: var ~ sequence + period + formulation
Random 1:
Model: period
Type: VarianceComponents (4)
Coefnames: ["period: 1", "period: 2", "period: 3", "period: 4"]
Random 2:
Model: formulation
Type: VarianceComponents (2)
Coefnames: ["formulation: 1", "formulation: 2"]
Repeated:
Model: nothing
Type: ScaledIdentity (1)
Coefnames: -
Status: converged
-2 logREML: 25.1295
Fixed effects:
Name Estimate SE
(Intercept) 1.61 0.249491
sequence: 2 -0.170833 0.192487
period: 2 0.144167 0.269481
period: 3 0.08 0.266717
period: 4 0.144167 0.269481
formulation: 2 -0.0791667 0.192487
Random effects:
θ vector: [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.421717]
Random 1 period: 1 var 0.0
Random 1 period: 2 var 0.0
Random 1 period: 3 var 0.0
Random 1 period: 4 var 0.0
Random 2 formulation: 1 var 0.0
Random 2 formulation: 2 var 0.0
Repeated Var var 0.177845
=#
#EXAMPLE 5
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#=
PROC MIXED data=df0;
CLASSES subject sequence period formulation;
MODEL var = sequence period formulation/ DDFM=SATTERTH s;
RANDOM formulation/TYPE=UN(1) SUB=subject G V;
RUN;
REML: 16.24111264
=#
lmm = LMM(@formula(var ~ sequence + period + formulation), df;
random = VarEffect(@covstr(formulation), VC),
subject = :subject)
fit!(lmm)
#=
Linear Mixed Model: var ~ sequence + period + formulation
Random 1:
Model: formulation
Type: VarianceComponents (2)
Coefnames: ["formulation: 1", "formulation: 2"]
Repeated:
Model: nothing
Type: ScaledIdentity (1)
Coefnames: -
Status: converged
-2 logREML: 16.2411
Fixed effects:
Name Estimate SE
(Intercept) 1.61 0.334718
sequence: 2 -0.170833 0.277378
period: 2 0.144167 0.289463
period: 3 0.08 0.117047
period: 4 0.144167 0.289463
formulation: 2 -0.0791667 0.277378
Random effects:
θ vector: [0.447322, 0.367367, 0.185068]
Random 1 formulation: 1 var 0.200097
Random 1 formulation: 2 var 0.134959
Repeated Var var 0.0342502
=#
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