[ANN] Metida.jl: mixed-effects models fitting package

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22

Is the unstructure covariance structure the same as in MixedModels.jl without zerocorr()?

23

Yes:

using Metida, CSV, DataFrames, CategoricalArrays, MixedModels;
rds2 = CSV.File(joinpath(dirname(pathof(Metida)), "..", "test", "csv",  "ftdf3.csv"); types = [String,  Float64, Float64, String, String, String, String, String, Float64]) |> DataFrame

MixedModels:

mm = fit(MixedModel, @formula(response ~ factor+ (0+r1|subject)), rds2, REML = true)

Linear mixed model fit by REML
 response ~ 1 + factor + (0 + r1 | subject)
 REML criterion at convergence: 705.3822336725552

Variance components:
         ColumnVariance Std.Dev.  Corr.
subject  r1: A   8.51765 2.91850
         r1: B  12.72191 3.56678 +0.46
         r1: C  21.13547 4.59733 +0.46 +0.58
Residual         1.01648 1.00820
 Number of obs: 168; levels of grouping factors: 24

  Fixed-effects parameters:
──────────────────────────────────────────────────
                Coef.  Std. Error      z  Pr(>|z|)
──────────────────────────────────────────────────
(Intercept)   40.1983     0.79166  50.78    <1e-99
factor       -11.0272     1.11958  -9.85    <1e-22
──────────────────────────────────────────────────

Metida:

lmm = Metida.LMM(@formula(response~factor), rds2;
    random = Metida.VarEffect(Metida.@covstr(r1|subject), UN),
    )
Metida.fit!(lmm)

Linear Mixed Model: response ~ factor
Random 1:
    Model: r1|subject
    Type: UN (6), Subjects: 24
Repeated: 
    Residual only
Blocks: 24, Maximum block size: 7
Status: converged (No Errors)
    -2 logREML: 705.382    BIC: 741.166

    Fixed-effects parameters:
──────────────────────────────────────────────────
                Coef.  Std. Error      z  Pr(>|z|)
──────────────────────────────────────────────────
(Intercept)   40.1983    0.791652  50.78    <1e-99
factor       -11.0271    1.11956   -9.85    <1e-22
──────────────────────────────────────────────────
    Variance components:
    θ vector: [2.91848, 3.56669, 4.59709, 0.458287, 0.463127, 0.575315, 1.00823]
  Random 1   σ² r1: A           var   8.51753
  Random 1   σ² r1: B           var   12.7213
  Random 1   σ² r1: C           var   21.1332
  Random 1   ρ: r1: A × r1: B   rho   0.458287
  Random 1   ρ: r1: A × r1: C   rho   0.463127
  Random 1   ρ: r1: B × r1: C   rho   0.575315
  Residual   σ²                 var   1.01653
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24

Metida 0.16.3 released.

Add covariance modificator.

With ACOV covariance structure it is possible to change existed covariance structure and add covariance with AR or CH pattern.

So…

LMM(@formula(response ~ 1), ftdf3;
    repeated = [VarEffect(@covstr(r1|subject), DIAG), 
                VarEffect(@covstr(1|subject), ACOV(AR))])

is the same as:

LMM(@formula(response ~ 1), ftdf3;
repeated = VarEffect(Metida.@covstr(r1|subject), ARH))

But other blocking factors can be used for covariation pattern:

LMM(@formula(response ~ 1), ftdf3;
    repeated = [VarEffect(@covstr(r1|subject), DIAG), 
                VarEffect(@covstr(1|r2), ACOV(CS))])

Or some complicated structures can be build by this way:

LMM(@formula(resp ~ 0 + device), devday;
    repeated = [VarEffect(Metida.@covstr(device|subj&day), UN), 
                VarEffect(Metida.@covstr(1|subj&device), ACOV(AR))])

see example here

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