First step · Metida.jl

Installation

import Pkg; Pkg.add("Metida")

Simple example

Step 1: Load data

Load provided data with CSV and DataFrames:

using Metida, CSV, DataFrames, CategoricalArrays

df = CSV.File(joinpath(dirname(pathof(Metida)), "..", "test", "csv", "df0.csv")) |> DataFrame;

Note

Check that all categorical variables are categorical.

transform!(df, :subject => categorical, renamecols=false)
transform!(df, :period => categorical, renamecols=false)
transform!(df, :sequence => categorical, renamecols=false)
transform!(df, :formulation => categorical, renamecols=false)

Make model with @formula macro from StatsModels. Define random and repreated effects with Metida.VarEffect using Metida.@covstr macros. Left side of @covstr is model of effect and right side is a effect itself. Metida.HeterogeneousCompoundSymmetry and Metida.Diag (Diagonal) in example bellow is a model of variance-covariance structure. See also Metida.@lmmformula macro.

Note

In some cases levels of repeated effect should not be equal inside each level of subject or model will not have any sense. For example, it is assumed that usually CSH or UN (Unstructured) using with levels of repeated effect is different inside each level of subject. Metida does not check this!

lmm = LMM(@formula(var~sequence+period+formulation), df;
random = VarEffect(@covstr(formulation|subject), CSH),
repeated = VarEffect(@covstr(formulation|subject), DIAG));

Linear Mixed Model: var ~ sequence + period + formulation
Random 1: 
    Model: formulation|subject
    Type: CSH (3), Subjects: 5
Repeated: 
    Model: formulation|subject
    Type: DIAG (2)
Blocks: 5, Maximum block size: 4
Not fitted.

Also Metida.@lmmformula macro can be used:

lmm = LMM(@lmmformula(var~sequence+period+formulation,
    random = formulation|subject:CSH,
    repeated = formulation|subject:DIAG),
    df)

Step 3: Fit

Just fit the model.

fit!(lmm)

Linear Mixed Model: var ~ sequence + period + formulation
Random 1: 
    Model: formulation|subject
    Type: CSH (3), Subjects: 5
Repeated: 
    Model: formulation|subject
    Type: DIAG (2)
Blocks: 5, Maximum block size: 4
Status: converged (No Errors)
    -2 logREML: 10.0652    BIC: 23.9282

    Fixed-effects parameters:
───────────────────────────────────────────────────────
                     Coef.  Std. Error      z  Pr(>|z|)
───────────────────────────────────────────────────────
(Intercept)      1.57749     0.334543    4.72    <1e-05
sequence: 2     -0.170833    0.384381   -0.44    0.6567
period: 2        0.195984    0.117228    1.67    0.0946
period: 3        0.145014    0.109171    1.33    0.1841
period: 4        0.157363    0.117228    1.34    0.1795
formulation: 2  -0.0791667   0.0903709  -0.88    0.3810
───────────────────────────────────────────────────────
    Variance components:
    θ vector: [0.455584, 0.367656, 1.0, 0.143682, 0.205657]
  Random 1   σ² formulation: 1   var   0.207557
  Random 1   σ² formulation: 2   var   0.135171
  Random 1   ρ                   rho   1.0
  Residual   σ² formulation: 1   var   0.0206445
  Residual   σ² formulation: 2   var   0.0422948

Check warnings and errors in log.

lmm.log

3-element Vector{Metida.LMMLogMsg}:
   INFO  : Initial θ: [0.21085850593184405, 0.21085850593184405, 0.0001, 0.21085850593184405, 0.21085850593184405]

   INFO  : Resulting θ: [0.455584290622586, 0.36765619780142395, 0.9999999999967146, 0.1436824286508881, 0.20565739028506558]; 25 iterations.

   INFO  : Model fitted.

Confidence intervals for coefficients

confint(lmm)

6-element Vector{Tuple{Float64, Float64}}:
 (0.543714563732745, 2.611271160890932)
 (-1.3939795005801323, 1.0523128339134646)
 (-0.07012519946854545, 0.46209405823764527)
 (-0.09895082360335769, 0.3889793743560057)
 (-0.10874644952798812, 0.4234728081782028)
 (-0.3056725658640148, 0.14733923253068223)

Note

Satterthwaite approximation for the denominator degrees of freedom used by default.

StatsBsae API

StatsBsae API implemented: Metida.islinear, Metida.confint, Metida.coef, Metida.coefnames, Metida.dof_residual, Metida.dof, Metida.loglikelihood, Metida.aic, Metida.bic, Metida.aicc, Metida.isfitted, Metida.vcov, Metida.stderror, Metida.modelmatrix, Metida.response, Metida.crossmodelmatrix, Metida.coeftable, Metida.responsename

Type III Tests of Fixed Effects

Warning

Experimental

typeiii(lmm)

 ------------- ---------- ----- --------- -----------
         Name          F   ndf       ddf        pval
 ------------- ---------- ----- --------- -----------
  (Intercept)    22.2346   1.0   3.16597   0.0159885
     sequence   0.197525   1.0   3.00055    0.686828
       period     1.0789   3.0   8.66853    0.407683
  formulation   0.767409   1.0   5.46311    0.417867
 ------------- ---------- ----- --------- -----------

Model construction

To construct model you can use LMM constructor.

model - example: @formula(var ~ sequence + period + formulation)
random - effects can be specified like this: VarEffect(@covstr(formulation|subject), CSH). @covstr is a effect model: @covstr(formulation|subject). CSH is a CovarianceType structure. Premade constants: SI, DIAG, AR, ARH, CS, CSH, ARMA, TOEP, TOEPH, UN, ets. If not specified only repeated used.
repeated - can be specified like random effect. If not specified VarEffect(@covstr(1|1), SI) used. If no repeated effects specified vector of ones used.