MDL Model Selection Criterion for Mixed Models with an Application to Spline Smoothing

Model Selection in Linear Mixed Models

“…For a geostatistical model [the linear mixed model with Γ = 0 and Σ = σ 2 R(δ), where the parameters δ describe the spatial correlation between observations, so τ = (δ T , σ 2 ) T and q = q δ + 1], Hoeting et al (2006) use the two-stage code and propose the minimum description length criterion BIC /2. Liski and Liski (2008) consider spline smoothing by fitting the random effect model with one variance component (q γ = 1) and Σ = σ 2 I n . They use the normalized maximum likelihood coding scheme to produce the conditional criterion MDL = −ℓ( θ| u) + log f {q| u(q); θ(q)} dq , where f (y|u; θ) = exp{ℓ(θ|u)} is the conditional density of y|u.…”