Random Effect and Latent Variable Model Selection by David B. Dunson

Author:David B. Dunson
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

(2)λ = (0.2, 0, 0.7, 0, 0.5)′ and γ = (0,0.4, 0, 0,0, 0,0.8, 0, 0.1, 0)′, implying that the second and the fourth random effects are excluded from the model.

(3)λ = (0.5,0.8, 0.9,0.2, 0.1,0.1, 0.6,0)′ and γ = (0.3,0.6,0.5,0.4,0.2,0.1, 0.2, 0.3, 0.4, 0.3, 0.6, 0.1, 0.2, 0.1, 0.8,0.3, 0.4,0.8, 0.6,0.3, 0.2, 0, 0, 0, 0, 0, 0, 0)′, implying that the last random effect is excluded from the model.

The corresponding covariance matrices for random effects are shown in the first row in Fig. 1. For the GLMM with identity link, y ij ~ N(x′ ij β + z′ ij ζ i , σ−2) with σ−2 = 2. For the GLMM with logit link, y ij ~ Bernoulli(π ij ) with logit(π ij ) = x′ ij β + z′ ij ζ i . For the GLMM with log link, y ij ~ Poisson(λ ij ) with log(λ ij ) = x′ ij β+z′ ij ζ i .

Fig. 1Image plots of the true and estimated random effects covariance matrices for simulated data under the identity link, logit link and log link with the number of candidate random effect predictors being 3, 5 and 8. The darker the color appears, the larger the value of the element is, with the white color corresponding to zero

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