Table 5.

Comparisons of various GAMLSS models with different distributions and different levels of modeling of parameters.

Model	Global Deviance	df for μ	df for σ	df for ν	df for τ	df	AIC	BIC
IG, μ	10,450	104.47	1.00	0	0	105.47	10,661	11,224
IG, μ and σ	10,246	117.55	52.38	0	0	169.93	10,586	11,492
DEL, μ	10,456	79.73	1.00	1	0	81.73	10,619	11,055
DEL, μ and σ	10,356	83.24	20.42	1	0	104.66	10,565	11,123
DEL, μ, σ, and ν	10,344	83.14	18.86	4.00	0	106.00	10,556	11,121
BCCG, μ	10,424	105.68	1.00	1	0	107.68	10,640	11,214
BCCG, μ and σ	10,222	121.08	48.71	1	0	170.79	10,563	11,474
BCCG, μ, σ, and ν	10,219	121.38	49.42	3.00	0	173.80	10,567	11,494
BCT, μ	10,403	109.62	1.00	1	1	112.62	10,628	11,228
BCT, μ and σ	10,199	123.14	53.59	1	1	178.73	10,557	11,510
BCT, μ, σ, and ν	10,184	124.54	55.24	6.22	1	187.00	10,558	11,555
BCT, μ, σ, ν, and τ	10,184	124.54	55.24	6.22	1	187.00	10,558	11,555

In each model, a penalized P-spline smooth function is used for the three continuous predictors, and a penalized random effect smoother for the categorical variable. The three lowest AIC and BIC are in bold. IG, inverse-Gaussian; DEL, Delaporte; BCCG, Box-Cox Green and Cole; and BCT, Box-Cox t