Table 3.

Analysis of residuals for in-sample posterior predictions and out-of-sample cross-validations (X-val)

Parameter	Prediction	Bias	Imprecision	Inaccuracy	$r^2$
$N_i$	In sample	34 (0.06)	252 (0.50)	179 (0.38)	0.38
$N_i$	X-val random	36 (0.04)	284 (0.57)	199 (0.43)	0.26
$N_i$	X-val state	121 (0.11)	313 (0.54)	257 (0.43)	0.08
$D_i$	In-sample	7 (0.06)	86 (0.50)	61 (0.38)	0.57
$D_i$	X-val random	8 (0.04)	96 (0.57)	67 (0.43)	0.46
$D_i$	X-val state	24 (0.11)	121 (0.54)	92 (0.43)	0.40

Residuals (predicted minus observed) were calculated based on the mean of the posterior predicted distribution. Bias is the mean of residuals; imprecision is the SD of residuals; inaccuracy is the mean of absolute residuals; r₂ is the squared Pearson correlation coefficient for observed versus predicted values. Values in parentheses are based on scaled residuals (residual/predicted).