20 
Fishery Bulletin 115(1) 
Table 4 
Summary of chain diagnostics for the fitted models: effective sample size (ESS), credibility R of Gelman index, Geweketest 
(G), Heidelberger-Welch test (HW), and Raftery-Lewis test (RL). In addition, the deviance information criterion (DIG) 
and widely applicable information criterion (WAIC) values for each model are reported, with their estimated number 
of parameters, Pd/c and pwA/c> respectively. The parameters are the asymptotic length (L^), growth rate coefficient (K), 
theoretical age in years when the length is zero (-?o), dispersion (a^), heteroscedasticity (p), skewness (A), and degrees 
of freedom (v). 
Model Parameter ESS 
R 
G 
HW 
RL 
Die 
Pdic WAIC 
PWAIC 
Log-normal (type I) 
Constant 
Loo 
1134.673 
1.002 
1.543 
0.817 
39.4 
-65275.66 
4.338 -65275.66 
7.079 
K 
760.156 
1.003 
-1.241 
0.850 
82.6 
~^0 
934.834 
1.003 
1.518 
0.799 
63.0 
52477.971 
1.000 
1.111 
0.572 
4.6 
Log-normal (type II) 
Constant 
749.129 
1.005 
-1.891 
0.226 
32.4 
-65275.659 
4.338 -66623.850 
8.181 
K 
463.168 
1.008 
1.499 
0.050 
50.3 
0 
569.197 
1.008 
-1.817 
0.456 
35.3 
29883.554 
1.000 
1.510 
0.093 
3.4 
Log-skew-? 
Constant 
Loo 
211.801 
1.022 
1.665 
0.143 
14.9 
-66231.757 
2.918 -66227.642 
6.133 
K 
81.302 
1.037 
-1.118 
0.500 
30.0 
0 
91.705 
1.041 
1.230 
0.393 
60.5 
(fi 
656.456 
1.002 
1.662 
0.654 
6.7 
A 
596.318 
1.004 
-1.598 
0.638 
13.3 
V 
1927.670 
1.005 
-1.232 
0.408 
5.1 
Log-skew-? 
Exponential 
Loo 
204.714 
1.054 
-1.174 
0.436 
8.2 
-66559.569 
6.420 -66556.535 
9.048 
K 
112.927 
1.077 
1.232 
0.471 
43.7 
~^0 
162.885 
1.078 
-1.696 
0.264 
16.9 
p 
561.808 
1.013 
-1.335 
0.504 
8.5 
179.131 
1.029 
1.015 
0.673 
116.0 
A 
1404.850 
1.010 
1.490 
0.247 
8.7 
V 
856.653 
1.007 
-0.771 
0.159 
10.9 
Log-skew-? 
Power 
L„ 
200.944 
1.008 
-1.293 
0.087 
7.7 
-66625.510 
6.482 -66623.850 
8.181 
K 
99.489 
1.052 
0.979 
0.086 
16.0 
“^0 
128.952 
1.053 
-1.223 
0.052 
16.9 
p 
706.436 
1.008 
-0.580 
0.096 
8.7 
(d- 
189.195 
1.029 
0.631 
0.615 
23.6 
A 
1656.937 
1.004 
1.700 
0.355 
5.6 
V 
289.711 
1.016 
-0.481 
0.495 
24.5 
le fitted log-skew-? model (Fig. 3), we can observe that 
(Fig. 
4). As expected. 
we found that the 
log-norm. 
residuals indicate a flat pattern and that their mean is 
concentrated around zero. We noted also a decreasing 
variance in older fish, produced in part by the negative 
value of the estimated heteroscedasticity (p = -0.18). 
Furthermore, extreme values for younger and older fish 
(<6 and >15 years) were detected by the estimated de- 
gree of freedom (u =14.32; Table 3). 
Influential analysis 
Peng-Dey’s criterion (Eq. 17, p; = 0.5) is suitable for 
certain nonlinear regression models with normal er- 
rors and many observations are considered influential 
model has more influential observations than the pow- 
er log-skew-f model for each probability. Therefore, we 
selected, in Table 5, only the probabilities 0.70, 0.60, 
0.55, and 0.51 for those influential observations in log- 
normal and power log-skew-i models. For the selected 
model, when p; = 0.51, the largest number of restricted 
observations was recorded and the RC of the error dis- 
tribution parameters was raised. When the number of 
influential observations increased (in terms of the pj) 
and were removed, the degree of freedom parameter 
also increased. Because several of these observations 
are extreme values (Contreras-Reyes et al., 2014), the 
error distribution shifts from log-skew-? to log-skew-? 
