328 



Fishery Bulletin 89(2), 1991 



The above model descriptions are a common way of 

 representing loglinear models. Model 1 indicates that 

 the logarithm of the count in any cell can be predicted 

 as the sum of the main effects for molt status, year of 

 tagging, and location, i.e., these factors act indepen- 

 dently. Model 3 is the same as model 1 except that an 

 interaction term (or dependency) between year of tag- 

 ging and location of anchor is also needed to predict 

 the counts. Model 4 has a similar interpretation but the 

 logarithm of the count depends on an interaction be- 

 tween anchor location and molt status. Model 5 includes 

 the interaction between year and location and between 

 molt status and location. Thus, models 1 and 3 imply 

 no differential survival/tag retention among tagging 

 locations, whereas models 4 and 5 imply that tagging 

 location has an effect on the probability of surviving 

 a molt with the tag still in place. 



The difference between models 1 and 3 is that model 

 3 implies that the proportions of animals tagged in each 

 location varied between the two years while model 1 

 implies the same proportions occurred in both years. 

 If year has no effect on location (i.e., the interaction 

 between year and location is unimportant), then a test 

 of the effect of location on survival/retention through 

 molt can be achieved by comparing models 1 and 4. But, 

 if the proportions tagged in each location varied among 

 the years, then the comparison that isolates the effect 

 of tagging location on survival/retention through molt 

 is the comparison of models 3 and 5. 



The choice between two nested models can be made 

 on the basis of a likelihood ratio test by subtracting the 

 log-likelihoods and referring to a x 2 table with degrees 

 of freedom equal to the difference in degrees of free- 

 dom for the two models. The computed test statistic 

 for comparing models 1 and 3 is 



X 2 com P = 13.31 - 7.03 = 6.28, df = 10 - 7 = 3 



and the resulting P -value is 0.099. We fail to reject 

 model 1 in favor of model 3 at the 5% level and con- 

 clude that the evidence is not strong enough to con- 

 clude that the proportions tagged in each body loca- 

 tion varied by year. However, the test results could be 

 considered marginally or nearly significant. 



The hypothesis of interest is whether the tagging 

 location affects the survival/retention through molt. 

 This can be accomplished by comparing models 1 and 4, 



X 2 com P = 13.31-8.11 = 5.20, df = 10-7 = 3, 



for which the P-value is 0.1577. Alternatively, we can 

 compare models 3 and 5 and obtain virtually the same 

 results. Thus, the statistical evidence is not strong 

 enough to conclude that location affects survival/reten- 

 tion through molt at the customary 5% level. However, 



in light of the small sample sizes and possible low power 

 of the test, the results provide some evidence, albeit 

 weak, that location may be important. 



Since at least one two-factor interaction involving 

 year is not significant in each of the models we con- 

 sidered, one can validly collapse the three-dimensional 

 table over year to obtain a 2 x 4 table. The estimated 

 relative retention/ survival rates, a, can be computed 

 from the pooled data (Table 1). Relative to animals 

 tagged in the dorsal musculature, the tag retention/ 

 survival of animals with tag anchors loose in the body 

 cavity, embedded in shell, and in the dorsal leg 

 musculature are estimated to be 0.23, 0.95, and 1.10, 

 respectively. 



Although 18% of the dissected animals had some 

 blackening around the anchor of the tag, only 2 animals 

 (1.5%) had extensive areas of necrosis. All animals had 

 been at liberty for at least a year. The proportion of 

 animals with necrotic tissue did not appear to vary 

 much among the different tagging locations (Table 2). 



Discussion 



Although the laboratory study indicated that tagged 

 animals die at the time of molting if the tag anchor 

 lodges in the basal leg musculature, there was no evi- 

 dence of this in the field data. We hypothesize that this 

 is because the field-tagged animals were larger than 

 the laboratory animals, and larger animals may toler- 

 ate a tag in the leg musculature better than smaller 

 animals. If relative retention/survival due to anchor 

 location depends on size of the animals, then size cate- 

 gory should be considered as another variable in the 

 analysis. However, in our field study only animals in 

 a narrow range of sizes (82- 120 mm CW at tagging) 

 were examined so that there seems little point in 

 dividing the limited number of recaptures into size 

 classes. 



Since the field data indicate that having the end of 

 the tag loose in the body cavity reduces the chances 

 of recovering the animal with tag intact (a 0.23), and 

 the laboratory data indicate that tagging in the basal 

 leg musculature reduces recoveries, it seems prudent 

 to try to insert the tag anchor into the dorsal muscu- 

 lature. Our lack of statistically significant results does 

 not imply that tagging location is not a significant 

 biological factor in determining the success of a tag- 

 ging program. Rather, it may simply indicate that our 

 sample sizes were inadequate to obtain strong evidence 

 of the importance of location. We recommend that, 

 prior to initiating a field tagging program, a few trial 

 animals be sacrificed to determine how consistently the 

 tag anchor is being placed into the targeted dorsal 

 musculature. 



