de Silva and Condrey: Patterns in patchy data discerned from Brevoortia patronus bycatch 
197 
models were examined to determine if 
o o 
model assumptions were met. § S 
Spatial and temporal patterns in by- 
catch For our analysis using loglinear 
and logit models with categorical explana- 
tory variables, we used a four-way con- 
tingency table with a unit of effort (the 
set) as the count. Our main interest was 
1) to examine the spatial and temporal 
patterns in bycatch and 2) to determine 
if the presence of dolphins in the vicinity 
when the set was made might be an indi- 
cator of bycatch patterns. 
Exploratory analysis with loglinear and 
logit models To examine bycatch as a 
response of interest with categorical mod- 
els, a new dichotomous categorical vari- 
able, bycatch, based on the median bycatch 
percentage, was created. Each set was clas- 
sified either as high bycatch if the bycatch 
rate of the set was greater than the me- 
dian value of all sets or as low bycatch if 
the bycatch rate of the set was less than or 
equal to the median bycatch of all the sets. 
We used the median rate because it is a 
robust measure of central tendency. In de- 
ciding on possible criteria for defining this 
variable, more extreme conditions, such as 
bycatch rates greater than the 75 th percen- 
tile, were considered. However, by choosing 
more extreme values, we increased the 
number of sparse cells and thus affected 
the validity of the G 2 test statistic. 
In analyzing contingency tables, it is 
necessary that the number of cell counts 
with zero frequencies be low (a minimum 
expected value of 1 is satisfactory as long 
as <20% of cells have counts of 5 or less) 
for the test statistic to be valid (Agresti, 
1990). To reduce the number of cells with 
zero frequencies, months and zones were 
combined, generating two new variables, 
season and area, corresponding to those 
used in the AN OVA. The presence of dol- 
phins was used as a dichotomous variable, 
dolphins (D). 
To identify the most appropriate and 
simplest loglinear model for the data us- 
ing the variables season, area, bycatch, 
and dolphins, we employed a stepwise 
backward solution procedure commenc- 
ing with the saturated loglinear model 
(Agresti, 1990). Here the saturated model 
Figure 1 
Map encompassing the extent of the U.S. gulf menhaden fishery from the Texas to Alabama coasts. The eight fishing zones numbered 11-18 are from NMFS (after 
Kutkuhn, 1962). 
