149 
Abstract.-Many tuned assessment 
models, such as sequential population 
analysis and nonequilibrium produc- 
tion models, are cast in the form of 
least-squares minimization routines. It 
is well known that outliers can substan- 
tially alter the results of least-squares 
methods. Indeed, in the process of con- 
ducting stock assessments, much time 
and effort are often spent in discussing 
the merits of individual data points and 
in evaluating the impact that includ- 
ing or excluding them has on the per- 
ceived stock status. Unfortunately, 
straight-forward statistical tests for 
detecting outliers have been developed 
only for univariate statistics or for the 
simplest of linear models and are gen- 
erally useful to test for a single outlier 
only. In this paper, we apply a high- 
breakdown robust regression tech- 
nique, least trimmed squares, to two 
assessment models using North Atlan- 
tic swordfish and West Atlantic bluefin 
tuna as examples. We illustrate how 
robust regression can be used as an ini- 
tial step in statistically detecting out- 
liers before the more efficient least- 
squares minimization can be used. 
Manuscript accepted 30 July 1996. 
Fishery Bulletin 95:149-160 (1997). 
Application of high-breakdown 
robust regression to tuned 
stock assessment models 
Victor R. Restrepo 
Rosenstie! School of Marine and Atmospheric Science, Cooperative Unit for Fisheries 
Education and Research 
University of Miami, 4600 Rickenbacker Causeway, Miami, Florida 33 1 49 
E-mail address: vrestrepo@rsmas.miami.edu 
Joseph E. Powers 
National Marine Fisheries Service, Southeast Fisheries Science Center 
75 Virginia Beach Drive, Miami, Florida 33149 
Tuned stock assessment models are 
statistical methods that analyze 
time series of fishery catch data in 
conjunction with auxiliary informa- 
tion (indices of relative abundance, 
fishing effort, etc. ) to yield estimates 
of stock abundance and exploitation 
rates over time. Such methods are 
widely used today by stock assess- 
ment working groups throughout 
the world because they provide an 
objective and statistically defensible 
way to assess the status of stocks 
and to derive management advice. 
The two primary methods are se- 
quential population analysis (SPA: 
Fournier and Archibald, 1982; 
Deriso et al., 1985; Pope and Shep- 
herd, 1985; Kimura, 1989; Methot, 
1990; Powers and Restrepo, 1992; 
Gavaris 1 ) and nonequilibrium pro- 
duction models (Pella and Tom- 
linson, 1969; Hilborn, 1990; Hilborn 
and Walters, 1992; Prager, 1994). 
SPA’s are typically age structured 
and production models are not, al- 
though there are exceptions to this 
generalization in the references just 
cited. Both types of methods, how- 
ever, share the commonality of of- 
ten being cast as nonlinear least- 
squares minimization problems. 
Despite efforts to standardize all 
steps involved in a stock assessment 
(from data collection, preparation of 
model inputs, to running the mod- 
els), stock assessments are rarely 
automated and, more often than 
not, generate controversy. In our 
experience with different fora, a 
common cause for controversy is as 
follows: various data sets are pre- 
sented to a working group and then 
the group collectively decides on the 
sets of data and model assumptions 
to be used. The consensus selection 
is typically termed the “base case.” 
Individual data points are then 
scrutinized for exclusion from fur- 
ther analyses to determine the ro- 
bustness of the overall assessment 
to the sensitivity changes. This par- 
tial “sensitivity analysis” can, in 
practice, be undesirable because 
perceptions of what results ought to 
be like may influence which data or 
data points are scrutinized and thus 
generate controversy; not every 
working group participant has the 
same perception. The lack of an a 
priori objective selection process 
could lead working groups astray 
(Restrepo and Powers, 1995). A so- 
1 Gavaris, S. 1988. An adaptive frame- 
work for the estimation of population size. 
Can. Atl. Fish. Sci. Adv. Comm. (CAFSAC) 
Res. Doc. 88/29, 12 p. Biological Station, 
Department of Fisheries and Oceans, St. 
Andrews, New Brunswick, Canada EOG 
2X0. 
