For. Snow Landsc. Res. 81, 1/2: 163–174 (2007)
163
Linking agent-based and choice models to study outdoor
recreation behaviours: a case of the Landscape Fisheries Model
in northern Ontario, Canada
Len M. Hunt1, Rob Kushneriuk1 and Nigel Lester2
1
2
Centre for Northern Forest Ecosystem Research, Ontario Ministry of Natural Resources, 955 Oliver
Road, Thunder Bay, ON, Canada, P7B 5E1. [email protected], [email protected]
Aquatic Research and Development Section, Ontario Ministry of Natural Resources, 2140 East
Bank Drive, Peterborough, ON, Canada, K9J 7B8, [email protected]
Abstract
Agent-based and choice models represent two popular approaches for modelling recreational
behaviours. While these approaches investigate similar research questions and focus on individual
behaviours, there is no formal link between these approaches within outdoor recreation research.
This article demonstrates an initial attempt to benefit from the marriage of agent-based and
choice modelling approaches. After assessing the strengths and weaknesses of each approach, we
illustrate our Landscape Fisheries Model. This model predicts the amount, timing, type, location
and value of recreational fishing trips at a landscape scale. Choice models of participation and site
choice decisions are used to guide the behaviours of the agents. The resulting model benefits from
the virtual world of the agent-based model and the theoretical grounding of choice models.
Keywords: agent-based model, choice model, recreational fishing, behaviour, forecast, landscape
scale, scenario
1
Introduction
Recreational management requires a careful balance of providing opportunities while
minimizing impacts to the environment and the experiences of recreationists. Effective
management of recreation resources requires good information about these impacts, which
one can provide, in part, by models of recreational behaviours.
Models can provide two types of information that are important for recreational
managers. First, models can describe the status of recreational use and associated impacts
from such use. Sometimes models can provide opportunities to describe information that is
often difficult to capture solely from monitoring efforts (e.g., the frequency of encounters
among recreationists).
Second, researchers and managers can use models for forecasting purposes through
scenarios. Scenarios that evaluate both changes to resource quality or the management of
the resource may be explored. The forecast models can help researchers and managers
evaluate possible consequences of the scenario on the behaviours of outdoor recreationists.
These predictions allow managers to understand the consequences of change without
implementing the scenario.
Agent-based (ABM) and choice models (CM) represent two popular approaches to
model outdoor recreation behaviours. The ABMs adopt a simulated world from which
artificial agents (i.e., recreationists) can interact and behave. Predefined levels of mobility,
164
Len M. Hunt et al.
cognition, and preferences affect the behaviours of agents (ITAMI et al. 2003). Rules, which
are typically defined through observation and expert judgement (MANNING et al. 2005), also
guide the behaviours of agents. Agents use these rules to navigate through the simulated
environments and encounters with other agents. The ABMs can describe current recreational
use patterns and forecast the effects of management scenarios on these use patterns.
Choice models (CM) are statistical models that are developed from theories of human
behaviour (utility maximization) and behavioural modelling (random utility theory).
Individuals are assumed to choose the one alternative from a set of discrete alternatives
(e.g., recreational sites) that provides him/her with maximum utility (i.e., an abstract
measure of aggregate preference). Since one cannot expect to understand all aspects that
lead to utility, researchers incorporate randomness when modelling choice (BEN-AKIVA and
LERMAN 1985; MANSKI 1977). The CMs provide probabilistic models that predict the
likelihood that an individual will select a certain alternative from a set of alternatives. One
can estimate these models with actual (i.e., revealed preference) or hypothetical (i.e., stated
preference) data on choices. Some researchers have also estimated CMs from both stated
and revealed choice data (BEN-AKIVA and MORIKAWA 1990; ADAMOWICZ et al. 1997).
Despite the popularity of ABMs and CMs for studying recreational behaviours, the merger
of the two approaches is absent from the published literature on outdoor recreation. This
absence is surprising since both modelling approaches are used to investigate similar
research questions and the approaches rely on similar data. We illustrate a model that takes
advantage of both modelling approaches to examine outdoor recreational behaviours. The
Landscape Fisheries Model (LFM) was developed as a spatial database and forecasting tool
for scenario planning in recreational fishing. The application of the LFM comes from data
calibrated for fishing participation and site choices by resident anglers of northern Ontario,
Canada. With appropriate data and model calibration, one may employ the LFM in other
landscapes.
The next section closely assesses the strengths and weaknesses of traditional ABM and
CM approaches, and examines the benefits of linking both approaches. The third section
describes our empirical application of recreational fishing. Finally, the paper highlights the
contributions of our model and identifies further opportunities for researchers to link the
two approaches.
2
Comparing agent-based and choice models
We evaluate ABMs and CMs on several dimensions and compare their strengths and weaknesses. Both modelling approaches examine recreational behaviours from the perspective of
the individual (see Table 1). As such, it is possible to assess how individual decisions are
likely to affect overall patterns of recreational use. While CMs are developed explicitly from
contemporary interpretations of random utility theory (MANSKI 1977), theoretical justification for ABMs is weak. The ABMs, instead, are justified on the ability of the agents to
reproduce behaviours from real world data (COLE et al. 2005).
165
For. Snow Landsc. Res. 81, 1/2 (2007)
Table 1. Comparison of agent-based and choice models.
Model focus
Theoretical justification
Landscape scale application
Site scale application
Agent behavioural rules
Agent learning
Agent heterogeneity
Multiple agents
Scenario testing
Economic welfare
Communication potential
Communication practice
Agent-based model
Individual behaviours
Weak
Moderate
Easy
Expert opinion
Moderate
Easy
Easy
Yes
No
High
High
Choice model
Individual behaviours
Strong
Easy
Difficult
Statistically derived
Difficult
Moderate
Difficult
Yes
Yes
High
Low
Agent-based models are ideally suited to study the behaviours of recreationists at the site
scale. The intense data collection, flexibility of the models, and the emphasis on traffic
simulation all make ABMs better suited than CMs to examine fine scale behaviours of
recreationists. The reliance of the CMs on theory and the resulting less intense demands for
data collection makes application of CMs better suited for landscape level behaviours than
ABMs.
A CM predicts behaviours of individuals by statistically estimating the parameters of
models that are consistent with random utility theory. Agent-based models often appeal to
experts for identifying rules to govern agent behaviours. The independence from a statistical
model makes the ABMs much more flexible at accommodating learning and heterogeneity
in preferences than choice models. Developments to CMs such as the random parameters
logit (see TRAIN 1998) and latent class choice model (SWAIT 1994) are permitting greater
opportunities to accommodate heterogeneous preferences among recreationists. Estimating
choice models with learning remains a difficult task.
Accounting for multiple agents is simpler within an ABM than a CM. For example,
researchers can account for outdoor recreation and biological (e.g., wildlife, fish, etc.) agents
within ABMs by specifying the behavioural rules for each agent. While some researchers
have used choice models to estimate behaviours of wildlife (COOPER and MILLSPAUGH
1999), there is no theoretical reason to support the use of choice models in such situations.
As well, it is often difficult to estimate interactions between multiple agents within CMs
(e.g., the interactions among hunters and hunted game).
Both ABMs and CMs are ideally suited for scenario testing. These models describe the
changes to patterns of recreational behaviours that are likely to arise from management
decisions. The CMs dependence on random utility theory allows individuals to estimate
changes to economic value (i.e., economic welfare), whereas ABMs have no connection with
economic theory.
Agent-based and choice models have high potential for communicating information to
researchers and other individuals. While communication of information is explicitly part of
most ABMs, researchers who employ CMs in practice spend little effort to communicate
results over space and time. Instead, these researchers usually focus on economic welfare
implications from different scenarios.
166
Len M. Hunt et al.
The evaluation suggests that CMs are well suited to examine landscape scale behaviours
of recreationists such as participation and choices of aggregated recreational sites (e.g.,
parks, lakes). The ABMs are better suited to accommodate: detailed site scale behaviours;
learning by the agents; and multiple agents. The use of a simulated spatial environment provides a better practice for communicating results within ABM than CMs.
3
Combining agent-based and choice models
Our combined model employs the rigour of the choice model to govern agent behaviours
and the simulated world of the agent-based model for communicative purposes. While
agent-based models are ideally suited to study site scale behaviours, the Landscape Fisheries
Model (LFM) was developed to estimate fishing participation at different water bodies and
not to investigate detailed behaviours that occur at individual water bodies. Future developments to LFM will include biological fish agents that will accommodate dynamic relationships among anglers and fish.
The logic of our model is illustrated with the application of recreational fishing in northern
Ontario, Canada. Extensive details about the statistical modelling approach, attributes,
parameter estimates, and varying preferences are already published (HUNT 2006; HUNT and
MOORE 2006; HUNT et al. in press). We do, however, present a new choice model for the
decision by anglers to participate in a multiple day trip.
Revealed preference choice models (random utility models) were used to guide the site
and participation choice behaviours of our angling agents. Estimation of these models
required information on chosen alternatives (e.g., fishing sites), available alternatives, and
attributes that define the alternatives (e.g., fishing quality).
Information on chosen alternatives comes from a diary of anglers from northern Ontario,
Canada. Anglers were asked to record details about the timing, duration, location and
context of fishing trips that occurred between May 1 and September 30, 2004. Of the 650
recruited anglers from the Thunder Bay area, 347 provided complete diary information.
These anglers reported taking 2121 fishing trips covering 4358 days.
Information about available fishing sites was determined through local knowledge and
field validation of sites. A total of 417 accessible fishing alternatives are used in this application of the LFM along with the alternatives of fishing to unknown locations or outside the
study area1. Information about site attributes was collected during visits to the sites and
from other databases (e.g., fish species database).
Figure 1 shows the logic for estimating the behaviours of agents for participation, trip
type, trip duration, and site choice decisions. For each agent and each day, we assume that
the agent first decides whether to undertake a multiple day trip. For agents who choose to
participate in a multiple day trip, we next estimate whether the agent will choose a public
access fishing trip or some other type of trip. The allowance of these different fishing trip
contexts is important for two reasons. First, the factors that will affect an angler’s choice of
a publicly accessible fishing trip will likely be different from those factors affecting choices
of other fishing trips (e.g., trips to cottages, trips to tourism establishments, multipurpose
fishing trips, etc.). Second, the focus of LFM is to estimate recreational fishing effort at
publicly accessible fishing sites.
1
Some anglers reported taking fishing trips that were thousands of kilometres away from their home.
To develop a tractable model, our study area is about 500 km2.
167
For. Snow Landsc. Res. 81, 1/2 (2007)
For every day and every agent
no
Participate in a
multiple day trip
Participate in a
day trip
yes
Do not
participate
yes
Type of multiple
day trip
no
Type of day trip
Public access
fishing trip
Other trip
Trip duration
Trip duration
Public access
fishing trip
Other trip
Determine
fishing site
Determine
fishing site
Fig. 1. Angler agent decision-making process.
After choosing a trip context, the agent next decides about the duration of the multiple day
trip. For agents who chose a publicly accessible fishing trip, we also estimate the location of
that trip. Agents who did not choose to participate in a multiple day fishing trip will consider
participating in a day trip following a similar logic as with the multiple day trip decisions.
Three choice models and one probability distribution are used to guide the behaviours of
the angling agents as depicted in Figure 1. A cross-nested logit model (BHAT and GUO 2004)
was used to estimate a model for day and multiple day site choices for publicly accessible
sites (see equation 1).
μ −1
1
Jm
1
⎡
⎤
β' X njd μ ⎞
β ' X nid μ ⎛
⎜ ∑ α jm e
⎟ ⎥
⎢ α im e
⎜
⎟ ⎥
M
⎢
j =1
⎝
⎠
Pnid = ∑ ⎢
⎥
μ
1
M ⎛ Jl
m =1
β ' X njd μ ⎞
⎢
⎥
⎜ ∑ α jl e
⎟
∑
⎜
⎟
⎢
⎥
l =1 ⎝ j =1
⎠
⎣
⎦
(
(
)
(
)
)
(1)
168
Len M. Hunt et al.
The probability (P) of individual n selecting alternative i on day d depends upon known
measures of attributes (X) and allocation (α) of sites to M different researcher defined nests
(i.e., groups). Maximum likelihood estimation is used to estimate (i.e., calibrate) the preferences (β) for the attributes and a dissimilarity parameter (μ). The preferences convert
(weight) the attributes into a utility metric while the dissimilarity parameter accommodates
flexible patterns of substitution among fishing sites (see HUNT [2006] for more details).
Since the parameter estimates from the site choice model are presented elsewhere
(HUNT and MOORE 2006; HUNT et al. in press), they are not duplicated here. The main
results from the cross-nested logit model are as follows. Anglers are more likely to select
fishing sites that are nearby their residences, are easily accessible and have multiple access
points, are water bodies with large surface areas, have desirable fish species in high
abundance, have good quality boat launches, and little cottage development. Anglers who
take trips of different duration and/or have different participation rates in ice fishing exhibit
some differences in the strength of these preferences. The model results also suggest that
fishing sites in near proximity act as better substitutes than do further fishing sites, all else
considered equal. Using the actual parameter estimates (β and μ) in equation 1 allows a
researcher to predict the likelihood of an angling agent taking a fishing trip to a specific site
on a given day.
The day and multiple day participation models were estimated separately. These models
used a multinomial logit to predict the start of multiple and day trips and trip type (i.e.,
context) for the anglers (see equation 2).
Pnqd =
e
Q
γ 'q Z nqd +θIVnqd
∑e
γ 'k Z nkd +θIVnkd
(2)
k =1
The model predicts the probability of individual n selecting trip type q on day d. This
probability is influenced by attributes of each day (Z), preferences for these attributes (γ)
and the preference (θ) for the expected maximum utility (IV) derived from a translation of
equation 1. Trip types include publicly accessible sites, other context and do not participate
alternatives. Attributes (Z) for each day include calendar events (e.g., day of week, statutory
holiday), culturally important times (e.g., summer days), and weather. The inclusion of the
expected maximum site utility (IV) into the participation choice model links the site and
participation choice models through a repeated nested logit model (MOREY et al. 1993).
Preferences (γ), which vary by angler characteristics (e.g., cottage owners, boat owners, etc.),
are estimated for these day attributes.
While parameter estimates for the day trip participation model are published elsewhere
(HUNT et al. in press), a new choice model that focuses on the timing of multiple day fishing
trips is presented here. Anglers chose among the three alternatives of a multiple day trip to
a publicly accessible site, to an other context, or to not participate in a multiple day trip.
Table 2 lists the attributes included in this model.
For. Snow Landsc. Res. 81, 1/2 (2007)
169
Table 2. Attributes used for multiple day, trip participation model.
Label
PART
THURSDAY
FRIDAY
SATURDAY
HOLIDAY
VICTORIA
PRE_WALL
LABOUR
TEMP
COTTAGE
ATV
TRUCK
BOAT
YRS
IV
PUB*XXX
Description
Participate
Begin a multiple day trip on a Thursday
Begin a multiple day trip on a Friday
Begin a multiple day trip on a Saturday
Take a multiple day trip during a holiday weekend
Take a multiple day trip during the Victoria Day long weekend (May 21–23, 2004)
Begin a multiple day trip before walleye season (before May 15, 2004)
Take a multiple day trip after the Labour Day weekend (After September 6, 2004)
Participation * expected maximum temperature (C)
Participation by cottage owners
Participation by ATV owners
Participation by truck owners
Participation by boat owners
Participation * years fished
Expected maximum utility from site choice model
Public access trip alternative (1 public access, 0 other context) * attribute XXX
The choice model parameter estimates are provided in Table 3. The model fits the data very
well with an adjusted ρ2 of 0.923. Without any other information, most anglers will not
choose to participate in a multiple day fishing trip. Anglers do express a greater likelihood
for multiple day trips that begin on Thursdays, Fridays, and Saturdays and that occur during
weekend days with statutory holidays (HOLIDAY). The importance of the statutory holiday
is lessened for multiple day trips to publicly accessible sites (MD*HOLIDAY). Anglers were
less likely to take multiple day trips before the walleye season (PRE_WALL) and after the
Labour Day weekend (LABOUR) and more likely during the Victoria Day statutory
holiday (VICTORIA). Days with greater expected maximum utility (IV) derived from the
site choice model were also more likely chosen for multiple day trips than were other days.
Expected temperature (TEMP, MD*TEMP) had little effect on decisions to take other trip
contexts and a negative effect on decisions to take publicly accessible trips for multiple days.
The negative relationship likely arises from a preference that anglers have for fishing during
the start of the walleye season, which coincides with cool expected temperatures.
Ownership of boats (BOAT) increased the propensity of an angler to take a multiple day
fishing trip. Ownership of trucks (TRUCK, MD*TRUCK) or all terrain vehicles (ATV,
MD*ATV) increased the likelihood of anglers to take a multiple day fishing trip to a
publicly accessible site. Cottage ownership (COTTAGE, MD*COTTAGE) increased the
likelihood of taking a multiple day trip of an other context. By using these parameter
estimates from Table 3 along with equation 2, one can estimate probabilities that an angler
may select a multiple day trip to publicly accessible sites and other contexts.
The model for day trip participation was similar to the multiple day model with the
following exceptions: no significant effect for trips on Thursdays or Fridays; and positive and
significant effects for Sunday trips and for rain free days. Also only boat owners and anglers
with more years fished were more likely to take day trips to publicly accessible sites than
were other anglers.
170
Len M. Hunt et al.
Finally, the duration of an angling trip is estimated from a probabilistic simulation based
on respondents’ reported trip duration lengths for multiple day trips. For an agent who is
pursuing a multiple day trip, random draws are taken from the observed trip duration
distribution associated with a given day of the week and the presence of statutory holidays.
A final constraint is that any agent who takes a multiple day trip is restricted from taking
another fishing trip until one full day after their return.
We illustrate LFM through a scenario. The management scenario involves the loss of
walleye (Sander vitreus) from a popular water body that is predicted to have a significant
percentage (7.4 %) of all publicly accessible fishing trips. Walleye is a desired fish species for
over 80 % of northern Ontario anglers (HUNT 2006). We estimated the average expected
consequences from this scenario change from 100 replications of the LFM. All other data
was held constant for the year 2004.
Figure 2 shows the expected temporal changes in recreational fishing participation at this
water body. No change in baseline angling effort occurs until the legal season for possessing
walleye in northern Ontario (May 15 for the year 2004). After May 15, the model predicts a
variable pattern of fishing participation at this water body with peaks on each weekend. The
maximum peak on the May 22 weekend coincides with the Victoria Day holiday, which is a
culturally important time for Canadians to connect with forested settings.
Table 3. Parameter estimates for multiple day, trip participation model.
* p < 0.10, ** p < 0.05, *** p < 0.01.
Label
PART
THURSDAY
FRIDAY
SATURDAY
HOLIDAY
VICTORIA
PRE_WALL
LABOUR
TEMP
COTTAGE
ATV
TRUCK
BOAT
IV
Significant Interactions
PUB*HOLIDAY
PUB*TEMP
PUB*COTTAGE
PUB*ATV
PUB*TRUCK
Log likelihood
Adjusted ρ2
Parameter Estimate
–7.564 ***
0.662 ***
2.063 ***
1.679 ***
0.991 ***
0.978 ***
–2.464 ***
–0.690 ***
0.024
1.085 ***
–0.043
–0.005
0.917 ***
0.314 ***
–0.357 **
–0.117 ***
–1.538 ***
0.370 **
0.403 **
–13315
0.923
t-value
–18.45
4.91
21.95
17.24
9.19
5.97
–5.82
–5.97
1.34
9.06
–0.46
–0.06
6.57
8.17
–2.00
–4.21
–8.65
2.30
2.24
171
For. Snow Landsc. Res. 81, 1/2 (2007)
600
Baseline
Walleye loss
500
Angler days
400
300
200
100
18 Sep
25 Sep
11 Sep
4 Sep
28 Aug
21 Aug
7 Aug
14 Aug
31 Jul
17 Jul
24 Jul
10 Jul
3 Jul
26 Jun
19 Jun
12 Jun
5 Jun
29 May
22 May
8 May
15 May
1 May
0
Fig. 2. Expected changes in fishing at a popular northern Ontario site before and after the loss of
walleye.
The extirpation of walleye is expected to cause a loss of almost 9400 angling days to this
water body (–91.74 %). The model, however, predicts a loss of only 2011 angling days to the
entire system of publicly accessible water bodies (–1.45 % change in overall angling). The
discrepancy between the site and system change is due to the expected substitutability that
other waters have for this water body.
The predicted redistribution of fishing effort from this scenario is shown in Figure 3. Two
points are apparent from the figure. First, all else considered equal, increases in fishing days
are predicted to be greater at larger than smaller water bodies. This finding illustrates the
importance of water body size within the fishing site choice model. Second, expected
increases in fishing are greater nearer than farther from the affected water body. This result
arises from the importance of travel distance and spatial substitution within the fishing site
choice model. Although not decipherable from the figure, water bodies with walleye have
greater predicted increases in fishing than do water bodies without walleye. The figure
demonstrates the landscape level implications of walleye extirpation from this single water
body. The use of a choice model to govern the angling agent behaviours reveals important
expected spatial and temporal predictions from this scenario. The animation of agents also
provides another level of communication for users of the LFM software.
172
Len M. Hunt et al.
Fig. 3. Expected increase in fishing (days) at other water bodies from walleye extirpation at affected
water body.
4
Discussion and conclusions
Choice models and agent-based models are popular approaches to investigate recreational
behaviours. Both approaches rely upon individual decision-making to determine patterns of
recreational use. The approaches also afford managers and users an opportunity to investigate
the likely consequences of many different management scenarios before implementing
these scenarios.
Agent-based and choice models each have strengths and weaknesses. Agent-based
models provide a flexible approach to investigate learning and behaviours at a site scale for
recreationists. Choice models provide greater rigour than agent-based models for defining
behavioural rules and are ideally suited to investigate behaviours at a landscape scale.
Choice models are formally linked to behavioural theory making it possible to estimate
For. Snow Landsc. Res. 81, 1/2 (2007)
173
changes in economic welfare from scenarios. While both approaches have great potential for
communicating results over space and time, most choice model applications have not
focused on this communication aspect.
The Landscape Fisheries Model application provides a small step towards linking the two
modelling approaches. We used the statistical rigour and theory of choice models to guide
behaviours of angling agents. This statistical rigour and theory provides a new arsenal to
researchers who typically use observation or expert judgement to develop rules for agent
behaviours (MANNING et al. 2005). The choice modelling method to derive rules embraces
randomness in decision-making, albeit randomness that arises from researchers’ inabilities
to understand decision-making processes (BEN-AKIVA and LERMAN 1985; MANSKI 1977).
Our application used the simulated world of agent-based modelling for communication
purposes. The use of a simulated world and visual inspection of our results provided an
additional benefit beyond communication. We were able to assess the face validity of our
results through animations (i.e., agent travels), charts and reports of angling behaviours2. For
example, the animations were very instructive in determining whether our transportation
network was identifying known travel routes for anglers.
The scenario provides a glimpse of the flexibility of the Landscape Fisheries Model. This
model allows users to construct a wide array of scenarios through manipulations of information on aspatial or spatial attributes. Scenario forecasts suggest that extirpation of
walleye from a popular water body will result in a large loss of fishing days from that water
body (91.7 % loss) but a much smaller impact to overall fishing trips (1.45 % loss). The
dampening effect from this scenario illustrates the importance of examining the angling
behaviours at a landscape scale where many other fishing sites act as substitutes.
A current limitation with the Landscape Fisheries Model is the omission of ecological
impacts that arise from angling use. We plan to address this limitation by adding agents for
the fish. Population dynamics, suitable habitat and exploitation from angler agents will affect
these fish agents. Therefore, the choice of a fishing site by angler agents will affect the
fisheries population at that site. Any changes in the quality of fishing will subsequently alter
the probability that angling agents will select this site in the future. By examining recreational
and biological components within the simulated world, it will be possible to observe impacts
and emergent patterns of behaviours that are not likely identifiable from independent
studies of angling behaviours or fish population dynamics.
Scale may provide another opportunity for further linking the ABM and CM approaches.
Researchers may use choice models to understand decisions of recreational participation
and choices of alternatives such as fishing sites, parks, or some other aggregation. The agentbased models may employ elements such as mobility and cognition besides preference
(ITAMI et al. 2003) to guide agents’ behaviours at the site scale. This site scale examination
can provide important information that emerges from the simulations such as the rate of
encounters among the agents. We hope that this paper illustrates the possibility of linking
agent-based and choice models and spurs further work to develop joint models. Researchers
who employ either choice or agent-based models should view both approaches as complementary rather than competitive.
2
Additional testing will involve comparisons of data from vehicle monitoring devices to forecasts
from the LFM model.
174
Len M. Hunt et al.
Acknowledgements
We thank the Ontario Ministry of Natural Resources for providing the support for the development of the Landscape Fisheries Model. Appreciation is also given to Ontario’s Living Legacy
Trust, Northwestern Ontario Sportsmen’s Alliance, Ontario Federation of Anglers and Hunters,
and the Northern Ontario Tourist Outfitter’s Association for funding the field and diary data
collection for our application. Finally, we thank Sarah Browne, Jeff Moore, and Mandie Ross for
helping to oversee the field data collection efforts.
5
References
ADAMOWICZ, W.L.; SWAIT, J.F.; BOXALL, P.C.; LOUVIERE, J.J.; WILLIAMS, M., 1997: Perceptions
versus objective measures of environmental quality in combined revealed and stated preference models of environmental valuation. J. Environ. Econ. Manage. 32: 65–84.
BEN-AKIVA, M.E.; LERMAN, S.R., 1985: Discrete choice analysis: theory and application to travel
demand. Cambridge, MA, MIT Press.
BEN-AKIVA, M.E.; MORIKAWA, T., 1990: Estimation of switching models from revealed preferences and stated intentions. Transp. Res. Part A 24, 6: 485–495.
BHAT, C.R.; GUO, J., 2004: A mixed spatially correlated logit model: formulation and application
to residential choice modeling. Transp. Res. Part B 38: 147–168.
COLE, D.N.; CAHILL, K.; HOF, M., 2005: Why model recreational use? In: COLE, D.N. (comp).
Computer simulation modeling of recreation use: Current status, case studies, and future
directions. Gen. Tech. Rep. USDA For. Serv. RMRS-GTR-143.
COOPER, A.B.; MILLSPAUGH, J.J., 1999: The application of discrete choice models to wildlife
resource selection studies. Ecology 80: 566–575.
HUNT, L.M., 2006: Modelling relationships between road access and recreational fishing site
choice while accounting for spatial complexities. Doctoral Dissertation. Waterloo, ON,
Department of Geography and Environmental Studies, Wilfrid Laurier University.
HUNT, L.M.; BOOTS, B.N.; BOXALL, P.C., 2007: Predicting fishing participation and site choice
while accounting for spatial substitution, trip timing and trip context. North Am. J. Fish.
Manage. 27: 832–847.
HUNT, L.M.; MOORE, J., 2006: The potential impacts of climate change on recreational fishing in
northern Ontario. Climate Change Research Report CCRR-04. Sault Ste Marie, ON, Queen’s
Printer for Ontario.
ITAMI, R.M.; RAULINGS, R.; MACLAREN, G.; HIRST, K.; GIMBLETT, R.; ZANON, D.; CHLADEK, P.,
2003: RBSim 2: Simulating the complex interactions between human movement and the outdoor recreation environment. J. Nat. Conserv. 11: 278–286.
MANNING, R.E.; ITAMI, R.M.; COLE, D.N.; GIMBLETT, R., 2005: Overview of computer simulation
modeling approaches and methods. In: COLE, D.N. (comp). Computer simulation modeling of
recreation use: Current status, case studies, and future directions. Gen. Tech. Rep. USDA For.
Serv. RMRS-GTR-143.
MANSKI, C.F., 1977: The structure of random utility models. Theory Decis. 8: 229–254.
MOREY, E.R.; ROWE, R.D.; WATSON, M., 1993: A repeated nested-logit model of Atlantic salmon
fishing. Am. J. Agric. Econ. 75: 578–592.
SWAIT, J.F., 1994: A structural equation model of latent segmentation and product choice for
cross-sectional revealed preference choice data. Journal of Retail and Consumer Services, 1, 2:
77–89.
TRAIN, K.E., 1998: Recreation demand models with taste differences over people. Land Econ. 74,
2: 230–239.
Revised version accepted May 31, 2007