Treating respondent uncertainty in contingent valuation: A comparison of empirical treatments

Abstract

This research examines the impact of uncertainty on contingent valuation responses using (1) a survey of Canadian landowners about willingness to accept compensation for converting cropland to forestry and (2) a survey of Swedish residents about willingness to pay for forest conservation. Five approaches from the literature for incorporating respondent uncertainty are used and compared to the traditional random utility model with assumed certainty. The results indicate that incorporating uncertainty has the potential to increase fit, but could introduce additional variance. While some methods for uncertainty can be an improvement over traditional approaches, it is imperative to exercise caution when making systematic judgments about the effect of uncertainty on contingent valuation responses.

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ANALYSIS
Treating respondent uncertainty in contingent valuation: A
comparison of empirical treatments
Sabina L. Shaikh⁎, Lili Sun, G. Cornelis van Kooten
A R T I C L E I N F OA B S T R A C T
Article history:
Received 15 November 2005
Received in revised form
19 April 2006
Accepted 26 May 2006
Available online 17 August 2006
This research examines the impact of uncertainty on contingent valuation responses using
(1) a survey of Canadian landowners about willingness to accept compensation for
converting cropland to forestry and (2) a survey of Swedish residents about willingness to
pay for forest conservation. Five approaches from the literature for incorporating
respondent uncertainty are used and compared to the traditional random utility model
with assumed certainty. The results indicate that incorporating uncertainty has the
potential to increase fit, but could introduce additional variance. While some methods for
uncertainty can be an improvement over traditional approaches, it is imperative to exercise
caution when making systematic judgments about the effect of uncertainty on contingent
valuation responses.
© 2006 Elsevier B.V. All rights reserved.
Keywords:
Respondent uncertainty
Willingness to accept
Contingent valuation
1.Introduction
The impact of uncertainty on contingent valuation estimates
has been discussed in the literature on both a theoretical and
empirical level. McFadden (1973) first incorporated observer
uncertainty about individuals' preferences using a random
utility maximization (RUM) framework. The RUM model postu-
lates that, from the point of view of the analyst, an individual's
utility consists of a deterministic component plus an unobserv-
able random error term. Hanemann (1984) applied this idea to
the valuation of non-market amenities using a contingent
valuation device where a respondent is faced with a choice to
accept or reject an offered ‘bid’ for an improvement in the
amenity. However, this approach addresses uncertainty on the
part of the investigator, not uncertainty on the part of the
respondent.
Hanemann and Kriström (1995) argued that, if respondents
truly know their valuation of a contingency, an open-ended
question format should be used to elicit this information. Yet,
the dichotomous-choice format is generally preferred because
it better simulates a ‘take it or leave it’ marketplace situation,
and results in lower variance than estimates from an open-
ended format. But there is also, in our view, an implicit recog-
nition with dichotomous choice that the random component
of the respondent's utility function is the result of respondent
uncertainty about the answer provided — this is precisely the
impression that one gets from Hanemann and Kriström. As
discussed in the next paragraph, the uncertainty in question
here is more general than a theoretical violation of ‘preference
certainty’. Thus, we do not directly test the fundamental eco-
nomic principle that individuals know their preferences with
certainty, but rather examine how various researchers have
dealt with respondents' uncertainty about their answers to
contingent valuation questions.
Uncertainty arises in a variety of ways, including the
following: (1) Uncertainty can originate with the public good or
contingencythatistobevalued.Respondentsmaybeuncertain
aboutwhatitisthattheyarevaluing,havingnoexperiencewith
it and perhaps never having seen it. (2) The value an individual
assigns to the specified non-market amenity is influenced by
prices of both substitutes and complements, if they even exist,
and markets for these goods may behave in ways that are
E C O L O G I C A L E C O N O M I C S 6 2 ( 2 0 0 7 ) 1 1 5 – 1 2 5
⁎Corresponding author.
E-mail address: sabina@uchicago.edu (S. Shaikh).
0921-8009/$ - see front matter © 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.ecolecon.2006.05.016
available at www.sciencedirect.com
www.elsevier.com/locate/ecolecon

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unpredictabletotheindividual(Wang,1997).(3)Uncertaintycan
originate with the questionnaire used to elicit information,
although this problem can be overcome to some extent by
improved survey design. Nonetheless, it is generally accepted
that the contingent valuation method (CVM) contributes to
potential measurement error, because it relies on hypothetical
scenarios (Loomis and Ekstrand, 1998). (4) Over and above the
hypothetical nature of the CVM, individuals may simply be
unableto make a tradeoff betweentheamenity inquestion and
the monetary good. (5) Respondents may not understand the
contingency in question and the manner in which it would be
achieved, perhaps being hesitant about the policy instrument
proposed for addressing the environmental spillover.
While some uncertainty can be resolved by providing res-
pondents with more complete information, or working with
them in controlled interactive environments, some uncertainty
canneverberesolved.1Preferencesareambiguous–theresponse
to a valuation question has more than one meaning – and,
consequently, a person might answer a valuation question but,
when probed about their response, will add caveats and/or
express uncertainty about the value provided. Researchers have
proposed a variety of empirical treatments for addressing this
typeofuncertainty,buttherehasbeennooverarchingagreement
on a unified approach, mainly because of the nature of the
uncertainty and different views about how it is to be interpreted.
Most researchers employ the standard RUM framework
when incorporating uncertainty in empirical applications. The
first to do so were Li and Mattson (1995) who used a follow-up
question to a dichotomous-choice valuation question that
asked respondents how certain or confident they were of their
previous ‘yes’/‘no’ answer. A similar ‘follow-up’ strategy for
addressing respondent uncertainty was employed by a number
of other researchers (Champ et al., 1997; Blumenschein et al.,
1998; Johannesson et al., 1998; Loomis and Ekstrand, 1998;
EkstrandandLoomis,1998;vanKootenetal.,2001),whileReady
et al. (1995), Wang (1997), Welsh and Poe (1998), Ready et al.
(2001), and Alberini et al. (2003) instead embedded information
about respondent uncertainty directly in the response options
to the valuation question, thereby jettisoning the straightfor-
ward ‘yes’/‘no’ choice.
While these disparate approaches for treating respondent
uncertainty have evolved, there has been no consensus
regarding an appropriate treatment and there have been few
attempts to compare approaches.2In the current paper, we
focus solely on comparing empirical treatments found in the
literature rather than postulating a unifying theory. We do this
using datasets from two very different surveys: (1) a survey of
landowners in western Canada that asked about willingness to
accept (WTA) compensation for converting marginal ag-
ricultural land to forestry for carbon uptake purposes, and (2) a
Swedish survey that asked people their willingness to pay for
forest protection. The data are analyzed using five different
methodsofaddressinguncertainty, and comparing thesetothe
standard RUM approach with assumed respondent certainty.
The research presented here does not develop the methods for
treating uncertainty and therefore does not discuss their
theoretical appropriateness. The objective of this study is only
toassessandcompareempiricalmethodsintheliteratureusing
the independent datasets. While economic intuition and
previous studies suggest that the inclusion of uncertainty will
lower WTP and raise WTA, results indicate that estimates of
average WTA or WTP vary substantially across approaches. To
avoid pitfalls concerning the interpretation of uncertainty, it is
defined throughout the paper as anything leading to an unsure
responsetoacontingentvaluationquestion.Thisdefinitionwill
be further developed in Section 2.
The paper is organized as follows. Models incorporating
uncertainty into dichotomous choice CVM are reviewed in
Section 2, while the datasets employed in the analysis are
described in Section 3. The empirical results are provided in
Section 4, followed by a discussion of policy implications and
considerations for further research.
2.Models incorporating uncertainty
Five econometric methods for incorporating respondent uncer-
tainty into the RUM framework are examined, as is the fuzzy
method proposed by van Kooten et al. (2001). The various
approaches are reviewed in this section.
2.1.Weighted Likelihood Function Model (WLFM)
Li and Mattson (1995) were the first to implement an
empirical framework for addressing uncertainty within the
RUM model. They retain the assumption that individuals have
a true value for the amenity, vi, but they have incomplete
knowledge about that value. Survey respondents arrive at
some value, v ˜=vi+ξi+εi, where vi is the individual's true
valuation of the resource and ξi and εi are stochastic
disturbances arising from uncertainty related to the respon-
dent and the observer, respectively. Standard assumptions
about ξi and εi can be employed, namely, that they are
normally distributed with zero mean and variance given by
the observations.
Observer uncertainty is treated the same as it is in the
standard RUM model, but a post-valuation question is used to
elicit information about the respondent's uncertainty. The
standard certainty model likelihood function for the dichoto-
mous-choiceRUMmodelismodifiedgenerallyfortheuncertain
case as:
L ¼
X
N
i¼1
wi ðyilnðUwtpÞÞ þ ð1−yiÞlnð1−UwtpÞ
??
ð1Þ
1This is why some prefer, as an alternative to valuation, a
facilitator/mediator who helps disparate groups of stakeholders
to identify their preferences and thus make decisions concerning
environmental amenities (Gregory et al., 1993).
2Some researchers do specify a broader concept of respondent
uncertainty, but the variety of approaches in the literature
indicates a lack of consensus. Our own view is that, if uncertainty
cannot be treated in a probabilistic framework, it may take some
time before a consensus can be reached. Progress has been made
in distinguishing between risk and uncertainty by, for example,
soliciting expert opinions about risk and/or updating probabilities
in a Bayesian sense (see, in particular, Shaw et al., 2005; Cameron,
2005). However, this is not the type of uncertainty addressed in
the studies we examine. Uncertainty is not about the probability
of the occurrence of the contingency, but about actual choice or
tradeoff that respondents make.
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where N is the number of survey respondents. The initial
dichotomous choice is given as y=1 for a ‘yes’ and y=0 for a
‘no’ answer, and Φ is the cumulative distribution function of
the maximum WTP. The weights, wi, are used as a measure
of certainty determined by the response to the follow-up
question.
Li and Mattson constructed a post-decisional confidence
rating for assessments of the preservation value of forests in
northern Sweden using a follow-up question that elicited a
respondent's certainty on a scale ranging from 0% to 100%
(with 5% intervals). The certainty percentages were used to
weight the individual dichotomous-choice responses directly
in the likelihood function. Before doing so, however, certainty
responses were recoded so that, for example, a ‘yes’ (‘no’)
response with 40% certainty was recoded to a ‘no’ (‘yes’)
response with 60% certainty. A ‘yes’ or ‘no’ with absolute
certainty in this case results in the standard dichotoous-
choice model with certainty.
2.2.Asymmetric Uncertainty Model (ASUM)
Champ et al. (1997) developed an alternative approach for
incorporating the certainty follow-up response. Using a scale
of 1 (very uncertain) to 10 (very certain), they elicited res-
ponses to the follow-up rating question: “How certain are
you that you would donate the requested amount [in the
valuation question]?” All ‘yes’ responses were recoded as a
‘no’ if the respondent was not completely certain (providing
a rating of 10). Ready et al. (2001) estimated the value of
avoiding episodes of respiratory illness using both dichoto-
mous-choice and payment-card survey techniques. In both
cases, the WTP question was posed using the following
choices: (1) ‘almost certainly yes’ (95% sure ‘yes’), (2) ‘most
likely yes’, (3) ‘equally likely yes and no’, (4) ‘more likely no’,
and (5) ‘almost certainly no’ (95% sure ‘no’). Like Champ et
al., responses were recoded so that only an ‘almost certainly
yes’ (choice 1) was treated as a ‘yes’, but the other four
categories were considered ‘no’ responses. In both of these
studies, the ‘yes’ response is only considered a valid ‘yes’ if
it is with near perfect certainty. As a result, Loomis and
Ekstrand (1998) refer to this type of model as an ‘asymmetric
uncertainty model’ (ASUM). This model would be most
appropriate if respondents answering ‘no’ are quite certain
they would not pay, but those answering ‘yes’ are more
uncertain about their response. As discussed below, evi-
dence of asymmetry exists in the willingness to accept a tree
planting program data (Fig. 1), suggesting that the ASUM
could perform well in this case.
2.3.Symmetric Uncertainty Model (SUM)
The symmetric uncertainty model (SUM) of Loomis and
Ekstrand (1998) provides an alternative to the ASUM by
attempting to preserve the initial ‘yes’ or ‘no’ response to the
dichotomous-choice question. To estimate the benefits of
preserving Mexican spotted owl habitat, they pose a dichot-
omous-choice referendum question with a certainty scale
follow-up rating question: “On a scale of 1 to 10, how certain
are you of your answer to the previous [valuation] question?”
Respondents are instructed to answer 1 for ‘not certain’ to 10
for ‘very certain’. As in the other cases, responses are recoded
for estimation purposes, but in this case the recoding converts
the dichotomous-choice dependent variable into a ‘continu-
ous’ variable taking on values over the closed interval [0 1].
The symmetric nature of the recoding is illustrated in the
following figure:
A ‘no’ response with perfect certainty takes on the usual
valueof 0, while a ‘yes’ with perfect certainty equals 1. If a ‘yes’
or ‘no’ answer to the dichotomous-choice valuation question
has an associated certainty of 50% or less, it is assigned a value
of 0.5. For a ‘yes’ response with certainty level greater than
50%, the dependent variable takes on the value associated
with the expressed certainty level; thus, a ‘yes’ response with
a follow-up certainty response of 60% is coded 0.6. In contrast,
for a ‘no’ response with certainty level greater than 50%, the
dependent variable takes on the value of 100% minus the
expressed certainty level; thus, a ‘no’ response with a follow-
up certainty response of 60% is coded 1−0.6=0.4. Following
Loomis and Ekstrand, the SUM can be estimated directly using
a maximum-likelihood procedure.
2.4.Random Valuation Model (RVM)
Wang (1997) views the value that an individual attaches to any
amenity (including market traded goods) to be a random var-
iable with an unspecified probability distribution. He assumes
that each respondent has in mind an implicit distribution of
values rather than a single true value. A respondent will ac-
cept to pay a particular amount for an increase in the level of
the amenity only if the latent compensating surplus (CS) is
‘sufficiently large’ relative to the bid, and reject the proposed
payment if latent CS is ‘sufficiently small’. A ‘don’t know’ (DK)
response occurs if latent CS lies in a ‘grey area’ where CS is
either not sufficiently large or sufficiently small relative to the
proposed payment. Since the valuation question permits a DK
response, no follow-up question is needed to elicit the
uncertainty of the response. Then, defining the mean value
of the WTP function vi=xiβ+εias, and assuming εiis normally
Fig. 1 – Comparison of certainty of yes and no responses.
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distributed, the log likelihood function for the three response
categories and a proposed one-time payment is:
logL ¼
X
þ
iayes
log 1−U
tiþ ai−xib
r
tiþ ai−xib
r
?
?
?
?
??
þ
?
X
ti−bi−xib
r
iano
log U
ti−bi−xib
r
?
?
???
X
iaDK
log U
−U
??
;
ð2Þ
where tiis the bid level assigned to respondent i, and ai=vi−S1i
and bi=S2i−vi, where S1 and S2 are the lower and upper
bounds of the DK region, respectively. If S1 and S2 are
constants, maximization of Eq. (2) effectively amounts to
estimating an ordered Probit model. The assumptions can be
relaxed to allow a and b to be functions of the variables
thought to affect individual variations. Wang also estimated
the model by treating the DKs as ‘no’ responses, similar to the
approaches of Ready et al. (2001) and Champ et al. (1997), and
alsoby deletingthemfromthe sample.Not surprisingly, Wang
found estimated WTP to be significantly lower when all DKs
were recoded as ‘no’ responses.
2.5.Multiple-bounded Discrete Choice (MBDC)
Although not implemented in the current study, an extension
of Wang's approach was implemented by Welsh and Poe
(1998), and Alberini et al. (2003). They adopt a ‘multiple-
bounded discrete choice’ (MBDC) approach that directly
incorporates certainty levels through a two-dimensional
decision matrix: One dimension specifies dollar amounts
that individuals would be required to pay on implementation
of the policy, and the second dimension allows individuals to
express their level of voting certainty via four response
options — ‘definitely no’, ‘probably no’, ‘not sure’, and
‘definitely yes’. This expands to four the three options
available in Wang (1997). A random-effects probit model is
used to estimate separate WTP functions for each certainty
level.
2.6. Fuzzy Model (FM)
Like Wang, van Kooten et al. (2001) also assume that an
individual does not know the amenity's precise (‘crisp’) value,
and will never know it with certainty. A respondent only
knows the level above which she will certainly reject the
proposed payment and the level below which she will
certainly accept it. In between these levels, the preferences
of the respondent are vague or ambiguous, so that the
respondent's WTP and willingness not to pay (WNTP) are
best viewed as fuzzy sets (Jang et al., 1997). That is, rather than
assuming the individuals know the distribution of the true
value,butnottheprecisevalueitself,theresearchers assumed
that CS can be a member of both the WTP and WNTP fuzzy
sets at the same time (which is a characteristic of fuzzy set
theory). In their application, follow-up information about how
confident or certain the respondent is about her response to
the valuation question is used to estimate both WTP and
WNTP fuzzy membership functions.
van Kooten, Krcmar and Bulte (2001) employ the same
data as Li and Mattson (1995). The latter assume that an
individual k who is 40% certain of a ‘yes’ response is also 60%
certain of a ‘no’ response, so wk=0.6 and yk=0 in (1) or
wk=0.4 and yk=1, but not both. The former assume, however,
that k's response is a member of the WTP fuzzy set with
membership value 0.4 and a member of the WNTP fuzzy set
with value 0.6. That is, the post-decisional confidence of a
response is used to determine the membership values of the
WTP and WNTP fuzzy sets. The intersection of the estimated
WTP and WNTP membership functions corresponds to the
‘comfort’ level of the associated welfare estimate. Fuzzy
estimates of WTP to protect forests in northern Sweden were
well below those estimated using the WLFM approach of Li
and Mattson.3
3.Background to the datasets
For our empirical application, we employ data from two
surveys, one of which elicited WTA compensation for planting
trees on marginal agricultural land and the other WTP for
preservation of forest ecosystems. We employ datasets from
twodifferentsurveys–onewithWTAandtheotherwithWTP–
in order to observe any consistent patterns across the various
treatments of uncertainty. The surveys are briefly discussed in
the following paragraphs.
3.1.Tree planting in Western Canada
A survey of landowners in Canada's Prairie region in 2000
elicited willingness to accept compensation for a tree planting
program on marginal agricultural land (Shaikh et al., in press).
The survey collected detailed information on farmers' agri-
cultural operations, opinions about and awareness of climate
change issues and carbon credits, and personal characteristics
and demographics. Not all returned surveys were used in the
current analysis because the survey design did not permit
those respondents who were unwilling to consider a tree
planting program to answer the valuation question. While
thesecould be construed as ‘no’ responses for any bid amount,
they are excluded here because we are primarily interested in
those who answered the valuation question and the follow-up
uncertainty question. After eliminating those who did not
answer the valuation section of the survey and those who
failed to provide other information required for the current
analysis, 122 observations remained.
In the survey, landowners were presented a hypothetical
10-year contract to plant trees on their most marginal land.
The contract would pay up-front planting costs and provide
an annual payment to compensate for lost agricultural
production. The contingent contract indicated that farmers
3Li and Mattsson estimated the overall mean to be SEK 12,817
(or SEK 8,578 using truncated mean), while the estimate of van
Kooten et al. was 3066 SEK (with membership of 0.75). In the
analysis below, we ‘correct’ both estimates. Instead of Li and
Mattsson's mean WTP and log–linear specification of the valua-
tion function, we use median WTP and a linear valuation
function; linear and exponential membership functions are used
in the fuzzy case rather than a hyperbolic tangent specification.
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had no right to harvest the trees before the contract expired,
but trees became their property at the end of the contract
period. No compensation was provided for conversion of land
back to agriculture; instead, it was explicitly noted in the
survey that a market for selling carbon credits might have
developed by that time or landowners could simply sell the
trees thereby covering the cost of converting land back to
agriculture if necessary. In the absence of a priori valuation
information, the compensation offers were selected on the
basis of results from a pilot study, and ranged from $1 to $60
per acre per year. The distribution of these bids is skewed
towards the lower end of the range in order to provide more
efficient estimates of WTA (Cooper, 1993). In a follow-up to
the dichotomous-choice valuation question, the respondent
was asked to rate the certainty of her response on a scale of
‘1’ for not certain to ‘10’ for very certain. Both questions are
provided in the Appendix.
The distributions of the ‘yes’ and ‘no’ responses to the
certainty follow-up question can be seen in Fig. 1. Around 50%
of those answering ‘no’ were very certain of their answers,
compared to only 15% of those responding ‘yes’. As was the
case for Welsh and Poe (1998), if respondents to a one-shot
dichotomous-choice question are unsure whether they would
pay the dollar threshold, they are most likely to report they
would vote ‘yes’ — an indicator of ‘yea saying’.
In the current context, there are some unique sources of
uncertainty that need to be explained. First, respondents (as
well as researchers) are uncertain of the effects of climate
change. While we asked the respondents to envision a par-
ticular scenario as detailed in the survey, there is still some
degree of uncertainty as to when and to what degree the
climate change would actually occur, and what this might
mean for the trees that are planted. The timing of unforeseen
events may be crucial as respondents were observed to be
much more likely to adopt a tree-planting contract of a short
time horizon (10 years vs. 20 years). The uncertainty attached
to future events, and individual discount rates can play a large
role in accepting a bid. Second, the tree plantation itself is a
source of uncertainty for the respondent. What will a
plantation look like compared to natural stands of trees?
Will it have a negative impact on agricultural operations (e.g.,
reduce soil moisture availability, increase the likelihood of
early frost) or provide benefits (e.g., reduce soil erosion and
drying from wind)? Third, in light of uncertainty about the
impact of trees and about future agricultural prices, there is a
(potentially quantifiable) risk to trading off agricultural
returns for a guaranteed annual payment. Finally, from
comments provided by respondents, it is clear that farmers
are hesitant to engage in contracts that might affect their
future eligibility for agricultural payments or compromise the
amount of their land base eligible for Canadian Wheat Board
quota. There are other sources for uncertainty; some can be
represented probabilistically, while others are truly ambigu-
ous (e.g., the use and non-use benefits that a respondent
might derive from a nearby tree plantation and the trade off
between such benefits and risky returns).
In the tree planting case, the choice of explanatory var-
iables is based on previous research (van Kooten et al., 2002;
Shaikh et al., in press). Summary statistics for the explanatory
variables are provided in Table 1.
3.2.Forest conservation in Northern Sweden
Li and Mattson (1995) used a contingent valuation survey to
assess the preservation value of forests. The survey asked
respondents what they would be willing to pay to continue to
visit, use and experience the forest environment in northern
Sweden. Bid amounts took one of the following values: 50, 100,
200, 700, 1000, 2000, 4000, 8000 and 16,000 SEK. A follow-up
question asked how certain the respondent was about her
‘yes’/‘no’ answer on a 0–100 percent scale with 5% intervals.
About 14% of the ‘yes’ respondents and 11% of the ‘no’
respondents reported confidence levels below 50%. Some 35%
of the ‘yes’ and 16% of the ‘no’ respondents indicated that they
had complete confidence in their response to the valuation
question. This is somewhat surprising and opposite of what
we saw for the WTA case in the tree-planting survey.
The Swedish survey also collected data on respondents' age,
gender,numberofforestvisits,educationandhouseholdincome.
The sample made available to us by Li and Mattsson consisted of
389 usable surveys, which, following their lead, was reduced to
344observationsbyexcludingobservationswithreportedincome
levels below 11,000 SEK and above 300,000 SEK, and with
education levels below 1 year and above 25 years.
Sources for uncertainty in the forest conservation survey
included, among others, uncertainty about what was being
protected. Given that Sweden cleared its northern forests
during the 1960s, planting faster growing (in many cases
non-native) species, respondents might be somewhat appre-
hensive about the nature of the resource that is protected
(which might explain why visits were included in Li and
Mattsson's regression model). Respondents are also uncer-
tain about the tradeoff between the amenity and money, or
the manner in which the contingency is expressed. This is
evidenced by the fact that some respondents indicated a
willingness to pay more than half of their annual income to
conserve northern forests; presumably they should also be
WTP to protect southern forests. Finally, there is the un-
certainty of fire, which characterizes mature boreal forests.
3.3.Accounting for uncertainty: a comparison of models
In this section, we compare the results of five approaches for
addressing respondent uncertainty, beginning with the survey
of western Canadian landowners. The ASUM of Champ et al.,
Li and Mattson's WLFM, Loomis and Ekstrand's SUM, and
Wang's RVM are all estimated as described earlier. (Lack of
Table 1 – Variable statistics for tree-planting program
(n=122)
Explanatory variableMeanS.D.Min Max
Compensation offered ($ per ha)
Brown soil zone (=1, 0 otherwise)
Forest landscape thought
visually unappealing
(Likert scale variable)
Acres of farmland covered
with trees
Age (median category variable
from 33 to 68 years with
5-year intervals)
26.090
0.156
2.008
16.860
0.364
1.032
3.00
0.00
1.00
60.00
1.00
5.00
41.861 72.9010.00525.00
55.541 9.69033.00 68.00
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