Directory UMM :Data Elmu:jurnal:A:Agricultural Systems:Vol67.Issue1.2001:
Agricultural Systems 67 (2001) 1±20
www.elsevier.com/locate/agsy
Logistic modelling to identify and monitor local
land management systems
A. Gobin *, P. Campling, J. Feyen
Institute for Land and Water Management, Katholieke Universiteit Leuven, Vital Decosterstraat 102,
3000 Leuven, Belgium
Received 17 February 2000; received in revised form 20 July 2000; accepted 25 August 2000
Abstract
In the wake of sustainable development, measurable indicators are needed to monitor land
resources management. Aerial photograph interpretation, participatory research methods and
logistic modelling were combined to establish indicators and to investigate their relationship
with local land management systems. Land tenure and customary laws explained the dierences in ®eld characteristics at Ikem (southeastern Nigeria). A binary followed by an ordinal
logistic model quanti®ed the relationship between ®eld characteristics and local land management. The odds for private land management increased with 102% per 100 m2 decrease in
®eld size and with 128% per unit increase in palm tree density. For communal land management, fallow periods were longer with increasing non-palm tree densities and ®eld sizes; odds
increased with 76 and 31%, respectively. Field size, total tree density and palm tree density are
important indicators to monitor local land management. # 2001 Elsevier Science Ltd. All
rights reserved.
Keywords: Land management; Indicator; Participatory Rural Appraisal; Logistic modelling; Southeastern
Nigeria
1. Introduction
Environmental degradation is of great concern in sub-Saharan Africa. Prima facie,
loss of sustainability seems linked to rural people's attitude towards land resources.
Villagers are often considered to be placing their own short-term survival ahead of
long-term land resource sustainability (IFPRI, 1994). In southeastern Nigeria, the
* Corresponding author. Tel.: +32-16-32-97-21; fax: +32-16-32-97-60.
E-mail address: anne.gobin@agr.kuleuven.ac.be (A. Gobin).
0308-521X/01/$ - see front matter # 2001 Elsevier Science Ltd. All rights reserved.
PII: S0308-521X(00)00043-3
2
A. Gobin et al. / Agricultural Systems 67 (2001) 1±20
increased needs of a rising population are regarded as particularly disruptive for the
environment since the level of resources per capita declines (Think Tank on Agriculture, 1993). These negative views are often based on an abstraction of personal
observations and judgements but do not necessarily re¯ect the complex reality.
Objective and measurable criteria with potential to compare between areas and
monitor changes over time are needed to describe the condition and management of
land resources and the pressures exerted upon the land (Young, 1998). International
organisations have initiated programmes on developing measurable and policyrelevant environmental indicators (UN, 1995; OECD, 1997) to monitor progress in
reaching sustainable development, as de®ned in Agenda 21 (UNCED, 1993). The
pressure-state-response approach (Pieri et al., 1995) provides a framework to
develop land quality indicators and to place pressure upon land resources, changes
in the state of land quality and responses by society to these changes, within the
context of policy and natural resource management. However, multiple stakeholders
are involved in moulding the desirable goal of sustainable natural resource management and each of them will ®nd dierent indicators relevant to their reasons for
monitoring change. Integrating these dierent perspectives, particularly those of
local people, into indicators could lead to a better understanding of the processes
that cause change (ILEIA, 1996; Abbot and Guijt, 1998). Much of the research has
focussed on establishing single indicators with threshold values beyond which sustainable land resource management would be at stake.
The objectives of this paper are to elicit local land management systems, to
establish indicators that are capable of identifying and hence monitoring local
land management, and to investigate the link between the indicators and local land
management. Aerial photograph interpretation, participatory research methods
and logistic modelling were combined to identify and predict local land management
systems on the basis of ®eld plot characteristics. Logistic modelling was used to
predict probabilities of local land management systems and to investigate the relationship between the response probability and the explanatory ®eld characteristics.
Field characteristics incorporated into the best performing models were regarded as
suitable indicators. The models and indicators could be used to monitor local land
management and to examine the pressures exerted upon the land.
2. Materials and methods
2.1. Regional setting
The region has a humid tropical climate with a distinct dry season between
November and March with annual rainfall averaging at around 1500 mm per year.
The case study area is situated in the transition zone between lowland, GuineaCongolian, wetter type rainforest and Guinea savannah, resulting in a mosaic vegetation pattern (Hopkins, 1979; White, 1992). Lush evergreen forest fringes the
river and perennial streams, whereas along seasonal streamlines corridors of semideciduous trees and bushes are found. Moist semi-deciduous forest occurs on the
A. Gobin et al. / Agricultural Systems 67 (2001) 1±20
3
shale dominant inter¯uve, whereas drought-tolerant tree species and tall grasses
mainly vegetate the denudated inter¯uve areas.
The 40 km2 Ikem case study is located at the con¯uence zone of two perennial
rivers of the River Ebonyi headwater catchment, southeastern Nigeria (Fig. 1).
According to the 1991 census, the population density for Ikem averages around 400
persons per square kilometre. Smallholder farmers constitute more than 80% of the
population with holdings ranging from 0.5 to 2 ha. The continuously rising population pressure has turned land into a scarce commodity.
2.2. Participatory Rural Appraisal
Participatory Rural Appraisals (Pretty et al., 1995) were conducted with the aid of
trained interpreters/facilitators from outside the village. An introductory meeting
and group interview with the village council of elders provided background information on the history and development at Ikem village. A time line was created to
Fig. 1. Location of strip transects as Ikem, southeastern Nigeria.
4
A. Gobin et al. / Agricultural Systems 67 (2001) 1±20
present the local history so that the sequence and relative proximity of dierent
events could be determined. A checklist of general questions using an open-ended
and semi-structured interviewing technique (Mettrick, 1993) provided information
on the community's social structure and organisations. The Ikem area was explored
with two local village guides to characterise the environment by observation and
short interviews. The village and hamlet boundaries, farming areas (including their
names), physical features, roads, markets, water supplies and public utilities were
outlined on a resource map and related to the 1:50,000 topographic map.
Transect walks (McCracken et al., 1988) were organised and observations made
were discussed with villagers met along the transects. A schematic diagram picturing
the land characteristics along the transects was produced and re®ned during discussions with various interest groups. Individual interviews across the existing social
classes and analytical games with social groups provided more insight in household
and group land management strategies. For the most common tree species, the local
name, use and importance of the tree to the local farming system were recorded, and
a branch sample collected. The local tree names were translated into taxonomic
names at the Department of Botany, University of Nigeria Nsukka, and the branches with leaves and, where possible, ¯orescences or fruits were crosschecked with
the Department's herbarium.
2.3. Selection of strip transects and ®eld plot analysis
Sixty pairs of 1:6000 aerial photographs (1982) from the Ministry of Land Resources were scanned, geo-referenced and related to a 1:50,000 topographic map. Strip
transects of 400 m wide and at 600 m intervals were drawn parallel to the direction of
the observed gradient in land cover, i.e. perpendicular to the main river (Fig. 1). Field
size, number of total trees, mature trees, shrubs and palm trees were recorded for all
388 ®eld plots located within the strip transects. The ®eld plots on the aerial photographs were related to the resource map, the name of the farming area was veri®ed
and the present land management was compared to the 1982 management by relating
practices in the particular area to events recorded on the time line. The land management system derived from villagers' accounts was crosschecked with own observations along the transects and aerial photograph interpretations.
The tree crown projection and morphology was used to distinguish between
shrub, mature tree and palm tree. Tree density derived from the scanned photographs was also crosschecked with stereoscopic analysis. The photographic threshold value for mature trees was set at a crown projection of 5 m in diameter. This
threshold value was calculated from the vertical projection of 50 mature tree crowns
derived by stretching a tape along the ground in two directions orthogonal to each
other and calculating an ellipse cover area.
2.4. Statistics and logistic modelling
Exploratory data analysis included descriptive statistics and a check for normality
by a Shapiro and Wilk test (SAS, 1990). A Fisher test was used to assess whether the
A. Gobin et al. / Agricultural Systems 67 (2001) 1±20
5
means per local land management system are dierent from each other at the 5%
signi®cance level for ®eld size and shrub, total tree, mature tree and palm tree density. Multiple comparison was accomplished through Duncan-Waller multiple range
tests at the 5% signi®cance level (SAS, 1990).
The nature of the cell distribution between local land management type and different intervals of tree densities and ®eld size were examined using frequency tables
and Pearson's, likelihood ratio and Mantel-Haenszel w2-tests for large sample sizes,
or Cochran-Mantel-Haenszel (CMH) statistics for smaller sample sizes. CMH statistics were also used to identify whether the pattern of association was ordinal (i.e.
determined by the order of land management).
Both univariate and multivariate logistic models (Hosmer and Lemeshow, 1989)
were constructed on two-thirds of the plots, i.e. a subsample of 260 ®eld plots, to
de®ne which independent variables are important to identify the type of local land
management. The land management types considered in each model were ranked
according to decreasing intensity of management. The conditional probability in a k
category model is:
Pr Y jjx j x
egj x
k
P
1 egj x
1
j1
where 1 4 j < k, Pr is probability, Y is the response variable local land management, k are categories. The link function is the logit transformation according to:
j x
2
gj x Bj Xj
logitdj xe ln
1 ÿ j x
where 1 4 j < k, Xj is a p1 matrix of (pÿ1) independent variables, Bj is a p1
matrix of intercepts and slope coecients ( ). The maximum likelihood estimates of
Bj in the logistic regression model are the values that maximise the log-likelihood
function [l (B)], according to:
ÿ 0
n
n
0 X
ÿ ÿ X
ln 1 e Bj Xji
Yj Bj Xji ÿ
ln l Bj
i1
3
i1
where n is the number of observations. The likelihood ratio statistic [=ÿ2 ln l (B)]
has an asymptotic w2-distribution with p degrees of freedom under the global null
hypothesis that all parameters ( ) equal zero, and was used to examine the signi®cance of individual models. Competing models were also compared using the
Akaike's Information Criterion (AIC) and Schwarz Criterion (SC), which are both
based on the likelihood ratio statistic but also take the number of observations into
account. The Wald test was obtained by comparing the maximum likelihood of each
individual slope parameter ( ) to an estimate of its standard error, and was used to
6
A. Gobin et al. / Agricultural Systems 67 (2001) 1±20
keep individual variables in the model applying a w2-criterion of P1) and negatively associated
with ®eld size (conditional odds w2
Intercept (p1)a
Intercept (p1+p2)a
Intercept (p1+p2+p3)a
Total tree density
1.1689
3.1505
4.9175
ÿ0.5710
0.2788
0.3493
0.4392
0.0568
17.5740
81.3377
125.3842
101.2096
Intercept (p1)a
Intercept (p1+p2)a
Intercept (p1+p2+p3)a
Shrub density
0.9492
2.9829
4.8610
ÿ0.6425
0.2573
0.3307
0.4330
0.0625
Intercept (p1)a
Intercept (p1+p2)a
Intercept (p1+p2+p3)a
Field size
3.5687
6.3280
8.7405
ÿ0.0028
a
Intercept (p1)
Intercept (p1+p2)a
Intercept (p1+p2+p3)a
(Total-Palm) density
a
Intercept (p1)
Intercept (p1+p2)a
Intercept (p1+p2+p3)a
(Total-Palm) density
Field size
Conditional
odds ratio
95% pro®le
likelihood CI
0.0001
0.0001
0.0001
0.0001
0.565
0.505±0.631
13.6048
81.3640
126.0420
105.6157
0.0001
0.0001
0.0001
0.0001
0.526
0.465±0.595
0.4357
0.6080
0.7534
0.00025
67.0929
108.3281
134.5943
121.3091
0.0001
0.0001
0.0001
0.0001
0.756
0.719±0.794
1.1724
3.2846
5.1648
ÿ0.6207
0.2747
0.3561
0.4561
0.0599
18.2163
85.0764
128.2278
107.3489
0.0001
0.0001
0.0001
0.0001
0.538
0.478±0.605
4.9570
9.2410
12.6041
ÿ0.5662
ÿ0.0027
0.5570
0.9172
1.1613
0.0738
0.0003
79.2109
101.5165
117.7906
58.9298
81.9435
0.0001
0.0001
0.0001
0.0001
0.0001
0.568
0.764
0.491±0.656
0.721±0.810
a
Communal land management systems were ranked prior to modelling: 1 is continuous cultivation, 2
is short-term fallow, 3 is medium-term fallow and 4 is long-term fallow management. Odds ratio is eb for
tree densities and e100b for ®eld size.
A. Gobin et al. / Agricultural Systems 67 (2001) 1±20
13
ratio w2-test was not signi®cant. The univariate ordinal model based on ®eld size
(AIC= 347, SC=360.3), followed by the model based on (total-palm) tree density (AIC= 417.7, SC= 431) were better than the models based on total tree density
(AIC=433.3, SC= 446.6) and shrub density (AIC=423.2, SC=436.5). The multivariate model (AIC=265.6, SC=282.3) shows the best ®t relative to a model without covariates (AIC=582.7, SC=592.7). The
measure of association is highest for
the multivariate model (0.934), followed by the univariate models with covariate
®eld size (0.819), (total-palm) tree density (0.733), shrub density (0.731) and total
tree density (0.7). Following Eq. (5) and Eq. (6), the cumulative probability (Fig. 5)
was calculated from the maximum likelihood estimates of all (Table 3). The conditional odds ratio indicates that an increasing intensity of communal management
is predicted with each unit decrease in total tree, (total-palm) tree and shrub density
(Table 3, Fig. 5). The odds of a more intensive communal land management are
0.756 times the odds for a less intensive fallow management per 100 m2 increase in
observed ®eld size. In the multivariate model, the odds for longer fallow management are 76% higher per unit increase in (total-palm) tree density and 31% higher
per 100 m2 increase in ®eld size.
The nested strategy comprising dichotomous models to distinguish private land
management followed by ordinal logistic models to predict dierent levels of communal land management, was compared to an ordinal logistic modelling strategy to
predict all types of land management at once. The univariate model based on total
tree density was rejected since the likelihood ratio w2-test was not signi®cant. Univariate models involving the other tree densities failed for the proportional odds test
Fig. 5. Univariate ordinal logistic models to predict dierent levels of communal land management.
Where Eq. (1) models Pr (Y42) and Eq. (3) models Pr (Y43).
14
A. Gobin et al. / Agricultural Systems 67 (2001) 1±20
or had non-signi®cant values (p>0.05) for some or all maximum likelihood parameter estimates. Only the univariate ordinal logistic model on the basis of ®eld size
was retained (Table 4). Longer fallow practices become 40% more likely per 100 m2
increase in ®eld size. Based on Eq. (5) and Eq. (6) and the parameter estimates
(Table 4), the cumulative probabilities were converted to probabilities for each local
land management type (Fig. 6), according to:
ÿ
7
Pr Y j jx Pr Y jjx ÿ Pr Y j ÿ 1jx
3.5. Validation of the models
The classi®cation tables for the binary logistic models allowed the speci®cation of
cut-o values based on a combination of maximum percentage of correct predictions and minimum percentages for false positive and false negative predictions
Table 4
Analysis of maximum likelihood estimates for logistic models predicting dierent levels of local land
management
Variable
b
S.E. (b)
Wald w2
P > w2
Intercept (p1)a
Intercept (p1+p2)a
Intercept (p1+p2+p3)a
Intercept (p1+p2+p3 +p4)a
Field size
1.9525
4.6105
7.6352
10.3323
ÿ0.00336
0.2817
0.4104
0.6214
0.7731
0.000259
48.0388
126.2357
150.9947
178.6035
169.3686
0.0001
0.0001
0.0001
0.0001
0.0001
Conditional
odds ratio
95% pro®le
likelihood CI
0.714
0.679±0.751
a
All local land management systems were ranked prior to modelling: 1 is private land management
(near and compound ®elds), 2 is continuous cultivation, 3 is short fallow, 4 is medium fallow and 5 is long
fallow management. Odds ratio is eb for tree densities and are e100b for ®eld size.
Fig. 6. Univariate ordinal logistic model to predict local land management from ®eld size.
Pr level
0.45
0.50
0.55
0.60
0.65
a
Multivariate (Size/Palm)
Univariate (Size)
Univariate (Palm)
Univariate (Mature)
Correct
False
positive
False
negative
Correct
False
positive
False
negative
Correct
False
positive
False
negative
Correct
False
positive
False
negative
98.1
98.5
98.5
98.1
98.1
5.7
3.8
3.8
3.9
3.9
1
1
1
1.4
1.4
94.2
94.2
94.2
95.0
94.2
18.6
17.5
16.4
13.2
13.7
2
2.5
2.9
2.9
3.8
94.6
95
94.6
94.6
94.6
10.4
6.7
6.8
6.8
4.8
4.2
4.7
5.1
5.1
5.5
90.4
89.2
90.0
89.6
89.6
11.4
12.5
3.6
0.0
0.0
9.3
10.5
10.8
11.5
11.5
Proposed cut-o values are in italic.
A. Gobin et al. / Agricultural Systems 67 (2001) 1±20
Table 5
Bias-adjusted classi®cation table for the best-®tted binary logistic models predicting private land management (see Table 2)a
15
16
Table 6
Classi®cation table for the best ®tted ordinal logistic models predicting communal land management levels (see Table 3) and validationa
Pr level
Short Fallow
Long Fallow
Correct
False
positive
False
negative
Correct
False
positive
False
negative
Correct
False
positive
False
negative
Correct
False
positive
False
negative
93.8
94.7
94.7
92.8
83.0
4.3
2.9
1.9
1.4
12.0
1.9
2.4
3.4
5.8
5.0
77.9
78.8
81.3
75.0
60.0
11.1
7.7
2.9
0.0
11.0
11.1
13.5
15.9
25.0
29.0
67.8
70.2
75.0
75.0
68.0
16.8
11.5
0.0
0.0
14.0
15.4
18.3
25.0
25.0
18.0
81.3
80.8
81.3
81.3
78.0
7.7
7.7
6.7
6.3
15.0
11.1
11.5
12.0
12.5
7.0
5.3
4.8
3.4
1.9
1.9
17.0
3.4
3.4
3.8
6.3
8.7
10.0
73.6
73.1
75.0
75.0
75.0
62.0
14.9
10.1
0.0
0.0
0.0
9.0
11.5
16.8
25.0
25.0
25.0
29.0
65.4
75.0
75.0
75.0
75.0
74.0
14.4
0.0
0.0
0.0
0.0
0.0
20.2
25.0
25.0
25.0
25.0
26.0
76.4
77.4
76.9
76.0
75.0
79.0
11.1
9.1
8.2
7.7
7.2
15.0
12.5
13.5
14.9
16.3
17.8
6.0
6.7
5.3
4.3
3.8
3.4
3.4
9.0
1.9
3.8
6.7
8.2
9.6
13.9
18.0
72.6
73.1
74.0
73.6
74.0
74.5
75.0
16.8
14.4
12.5
9.6
8.2
5.8
7.0
10.6
12.5
13.5
16.8
17.8
19.7
18.0
81.3
81.7
82.2
81.7
83.2
83.7
81.0
10.6
9.1
8.7
8.2
5.3
4.8
12.0
8.2
9.1
9.1
10.1
11.5
11.5
7.0
(Total-palm) tree density
0.40
91.3
0.45
91.8
0.50
92.8
0.55
91.8
0.60
89.4
Validation
73.0
Multivariate model (®eld size / (total-palm) tree density)
0.40
98.1
1.9
0.0
91.3
0.45
98.1
1.9
0.0
90.9
0.50
99.0
1.0
0.0
88.9
0.55
100.0
0.0
0.0
88.0
0.60
99.5
0.0
0.5
87.0
0.65
99.0
0.0
1.0
82.7
Validation
85.0
10.0
5.0
73.0
a
Medium Fallow
Proposed cut-o values are in italic.
A. Gobin et al. / Agricultural Systems 67 (2001) 1±20
Field size
0.45
0.50
0.55
0.60
Validation
Continuous Cultivation
A. Gobin et al. / Agricultural Systems 67 (2001) 1±20
17
(Table 5). The cut-o values were set at 0.55 for the univariate logistic model with
mature density, 0.50 for palm tree density, 0.6 for ®eld size and 0.55 for the multivariate model taking both palm tree density and ®eld size into account. Validation
of the models using the respective cut-o values showed that 72.7% of the new
observations were correctly classi®ed, whereas 6.8% were false positive and 20.5%
were false negative using a univariate binary logistic model with mature tree density.
The high percentage of false negative cases was due to the low number of mature
trees on some near-and-compound ®elds. The univariate model on the basis of ®eld
size classi®ed 76.5% of the ®elds as correct, 13.6% as false positive and 9.9% as
false negative. False positive cases were all small plots under continuous cultivation,
whereas false negative plots were the larger sized near-and-compound ®elds that
often occur near newer established settlements. Classi®cation on the basis of the
model with palm tree density was correct for 84.1%, false positive for 5.7% and
false negative for 10.2% of the validation observations. The multivariate model
combining palm tree density and ®eld size provided the best ®t with 86.4% correctly
classi®ed, 9.1% for false positive and 17.3% for false negative classi®cations. The
false negative classi®cations were small ®elds with a few palm trees that were in a
transition stage from communal to private ownership.
Classi®cation tables for the ordinal logistic models were constructed after converting the modelled conditional probabilities to single probabilities using Eq. (7). Cut-o
values were determined for each of the communal land management types based
on the same criteria as for the binary models. The cut-o values were set at 0.50±0.55
for the univariate model with ®eld size, 0.45±0.50 for (total-palm) tree density and
0.40±0.65 for the multivariate model incorporating both (total-palm) tree density
and ®eld size (Table 6). Validation of the univariate ordinal logistic model with ®eld
size resulted in 60±83% correctly classi®ed observations, 11±15% false positive and
5±29% false negative cases (Table 6). The univariate ordinal model on the basis of
(total-palm) tree density classi®ed 62±79% of the validation dataset as correct, 0±17%
as false positive and 6±29% as false negative (Table 6). Classi®cation on the basis of
the multivariate model combining (total-palm) tree density and ®eld size was correct
for 73±85%, false positive for 7±12% and false negative for 5±18% of the validation
observations (Table 6). False positive cases are all small plots under continuous cultivation, whereas false negative plots are the larger sized near-and-compound ®elds
that often occur near newer established settlements.
The ordinal univariate logistic model incorporating ®eld size predicted all local
levels of management with correct classi®cation of 76.5±95% for the modelled
and 71.9±80.5% for the validated ®elds at cut-o probabilities between 0.45 and
0.55 (Table 7). False positive cases accounted for 3.1±7.7% (modelled) and 2.3±
19.5% (validated), and false negative cases for 1.9±15.8% (modelled) and 2.3±22.7%
(validated).
3.6. Local land management indicators
The multivariate models showed the best goodness of ®t, the highest percentage of
correctly classi®ed observation, the minimum number of false positive and false
18
Pr level
0.40
0.45
0.50
0.55
0.60
Validation
a
Near and Compound ®elds
Continuos Cultivation
Correct
False
positive
False
negative
Correct False
False
Correct False
False
Correct False
False
Correct False
False
positive negative
positive negative
positive negative
positive negative
93.1
94.2
95.0
94.6
91.2
78.1
5.4
4.2
3.1
2.3
1.2
19.5
1.5
1.5
1.9
3.1
7.7
2.3
89.6
89.6
88.8
85.4
80.0
71.9
Proposed cut-o values are in italic.
7.3
5.0
3.8
2.7
0.0
10.2
3.1
5.4
7.3
11.9
20.0
18.0
Short Field
81.9
81.9
83.8
84.6
83.1
71.9
9.6
8.5
5.8
3.8
2.3
5.5
Medium Fallow
8.5
9.6
10.4
11.5
14.6
22.7
75.0
74.6
75.4
76.5
80.0
80.5
14.2
13.5
11.5
7.7
0.0
2.3
Long Fallow
10.8
11.9
13.1
15.8
20.0
17.2
85.8
86.2
85.0
84.6
85.0
80.5
6.5
6.2
6.2
6.2
5.4
14.8
7.7
7.7
8.8
9.2
9.6
4.7
A. Gobin et al. / Agricultural Systems 67 (2001) 1±20
Table 7
Classi®cation table for the ordinal logistic model based on ®eld size (see Table 4) and validationa
A. Gobin et al. / Agricultural Systems 67 (2001) 1±20
19
negative cases and the best model performances when using a validation data set.
The univariate ordinal model based on ®eld size only, showed a rather high percentage of false positive cases for the modelled probability of private land management
(Table 7). A nested strategy of estimating the probability of private land management using the multivariate binary logistic model (Table 2) and subsequently estimating the probability for each level of communal land management using the
multivariate ordinal logistic model (Table 3), enabled the best classi®cation. The
®tted models and respective cut-o value could then be used to classify future
observations in order to monitor changes and transitions to other types of local land
management or ownership. The most suitable land management indicators for the
area are the independent variables that feed the multivariate models: ®eld size, total
tree density and palm tree density.
4. Conclusions
A methodology is presented for establishing land management indicators and
investigating the link between the indicators and local land management. Participatory research methods helped elicit local land management systems and relate the
local terminology to quanti®able ®eld plot characteristics. Land tenure and customary laws explained the variation in ®eld characteristics between the local land
management systems. Logistic models were used to quantify the relationship
between ®eld characteristics and local land management systems. Field size, total
tree density and palm tree density proved the most successful land management
indicators in predicting probabilities of local land management systems.
The proposed indicators and logistic models can support policy-makers in monitoring land management changes, investigating transitions to other management
types and examining pressures exerted upon the land. The methodological approach
can be applied to other areas under similar farming systems. The models will gain
further importance if the independent variables for tree densities can be linked to
earth observation-derived land cover.
Acknowledgements
Funding for this research was provided by the Belgian Agency for Development
Co-operation (BADC) through the Inter-University Project on 'Water Resources
Development for domestic use and small scale irrigation in the rural areas of
southeastern Nigeria'. Special appreciation is extended to the project sta and
farmers of Ikem who contributed to this particular study.
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Agresti, A., 1990. Categorical Data Analysis. Wiley, New York.
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Gobin, A., Campling, P., Deckers, J., Feyen, J., 1998. Integrated toposequence analysis at the con¯uence
zone of the River Ebonyi headwater catchment (southeastern Nigeria). Catena 32, 173±192.
Hopkins, B., 1979. Forest and Savanna, 2nd edition. Heinemann Education Books, London, UK.
Hosmer, D.W., Lemeshow, S., 1989. Applied Logistic Regression. Wiley series in probability and mathematical statistics. John. Wiley, USA.
McCracken, J.A., Pretty, J.N., Conway, G.R., 1988. An introduction to Rapid Rural Appraisal for agricultural development. IIED, UK.
Mettrick, H., 1993. Development Oriented Research in Agriculture. An ICRA Notebook. CIP. The
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Anambra State. In: Igbozurike, U.M. (Ed.), Land Use and Conservation in Nigeria. University of
Nigeria Press, Nsukka, Nigeria, pp. 21±26.
Pieri, C., Dumanski, J., Hamblin, A., Young, A., 1995. Land Quality Indicators (World Bank Discussion
Paper No. 315). The World Bank, Washington DC, USA.
Pretty, J., Guijt, I., Thompson, J., Scoones, I., 1995. Participatory Learning and Action Ð A Trainer's
Guide. IIED participatory methodology series, London.
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Think Tank on Agriculture (Enugu State), 1993. Blue print on Enugu Agricultural State Programme.
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Commission on Sustainable Development, (E/CN.17/1995/7 February 1995). United Nations, New
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UNCED, 1993. Agenda 21: Programme of action for sustainable development. Proceedings UN Conference on Environment and Development, New York.
White, F., 1992. Vegetation map of Nigeria. In: Lanson, W. (Ed.), Plant Ecology in West Africa: Systems
and Processes. Bayero University, Kano, Nigeria.
Young, A., 1998. Land Resources: Now and for the Future. Cambridge University Press, UK.
www.elsevier.com/locate/agsy
Logistic modelling to identify and monitor local
land management systems
A. Gobin *, P. Campling, J. Feyen
Institute for Land and Water Management, Katholieke Universiteit Leuven, Vital Decosterstraat 102,
3000 Leuven, Belgium
Received 17 February 2000; received in revised form 20 July 2000; accepted 25 August 2000
Abstract
In the wake of sustainable development, measurable indicators are needed to monitor land
resources management. Aerial photograph interpretation, participatory research methods and
logistic modelling were combined to establish indicators and to investigate their relationship
with local land management systems. Land tenure and customary laws explained the dierences in ®eld characteristics at Ikem (southeastern Nigeria). A binary followed by an ordinal
logistic model quanti®ed the relationship between ®eld characteristics and local land management. The odds for private land management increased with 102% per 100 m2 decrease in
®eld size and with 128% per unit increase in palm tree density. For communal land management, fallow periods were longer with increasing non-palm tree densities and ®eld sizes; odds
increased with 76 and 31%, respectively. Field size, total tree density and palm tree density are
important indicators to monitor local land management. # 2001 Elsevier Science Ltd. All
rights reserved.
Keywords: Land management; Indicator; Participatory Rural Appraisal; Logistic modelling; Southeastern
Nigeria
1. Introduction
Environmental degradation is of great concern in sub-Saharan Africa. Prima facie,
loss of sustainability seems linked to rural people's attitude towards land resources.
Villagers are often considered to be placing their own short-term survival ahead of
long-term land resource sustainability (IFPRI, 1994). In southeastern Nigeria, the
* Corresponding author. Tel.: +32-16-32-97-21; fax: +32-16-32-97-60.
E-mail address: anne.gobin@agr.kuleuven.ac.be (A. Gobin).
0308-521X/01/$ - see front matter # 2001 Elsevier Science Ltd. All rights reserved.
PII: S0308-521X(00)00043-3
2
A. Gobin et al. / Agricultural Systems 67 (2001) 1±20
increased needs of a rising population are regarded as particularly disruptive for the
environment since the level of resources per capita declines (Think Tank on Agriculture, 1993). These negative views are often based on an abstraction of personal
observations and judgements but do not necessarily re¯ect the complex reality.
Objective and measurable criteria with potential to compare between areas and
monitor changes over time are needed to describe the condition and management of
land resources and the pressures exerted upon the land (Young, 1998). International
organisations have initiated programmes on developing measurable and policyrelevant environmental indicators (UN, 1995; OECD, 1997) to monitor progress in
reaching sustainable development, as de®ned in Agenda 21 (UNCED, 1993). The
pressure-state-response approach (Pieri et al., 1995) provides a framework to
develop land quality indicators and to place pressure upon land resources, changes
in the state of land quality and responses by society to these changes, within the
context of policy and natural resource management. However, multiple stakeholders
are involved in moulding the desirable goal of sustainable natural resource management and each of them will ®nd dierent indicators relevant to their reasons for
monitoring change. Integrating these dierent perspectives, particularly those of
local people, into indicators could lead to a better understanding of the processes
that cause change (ILEIA, 1996; Abbot and Guijt, 1998). Much of the research has
focussed on establishing single indicators with threshold values beyond which sustainable land resource management would be at stake.
The objectives of this paper are to elicit local land management systems, to
establish indicators that are capable of identifying and hence monitoring local
land management, and to investigate the link between the indicators and local land
management. Aerial photograph interpretation, participatory research methods
and logistic modelling were combined to identify and predict local land management
systems on the basis of ®eld plot characteristics. Logistic modelling was used to
predict probabilities of local land management systems and to investigate the relationship between the response probability and the explanatory ®eld characteristics.
Field characteristics incorporated into the best performing models were regarded as
suitable indicators. The models and indicators could be used to monitor local land
management and to examine the pressures exerted upon the land.
2. Materials and methods
2.1. Regional setting
The region has a humid tropical climate with a distinct dry season between
November and March with annual rainfall averaging at around 1500 mm per year.
The case study area is situated in the transition zone between lowland, GuineaCongolian, wetter type rainforest and Guinea savannah, resulting in a mosaic vegetation pattern (Hopkins, 1979; White, 1992). Lush evergreen forest fringes the
river and perennial streams, whereas along seasonal streamlines corridors of semideciduous trees and bushes are found. Moist semi-deciduous forest occurs on the
A. Gobin et al. / Agricultural Systems 67 (2001) 1±20
3
shale dominant inter¯uve, whereas drought-tolerant tree species and tall grasses
mainly vegetate the denudated inter¯uve areas.
The 40 km2 Ikem case study is located at the con¯uence zone of two perennial
rivers of the River Ebonyi headwater catchment, southeastern Nigeria (Fig. 1).
According to the 1991 census, the population density for Ikem averages around 400
persons per square kilometre. Smallholder farmers constitute more than 80% of the
population with holdings ranging from 0.5 to 2 ha. The continuously rising population pressure has turned land into a scarce commodity.
2.2. Participatory Rural Appraisal
Participatory Rural Appraisals (Pretty et al., 1995) were conducted with the aid of
trained interpreters/facilitators from outside the village. An introductory meeting
and group interview with the village council of elders provided background information on the history and development at Ikem village. A time line was created to
Fig. 1. Location of strip transects as Ikem, southeastern Nigeria.
4
A. Gobin et al. / Agricultural Systems 67 (2001) 1±20
present the local history so that the sequence and relative proximity of dierent
events could be determined. A checklist of general questions using an open-ended
and semi-structured interviewing technique (Mettrick, 1993) provided information
on the community's social structure and organisations. The Ikem area was explored
with two local village guides to characterise the environment by observation and
short interviews. The village and hamlet boundaries, farming areas (including their
names), physical features, roads, markets, water supplies and public utilities were
outlined on a resource map and related to the 1:50,000 topographic map.
Transect walks (McCracken et al., 1988) were organised and observations made
were discussed with villagers met along the transects. A schematic diagram picturing
the land characteristics along the transects was produced and re®ned during discussions with various interest groups. Individual interviews across the existing social
classes and analytical games with social groups provided more insight in household
and group land management strategies. For the most common tree species, the local
name, use and importance of the tree to the local farming system were recorded, and
a branch sample collected. The local tree names were translated into taxonomic
names at the Department of Botany, University of Nigeria Nsukka, and the branches with leaves and, where possible, ¯orescences or fruits were crosschecked with
the Department's herbarium.
2.3. Selection of strip transects and ®eld plot analysis
Sixty pairs of 1:6000 aerial photographs (1982) from the Ministry of Land Resources were scanned, geo-referenced and related to a 1:50,000 topographic map. Strip
transects of 400 m wide and at 600 m intervals were drawn parallel to the direction of
the observed gradient in land cover, i.e. perpendicular to the main river (Fig. 1). Field
size, number of total trees, mature trees, shrubs and palm trees were recorded for all
388 ®eld plots located within the strip transects. The ®eld plots on the aerial photographs were related to the resource map, the name of the farming area was veri®ed
and the present land management was compared to the 1982 management by relating
practices in the particular area to events recorded on the time line. The land management system derived from villagers' accounts was crosschecked with own observations along the transects and aerial photograph interpretations.
The tree crown projection and morphology was used to distinguish between
shrub, mature tree and palm tree. Tree density derived from the scanned photographs was also crosschecked with stereoscopic analysis. The photographic threshold value for mature trees was set at a crown projection of 5 m in diameter. This
threshold value was calculated from the vertical projection of 50 mature tree crowns
derived by stretching a tape along the ground in two directions orthogonal to each
other and calculating an ellipse cover area.
2.4. Statistics and logistic modelling
Exploratory data analysis included descriptive statistics and a check for normality
by a Shapiro and Wilk test (SAS, 1990). A Fisher test was used to assess whether the
A. Gobin et al. / Agricultural Systems 67 (2001) 1±20
5
means per local land management system are dierent from each other at the 5%
signi®cance level for ®eld size and shrub, total tree, mature tree and palm tree density. Multiple comparison was accomplished through Duncan-Waller multiple range
tests at the 5% signi®cance level (SAS, 1990).
The nature of the cell distribution between local land management type and different intervals of tree densities and ®eld size were examined using frequency tables
and Pearson's, likelihood ratio and Mantel-Haenszel w2-tests for large sample sizes,
or Cochran-Mantel-Haenszel (CMH) statistics for smaller sample sizes. CMH statistics were also used to identify whether the pattern of association was ordinal (i.e.
determined by the order of land management).
Both univariate and multivariate logistic models (Hosmer and Lemeshow, 1989)
were constructed on two-thirds of the plots, i.e. a subsample of 260 ®eld plots, to
de®ne which independent variables are important to identify the type of local land
management. The land management types considered in each model were ranked
according to decreasing intensity of management. The conditional probability in a k
category model is:
Pr Y jjx j x
egj x
k
P
1 egj x
1
j1
where 1 4 j < k, Pr is probability, Y is the response variable local land management, k are categories. The link function is the logit transformation according to:
j x
2
gj x Bj Xj
logitdj xe ln
1 ÿ j x
where 1 4 j < k, Xj is a p1 matrix of (pÿ1) independent variables, Bj is a p1
matrix of intercepts and slope coecients ( ). The maximum likelihood estimates of
Bj in the logistic regression model are the values that maximise the log-likelihood
function [l (B)], according to:
ÿ 0
n
n
0 X
ÿ ÿ X
ln 1 e Bj Xji
Yj Bj Xji ÿ
ln l Bj
i1
3
i1
where n is the number of observations. The likelihood ratio statistic [=ÿ2 ln l (B)]
has an asymptotic w2-distribution with p degrees of freedom under the global null
hypothesis that all parameters ( ) equal zero, and was used to examine the signi®cance of individual models. Competing models were also compared using the
Akaike's Information Criterion (AIC) and Schwarz Criterion (SC), which are both
based on the likelihood ratio statistic but also take the number of observations into
account. The Wald test was obtained by comparing the maximum likelihood of each
individual slope parameter ( ) to an estimate of its standard error, and was used to
6
A. Gobin et al. / Agricultural Systems 67 (2001) 1±20
keep individual variables in the model applying a w2-criterion of P1) and negatively associated
with ®eld size (conditional odds w2
Intercept (p1)a
Intercept (p1+p2)a
Intercept (p1+p2+p3)a
Total tree density
1.1689
3.1505
4.9175
ÿ0.5710
0.2788
0.3493
0.4392
0.0568
17.5740
81.3377
125.3842
101.2096
Intercept (p1)a
Intercept (p1+p2)a
Intercept (p1+p2+p3)a
Shrub density
0.9492
2.9829
4.8610
ÿ0.6425
0.2573
0.3307
0.4330
0.0625
Intercept (p1)a
Intercept (p1+p2)a
Intercept (p1+p2+p3)a
Field size
3.5687
6.3280
8.7405
ÿ0.0028
a
Intercept (p1)
Intercept (p1+p2)a
Intercept (p1+p2+p3)a
(Total-Palm) density
a
Intercept (p1)
Intercept (p1+p2)a
Intercept (p1+p2+p3)a
(Total-Palm) density
Field size
Conditional
odds ratio
95% pro®le
likelihood CI
0.0001
0.0001
0.0001
0.0001
0.565
0.505±0.631
13.6048
81.3640
126.0420
105.6157
0.0001
0.0001
0.0001
0.0001
0.526
0.465±0.595
0.4357
0.6080
0.7534
0.00025
67.0929
108.3281
134.5943
121.3091
0.0001
0.0001
0.0001
0.0001
0.756
0.719±0.794
1.1724
3.2846
5.1648
ÿ0.6207
0.2747
0.3561
0.4561
0.0599
18.2163
85.0764
128.2278
107.3489
0.0001
0.0001
0.0001
0.0001
0.538
0.478±0.605
4.9570
9.2410
12.6041
ÿ0.5662
ÿ0.0027
0.5570
0.9172
1.1613
0.0738
0.0003
79.2109
101.5165
117.7906
58.9298
81.9435
0.0001
0.0001
0.0001
0.0001
0.0001
0.568
0.764
0.491±0.656
0.721±0.810
a
Communal land management systems were ranked prior to modelling: 1 is continuous cultivation, 2
is short-term fallow, 3 is medium-term fallow and 4 is long-term fallow management. Odds ratio is eb for
tree densities and e100b for ®eld size.
A. Gobin et al. / Agricultural Systems 67 (2001) 1±20
13
ratio w2-test was not signi®cant. The univariate ordinal model based on ®eld size
(AIC= 347, SC=360.3), followed by the model based on (total-palm) tree density (AIC= 417.7, SC= 431) were better than the models based on total tree density
(AIC=433.3, SC= 446.6) and shrub density (AIC=423.2, SC=436.5). The multivariate model (AIC=265.6, SC=282.3) shows the best ®t relative to a model without covariates (AIC=582.7, SC=592.7). The
measure of association is highest for
the multivariate model (0.934), followed by the univariate models with covariate
®eld size (0.819), (total-palm) tree density (0.733), shrub density (0.731) and total
tree density (0.7). Following Eq. (5) and Eq. (6), the cumulative probability (Fig. 5)
was calculated from the maximum likelihood estimates of all (Table 3). The conditional odds ratio indicates that an increasing intensity of communal management
is predicted with each unit decrease in total tree, (total-palm) tree and shrub density
(Table 3, Fig. 5). The odds of a more intensive communal land management are
0.756 times the odds for a less intensive fallow management per 100 m2 increase in
observed ®eld size. In the multivariate model, the odds for longer fallow management are 76% higher per unit increase in (total-palm) tree density and 31% higher
per 100 m2 increase in ®eld size.
The nested strategy comprising dichotomous models to distinguish private land
management followed by ordinal logistic models to predict dierent levels of communal land management, was compared to an ordinal logistic modelling strategy to
predict all types of land management at once. The univariate model based on total
tree density was rejected since the likelihood ratio w2-test was not signi®cant. Univariate models involving the other tree densities failed for the proportional odds test
Fig. 5. Univariate ordinal logistic models to predict dierent levels of communal land management.
Where Eq. (1) models Pr (Y42) and Eq. (3) models Pr (Y43).
14
A. Gobin et al. / Agricultural Systems 67 (2001) 1±20
or had non-signi®cant values (p>0.05) for some or all maximum likelihood parameter estimates. Only the univariate ordinal logistic model on the basis of ®eld size
was retained (Table 4). Longer fallow practices become 40% more likely per 100 m2
increase in ®eld size. Based on Eq. (5) and Eq. (6) and the parameter estimates
(Table 4), the cumulative probabilities were converted to probabilities for each local
land management type (Fig. 6), according to:
ÿ
7
Pr Y j jx Pr Y jjx ÿ Pr Y j ÿ 1jx
3.5. Validation of the models
The classi®cation tables for the binary logistic models allowed the speci®cation of
cut-o values based on a combination of maximum percentage of correct predictions and minimum percentages for false positive and false negative predictions
Table 4
Analysis of maximum likelihood estimates for logistic models predicting dierent levels of local land
management
Variable
b
S.E. (b)
Wald w2
P > w2
Intercept (p1)a
Intercept (p1+p2)a
Intercept (p1+p2+p3)a
Intercept (p1+p2+p3 +p4)a
Field size
1.9525
4.6105
7.6352
10.3323
ÿ0.00336
0.2817
0.4104
0.6214
0.7731
0.000259
48.0388
126.2357
150.9947
178.6035
169.3686
0.0001
0.0001
0.0001
0.0001
0.0001
Conditional
odds ratio
95% pro®le
likelihood CI
0.714
0.679±0.751
a
All local land management systems were ranked prior to modelling: 1 is private land management
(near and compound ®elds), 2 is continuous cultivation, 3 is short fallow, 4 is medium fallow and 5 is long
fallow management. Odds ratio is eb for tree densities and are e100b for ®eld size.
Fig. 6. Univariate ordinal logistic model to predict local land management from ®eld size.
Pr level
0.45
0.50
0.55
0.60
0.65
a
Multivariate (Size/Palm)
Univariate (Size)
Univariate (Palm)
Univariate (Mature)
Correct
False
positive
False
negative
Correct
False
positive
False
negative
Correct
False
positive
False
negative
Correct
False
positive
False
negative
98.1
98.5
98.5
98.1
98.1
5.7
3.8
3.8
3.9
3.9
1
1
1
1.4
1.4
94.2
94.2
94.2
95.0
94.2
18.6
17.5
16.4
13.2
13.7
2
2.5
2.9
2.9
3.8
94.6
95
94.6
94.6
94.6
10.4
6.7
6.8
6.8
4.8
4.2
4.7
5.1
5.1
5.5
90.4
89.2
90.0
89.6
89.6
11.4
12.5
3.6
0.0
0.0
9.3
10.5
10.8
11.5
11.5
Proposed cut-o values are in italic.
A. Gobin et al. / Agricultural Systems 67 (2001) 1±20
Table 5
Bias-adjusted classi®cation table for the best-®tted binary logistic models predicting private land management (see Table 2)a
15
16
Table 6
Classi®cation table for the best ®tted ordinal logistic models predicting communal land management levels (see Table 3) and validationa
Pr level
Short Fallow
Long Fallow
Correct
False
positive
False
negative
Correct
False
positive
False
negative
Correct
False
positive
False
negative
Correct
False
positive
False
negative
93.8
94.7
94.7
92.8
83.0
4.3
2.9
1.9
1.4
12.0
1.9
2.4
3.4
5.8
5.0
77.9
78.8
81.3
75.0
60.0
11.1
7.7
2.9
0.0
11.0
11.1
13.5
15.9
25.0
29.0
67.8
70.2
75.0
75.0
68.0
16.8
11.5
0.0
0.0
14.0
15.4
18.3
25.0
25.0
18.0
81.3
80.8
81.3
81.3
78.0
7.7
7.7
6.7
6.3
15.0
11.1
11.5
12.0
12.5
7.0
5.3
4.8
3.4
1.9
1.9
17.0
3.4
3.4
3.8
6.3
8.7
10.0
73.6
73.1
75.0
75.0
75.0
62.0
14.9
10.1
0.0
0.0
0.0
9.0
11.5
16.8
25.0
25.0
25.0
29.0
65.4
75.0
75.0
75.0
75.0
74.0
14.4
0.0
0.0
0.0
0.0
0.0
20.2
25.0
25.0
25.0
25.0
26.0
76.4
77.4
76.9
76.0
75.0
79.0
11.1
9.1
8.2
7.7
7.2
15.0
12.5
13.5
14.9
16.3
17.8
6.0
6.7
5.3
4.3
3.8
3.4
3.4
9.0
1.9
3.8
6.7
8.2
9.6
13.9
18.0
72.6
73.1
74.0
73.6
74.0
74.5
75.0
16.8
14.4
12.5
9.6
8.2
5.8
7.0
10.6
12.5
13.5
16.8
17.8
19.7
18.0
81.3
81.7
82.2
81.7
83.2
83.7
81.0
10.6
9.1
8.7
8.2
5.3
4.8
12.0
8.2
9.1
9.1
10.1
11.5
11.5
7.0
(Total-palm) tree density
0.40
91.3
0.45
91.8
0.50
92.8
0.55
91.8
0.60
89.4
Validation
73.0
Multivariate model (®eld size / (total-palm) tree density)
0.40
98.1
1.9
0.0
91.3
0.45
98.1
1.9
0.0
90.9
0.50
99.0
1.0
0.0
88.9
0.55
100.0
0.0
0.0
88.0
0.60
99.5
0.0
0.5
87.0
0.65
99.0
0.0
1.0
82.7
Validation
85.0
10.0
5.0
73.0
a
Medium Fallow
Proposed cut-o values are in italic.
A. Gobin et al. / Agricultural Systems 67 (2001) 1±20
Field size
0.45
0.50
0.55
0.60
Validation
Continuous Cultivation
A. Gobin et al. / Agricultural Systems 67 (2001) 1±20
17
(Table 5). The cut-o values were set at 0.55 for the univariate logistic model with
mature density, 0.50 for palm tree density, 0.6 for ®eld size and 0.55 for the multivariate model taking both palm tree density and ®eld size into account. Validation
of the models using the respective cut-o values showed that 72.7% of the new
observations were correctly classi®ed, whereas 6.8% were false positive and 20.5%
were false negative using a univariate binary logistic model with mature tree density.
The high percentage of false negative cases was due to the low number of mature
trees on some near-and-compound ®elds. The univariate model on the basis of ®eld
size classi®ed 76.5% of the ®elds as correct, 13.6% as false positive and 9.9% as
false negative. False positive cases were all small plots under continuous cultivation,
whereas false negative plots were the larger sized near-and-compound ®elds that
often occur near newer established settlements. Classi®cation on the basis of the
model with palm tree density was correct for 84.1%, false positive for 5.7% and
false negative for 10.2% of the validation observations. The multivariate model
combining palm tree density and ®eld size provided the best ®t with 86.4% correctly
classi®ed, 9.1% for false positive and 17.3% for false negative classi®cations. The
false negative classi®cations were small ®elds with a few palm trees that were in a
transition stage from communal to private ownership.
Classi®cation tables for the ordinal logistic models were constructed after converting the modelled conditional probabilities to single probabilities using Eq. (7). Cut-o
values were determined for each of the communal land management types based
on the same criteria as for the binary models. The cut-o values were set at 0.50±0.55
for the univariate model with ®eld size, 0.45±0.50 for (total-palm) tree density and
0.40±0.65 for the multivariate model incorporating both (total-palm) tree density
and ®eld size (Table 6). Validation of the univariate ordinal logistic model with ®eld
size resulted in 60±83% correctly classi®ed observations, 11±15% false positive and
5±29% false negative cases (Table 6). The univariate ordinal model on the basis of
(total-palm) tree density classi®ed 62±79% of the validation dataset as correct, 0±17%
as false positive and 6±29% as false negative (Table 6). Classi®cation on the basis of
the multivariate model combining (total-palm) tree density and ®eld size was correct
for 73±85%, false positive for 7±12% and false negative for 5±18% of the validation
observations (Table 6). False positive cases are all small plots under continuous cultivation, whereas false negative plots are the larger sized near-and-compound ®elds
that often occur near newer established settlements.
The ordinal univariate logistic model incorporating ®eld size predicted all local
levels of management with correct classi®cation of 76.5±95% for the modelled
and 71.9±80.5% for the validated ®elds at cut-o probabilities between 0.45 and
0.55 (Table 7). False positive cases accounted for 3.1±7.7% (modelled) and 2.3±
19.5% (validated), and false negative cases for 1.9±15.8% (modelled) and 2.3±22.7%
(validated).
3.6. Local land management indicators
The multivariate models showed the best goodness of ®t, the highest percentage of
correctly classi®ed observation, the minimum number of false positive and false
18
Pr level
0.40
0.45
0.50
0.55
0.60
Validation
a
Near and Compound ®elds
Continuos Cultivation
Correct
False
positive
False
negative
Correct False
False
Correct False
False
Correct False
False
Correct False
False
positive negative
positive negative
positive negative
positive negative
93.1
94.2
95.0
94.6
91.2
78.1
5.4
4.2
3.1
2.3
1.2
19.5
1.5
1.5
1.9
3.1
7.7
2.3
89.6
89.6
88.8
85.4
80.0
71.9
Proposed cut-o values are in italic.
7.3
5.0
3.8
2.7
0.0
10.2
3.1
5.4
7.3
11.9
20.0
18.0
Short Field
81.9
81.9
83.8
84.6
83.1
71.9
9.6
8.5
5.8
3.8
2.3
5.5
Medium Fallow
8.5
9.6
10.4
11.5
14.6
22.7
75.0
74.6
75.4
76.5
80.0
80.5
14.2
13.5
11.5
7.7
0.0
2.3
Long Fallow
10.8
11.9
13.1
15.8
20.0
17.2
85.8
86.2
85.0
84.6
85.0
80.5
6.5
6.2
6.2
6.2
5.4
14.8
7.7
7.7
8.8
9.2
9.6
4.7
A. Gobin et al. / Agricultural Systems 67 (2001) 1±20
Table 7
Classi®cation table for the ordinal logistic model based on ®eld size (see Table 4) and validationa
A. Gobin et al. / Agricultural Systems 67 (2001) 1±20
19
negative cases and the best model performances when using a validation data set.
The univariate ordinal model based on ®eld size only, showed a rather high percentage of false positive cases for the modelled probability of private land management
(Table 7). A nested strategy of estimating the probability of private land management using the multivariate binary logistic model (Table 2) and subsequently estimating the probability for each level of communal land management using the
multivariate ordinal logistic model (Table 3), enabled the best classi®cation. The
®tted models and respective cut-o value could then be used to classify future
observations in order to monitor changes and transitions to other types of local land
management or ownership. The most suitable land management indicators for the
area are the independent variables that feed the multivariate models: ®eld size, total
tree density and palm tree density.
4. Conclusions
A methodology is presented for establishing land management indicators and
investigating the link between the indicators and local land management. Participatory research methods helped elicit local land management systems and relate the
local terminology to quanti®able ®eld plot characteristics. Land tenure and customary laws explained the variation in ®eld characteristics between the local land
management systems. Logistic models were used to quantify the relationship
between ®eld characteristics and local land management systems. Field size, total
tree density and palm tree density proved the most successful land management
indicators in predicting probabilities of local land management systems.
The proposed indicators and logistic models can support policy-makers in monitoring land management changes, investigating transitions to other management
types and examining pressures exerted upon the land. The methodological approach
can be applied to other areas under similar farming systems. The models will gain
further importance if the independent variables for tree densities can be linked to
earth observation-derived land cover.
Acknowledgements
Funding for this research was provided by the Belgian Agency for Development
Co-operation (BADC) through the Inter-University Project on 'Water Resources
Development for domestic use and small scale irrigation in the rural areas of
southeastern Nigeria'. Special appreciation is extended to the project sta and
farmers of Ikem who contributed to this particular study.
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