logistic modelling to derive agricultural land use determinants: a case study from southeastern...

Agriculture, Ecosystems and Environment 89 (2002) 213–228

Logistic modelling to derive agricultural land use determinants: acase study from southeastern Nigeria

A. Gobin∗, P. Campling, J. FeyenInstitute for Land and Water Management, Katholieke Universiteit Leuven, Vital Decosterstraat 102, 3000 Leuven, Belgium

Received 14 March 2000; received in revised form 3 November 2000; accepted 12 December 2000

Abstract

Human activity has a strong impact on spatial land cover patterns. Land cover characteristics show significant differencesbetween the five local agricultural land use (ALU) systems at Ikem, southeastern Nigeria. Aerial photograph interpretation(1:6000), participatory rural appraisal and logistic modelling were combined to elicit spatial determinants and to model ALUusing a partially nested strategy. The binary logistic model for estimating probabilities of private ALU correctly predicted95.7% of the 300 sample plots and 89.8% of the 88 validation plots, all located within nine strip transects. The odds for privateALU increased with 21.3% per 10 m distance closer to the settlement and were highest for a location on the accumulationglacis. An ordinal logistic model for predicting four communal ALU classes correctly classified 83.3% of the sample plotsand 78.3% of the validation plots. The odds for longer fallow periods increased with 21.8% per 100 m distance away fromthe settlement and were higher on both the mixed and erosion glacis. Landform, distance to the settlement and customaryownership were the most important of the local determinants for ALU. The ALU models could be incorporated into a landuse framework for planning purposes, scenario analysis or impact assessment at the local government level. © 2002 ElsevierScience B.V. All rights reserved.

Keywords:Agricultural land use; Land use determinant; Spatial analysis; Logistic modelling; Southeastern Nigeria

1. Introduction

The United Nations Conference on Environmentand Development (UNCED’s Agenda 21) endorsedan integrated approach to the sustainable planningand management of land resources (UNCED, 1993),which demands a balancing between social equity,economic development and environmental conserva-tion (Dovers et al., 1996). A spatial understanding ofthe relationships between different land uses and theirdeterminants is an important contribution towardssustainable land use planning (O’callaghan, 1995).

∗ Corresponding author. Fax:+32-16329760.E-mail address:[email protected] (A. Gobin).

In Africa, where data availability poses a knownconstraint, eliciting local land use determinants andmodelling actual land use is a first step in trackingland use change for purposes of land use planningand environmental monitoring.

Land use is closely related to land cover. Land coverrefers to all the natural and manmade features thatcover the earth’s surface, whereas land use refers tothe human activity that is associated with a specificland unit, in terms of utilisation, impacts or manage-ment practices (FAO, 1997). The interdependence be-tween land cover and land use has often resulted inland cover being used as a major diagnostic tool in theidentification of land use, leading to a common map-ping association. Although there is a trend towards the

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214 A. Gobin et al. / Agriculture, Ecosystems and Environment 89 (2002) 213–228

development of separate land cover and land use clas-sification schemes (Turner et al., 1995; FAO, 1997), inthis study a common mapping association was utilisedto reflect local land use and to suit the purposes oflocal agricultural land use modelling. Moreover, sig-nificant relationships were established between landcover characteristics and five local agricultural landuse (ALU) systems in southeastern Nigeria (Gobinet al., 2000a,b).

Human activity accounts for the majority of landcover change. Land use patterns are driven by a varietyof physical and socio-economic determinants and re-sult in land cover changes that affect the environment.Consequently, assessments of environmental impactrequire modelling of land use and land use change.The majority of land use studies, however, comprisesof theoretical classification followed by mapping andneglects a more analytical endeavour based on the-ory and modelling. Understanding the relationship be-tween local determinants and land use helps futuremonitoring and modelling of land cover/use change.

Many land use models predict continuous variablessuch as rates of deforestation (Angelsen, 1999) or landvalues (Alig, 1986; Geoghegan et al., 1997), whichallow for the use of standard statistical methods suchas linear programming, ordinary least squares regres-sion and computable general equilibrium approaches(Angelsen and Kaimowitz, 1999). The majority ofthese models include economic components and as-sume that land is a factor of production or can beexpressed in monetary terms. However, the complexland tenure situation in West Africa, which resultsfrom the coexistence of customary and state owner-ship (Delville, 1998; Gobin et al., 2000a,b), makesit impossible to attach a monetary value to land. Theprofit-maximising objective of market-oriented ac-tivities and the risk-aversive strategies of traditionalsubsistence agriculture, guide land use decisions fromtraditional and market norms to varying degrees andprovide a mechanism through which production canbe maintained or increased to satisfy social needs(Ellis, 1988; Ikubolajeh, 1995).

Categorical modelling efforts have mainly focussedon simulating land cover change or land conver-sion, mostly as binary variables, in studies of habitatfragmentation (Bian and West, 1997; Clark et al.,1999), loss of tropical forests (Reis and Margulis,1991; Chomitz and Gray, 1995; Mertens and Lambin,

1997) and urbanisation (Gore and Nicholson, 1991;Ganderton, 1994). The Markov-chain procedure(Brown, 1970) is commonly used to simulate landcover changes in terms of transition probabilities thatare statistically estimated from past transition propor-tions between different land cover classes (Turner,1987). Binary logistic models estimate the transitionprobabilities of land cover based on causative predic-tor variables (Lambin, 1997). The major advantagesof using binary logistic models are their explanatorypower, their capacity to model non-stationary landcover changes and their capability of simulating sce-narios. The predictor variables can be extracted fromaerial photographs, satellite images and georeferenceddatabases.

This paper outlines an integrated approach to derivelocal spatial determinants and to model five local agri-cultural land use systems in a way that is potentiallyuseful for policy analysis, environmental modellingand land use planning at the local government level inWest Africa. Logistic modelling techniques were usedto predict probabilities of local agricultural land usesystems at Ikem (southeastern Nigeria), where >80%of the population is engaged in small-scale oil palm(Elaeis guineensis) and root crop farming. Based on1:6000 aerial photographs and participatory rural ap-praisals (PRA), the local agricultural land use system(both present and past) was recorded for 388 fieldplots located within nine strip transects. A combinedbinary and ordinal logistic modelling approach wasused to predict probabilities of local agricultural landuse. The model predictors are land use determinantsthat are useful tools in land use planning and allow forincorporating likely responses in land use to changesin determinants.

2. Materials and methods

2.1. Regional setting

The 40 km2 Ikem case study is located at theconfluence zone of two perennial rivers of the riverEbonyi headwater catchment, southeastern Nigeria(Fig. 1). At the University of Nigeria Nsukka meteo-rological station (6◦51′57′′N, 7◦25′27′′E, 396 m), theaverage annual rainfall from 1966 to 1995 is about1500 mm year−1. A pronounced dry season occurs

A. Gobin et al. / Agriculture, Ecosystems and Environment 89 (2002) 213–228 215

Fig. 1. Regional setting and location of strip transects at Ikem, southeastern Nigeria.

between November and March, followed by rainfallduring the remaining months of the year. The casestudy area is situated in the transition zone betweenlowland, Guinea–Congolian, wetter type rainforestand Guinea savannah, resulting in a mosaic vegetationpattern of humid forest along permanent waterbodiesand savannah vegetation on the drier areas (Hopkins,1979; White, 1992).

Severe gully erosion in the friable sandstone forma-tions of the Udi-Nsukka Cuesta (Gobin et al., 1999)provides a heavy sediment load transported by theAmanyi and Ebonyi river systems and deposited onthe Enugu Shale (Fig. 1). At the confluence zone of thetwo rivers (Ikem community), the lowland fluvial land-scape comprises a meandering river channel bordered

by narrow sandy river banks, seasonally submergedloam to clay-loam backswamps and a clay-loam toclay river terrace (Gobin et al., 1998a,b). The upland,interfluvial landscape is a glacis and can be dividedinto erosion glacis and accumulation glacis. The ero-sion glacis is located on ridges and hills, and is char-acterised by the presence of ironstone lag gravel. Theaccumulation glacis has ironstone nodules occurring atgreater depth. Undulating zones of repeated accumu-lation and erosion glacis sequences are termed mixedglacis. There is a distinct relation between landformand soil in the study area (Table 1).

The 1991 census estimated the Ikem populationdensity at 300 persons km−2, whereas field estimatesbased on housing facilities amounted to 225 persons


Table 1Relation between landform and soil

Location Soil subunit (FAO et al., 1998)

Riverbank Areni-umbric fluvisolBackswamp Molli-orthiplinthic gleysolTerrace Abrupti-umbric acrisol (hyperferric)Accumulation glacis Abrupti-umbric acrisol (hyperskeletic)Erosion glacis Umbri-humic acrisol (episkeletic)

km−2. Since smallholder farmers constitute >80% ofthe population and farmholdings range from 0.5 to 2 ha(Think Tank, 1993), land has become a scarce com-modity. Previous studies in the area showed that thetraditional land use system comprises communal landownership in the farmlands and private land owner-ship in and immediately around the settlements (Gobinet al., 1997). Land allocation is to the extended fam-ily or kinship group (often called village and partof the community); private ownership by individualsor households is strictly usufructuary although theserights are often passed from generation to generation(Gobin et al., 1998a,b).

2.2. Geographic database development andcharacterisation of field plots

A participatory resource map and time line (Prettyet al., 1995) were used to elicit land use systemsat specific locations and to construct the history ofthe study area (Gobin et al., 2000a,b). The commu-nity and village boundaries, farming areas (includingtheir names), physical features, roads, markets, watersupplies and public utilities were outlined on a re-source map, related to the 1:50,000 topographic mapand further refined during subsequent discussionswith villagers. About 60 pairs of 1:6000 aerial pho-tographs (1982) from the Ministry of Land Resourceswere scanned and georeferenced. Thematic mapswere created by digitising the roads, tracks, riversand streams. A landform map and a land use/landcover map (Gobin et al., 1997; Gobin et al., 1998a,b)were derived from the 1:6000 aerial photographs anddigitised in ArcInfo (ESRI, 1996) (Fig. 2).

Nine strip transects of 400 m wide and at 600 minterval were drawn parallel to the direction of theobserved gradient in land cover, i.e. perpendicular tothe main river (Fig. 1). All plots located within the

nine strip transects were recorded apart from thoseneighbouring previously recorded plots. The 388 fieldplots on the aerial photographs were related to theresource map, the name of the farming area was ver-ified and the present land use was compared to the1982 management with the aid of the recorded timeline. The agricultural land use derived from villagers’accounts was crosschecked with the resource map, thetime line, field observations along transects and aerialphotograph interpretations (Gobin et al., 2000a,b).

Farmers distinguished five different agriculturalland use systems at the different plots. The privatelyowned ‘near-and-compound’ fields (NC) were associ-ated with the settlement area and oil palm dominatedforest (Fig. 2). The ‘near-and-compound’ fields arecustomary land use systems that have developed si-multaneously with communally organised land usesystems of shifting cultivation in the region (Okaforand Fernandes, 1987; Gobin et al., 2000a,b). Withinthe communal farmlands, local farmers distinguishedbetween continuous cultivation (CC, no fallow, re-turn period is <1 year), grass fallow (GF, shortfallow of between 1 and 3 years), grass and bushfallow (GBF, medium fallow of between 3 and 5years) and bush fallow (BF, long fallow of >5 years)(Gobin et al., 1997; Gobin et al., 1998a,b). Landcover characteristics such as tree density, tree typeand field size showed significant differences betweenthe five local agricultural land use (ALU) systems(Gobin et al., 2000a,b).

2.3. Predictor variables

The variables used to predict local agricultural landuse systems were elicited during participatory ruralappraisals conducted in the study area (Gobin et al.,1997) and quantified using GIS (ESRI, 1996a,b).

The landform classes were reduced to four classesfor use in logistic modelling (Hosmer and Lemeshow,1989): stream and river floodplain and terraces (LF1),accumulation glacis (LF2), mixed glacis (LF3) anderosion glacis including hills, ridges and seasonalstream valleys (LF4). For each landform class a bi-nary categorical variable was created, which resultedin four landform raster maps. Based on these fourraster maps, the correct code (1 or 0) for each ofthe four landform variables (LF) was assigned to themiddle point of each field plot.


Fig. 2. Land cover/use map of Ikem, southeastern Nigeria.

Spatial accessibility to sites of socio-economic im-portance (Geertman and Ritsema-van Eck, 1995) wasdetermined by the geographic location in relation toa line (e.g. road, river) or node (e.g. market, house)and by the transport network available to reach thetarget or facility. Spatial accessibility to the nearesttrack, house or settlement, main river and stream werecalculated for each 4 m× 4 m pixel as the Euclideandistance to the target location.

Least-cost routes to the market, major road, mainriver, stream and house were calculated for each 4 m×4 m pixel with the aid of a friction surface. A frictionsurface was constructed from the combined road/trackand river/stream maps. Since most people in the studyarea were walking to their destinations, travelling dis-tances on roads and established tracks were assumedonly twice as fast as elsewhere. Rivers and streamswere added as barriers to the friction surface.

An accessibility surface map was created for eachspatial accessibility variable and the values for themiddle point of each field plot were determined by in-tersecting the surface map and the middle point cover.

2.4. Exploratory statistics

Analysis of variance (SAS, 1990) was used to testthe hypothesis that the difference between the differentland use types equalled zero for each of the continuouspredictor variables. The nature of the cell distributionbetween local agricultural land use type and each ofthe predictor variables was examined using frequencytables and measures of association. Pearson’s, likeli-hood ratio and Mantel–Haenszelχ2 were tested forgeneral association, while Cochran–Mantel–Haenszel(CMH) statistics were used to further examine thestrength and type of association. The contingency


coefficient (between 0 and 1) represented a measurefor examining general association. All other measurestested for association between the ordinal variablesagricultural land use and each of the predictor vari-ables. Somers’D row/column was used as a measurefor examining proportional reduction of errors whenland use is predicted from each of the predictor vari-able (for example landform). The estimatorγ (seealso Eq. (2)) is based on the number of concordantand discordant pairs of observations, and tends to beclose to zero if the two variables are independent.Pearson’s and Spearman’s correlation coefficientswere calculated by using scores, and were used forexamining linear relations.

2.5. Logistic modelling

The proportional odds assumption was rejectedwhen applied to the whole data set (all five agricul-tural land use systems), but accepted when applied tothe plots under the four communal land use systems.Therefore, a partially nested strategy was adopted topredict the probabilities of local agricultural land use(Fig. 3). In a first step, a binary logistic model wasdeveloped to predict local agricultural land use underprivate ownership (near-and-compound fields) on thebasis of landform and spatial accessibility variables.In a next step, an ordinal logistic model (proportionalodds) was constructed to simulate probabilities of the

Fig. 3. Partially nested strategy to predict the probabilities of local agricultural land use.

four different levels of communal agricultural landuse. The rationale is that the privately managed agri-cultural lands (near-and-compound fields) representa traditional land use system that has simultaneouslydeveloped with, but is distinctly different from, thecommunal land use systems (Okafor and Fernandes,1987). Univariate and multivariate logistic models(Cox and Snell, 1989) were constructed on a subsetof 300 plots and validated on a subset of 88 plotsto define which variables were important to predictthe probability of local land use. The land use sys-tems considered in each model were ranked accord-ing to decreasing intensity of management (Fig. 3):near-and-compound fields (NC), continuous cultiva-tion (CC), grass fallow (GF), grass and bush fallow(GBF) and bush fallow (BF).

The response was binary in the case of private (Y =1) versus communal (Y = 2) agricultural land use; thelink function was log it according to

log it[Pr(Y = 1|x)] = ln

[Pr(Y = 1|x)

1 − Pr(Y = 1|x)

]

= B ′kxk = β0 + β1x1 + · · ·

+M−1∑m=1

βhmDhm + · · · + βkxk

(1)

where Pr is probability,Y the response variable local


land use,xk a p × 1 matrix of 1 followed by (p − 1)predictor variables,Bk a p × 1 matrix of interceptsand slope coefficients (β), D a design variable for thecategorical variablexh, m representsM categories ofbinary classes. The categorical variable landform hadfour (M) possible classes, so that three (M − 1) pos-sible binary design variables were created. The refer-ence class was the class with value 0 for each designvariables. Univariate logistic models were fit for eachof the predictor variables landform (split into designvariables) and spatial accessibility.

Prior to producing a multivariate model, collinear-ity was examined on the basis of tolerance. Eachpredictor variable was regressed on all other variablesin a weighted least square regression, i.e. adjusted bythe weight matrix used in the maximum likelihoodalgorithm. The tolerance was computed as (1− R2)and variables with values below 0.4 were removeduntil a satisfactory combination was obtained. Themultivariate solution was fitted on the retained vari-ables using a stepwise approach where thresholdsof the residualχ2 were 0.05 for entry and 0.15 forremoval. The likelihood ratio statistic (−2 lnL) hasan asymptoticχ2-distribution under the global nullhypothesis that all parameters (β) equal zero, andwas used in conjunction with Akaike’s informationcriterion (AIC) to examine the significance of indi-vidual models and to compare competing models.The AIC is based on the likelihood ratio statistic butalso takes the number of observations into account.The Wald test was used to keep individual variablesin the model applying aχ2-criterion of P < 0.05.The odds ratio (eβ ) represents the change in thelog it for a change in each independent variable (x).The association between predicted probabilities andobserved responses was examined using percentagesof concordant pairs, discordant pairs and the rankcorrelation indexγ to summarise goodness-of-fit,according to

γ = C − D

C + D(2)

whereC is the number of concordant pairs andD thenumber of discordant pairs. A pair of observations isconcordant (discordant) if the predicted event prob-ability is lower (higher) for an observation with alower-ordered value of the observed response.

The response was ordinal when modelling the fourordinal levels of communal agricultural land use. Thefollowing cumulative logit model was used:

log it[Pr(Y ≤ j |x)] = ln

[Pr(Y ≤ j |x)

1 − Pr(Y ≤ j |x)

]

= ln

[π1 + . . . + πj

πj+1 + . . . + πJ

]

= B ′ikxk = β0ik + β1x1 + · · ·

+M−1∑m=1

βhmDhm + βkxk (3)

whereπj = Pr(Y = j |x), 1 ≤ j ≤ J , 1 ≤ i < J ,J the maximum number of ordinal levels (equals 4for four agricultural land use types), andβ0i are theintercept parameters. Univariate and multivariate so-lutions were developed and compared on the basisof significant values for the tests described above.The odds for the response≤j are exp[B ′(x1 − x2)]higher atx = x1 than atx = x2 and are thereforeproportional (Agresti, 1990).

Influence statistics were calculated for binary re-sponse models to indicate whether individual caseshad undue impact on the fitted regression model andon the coefficients of individual predictors (SAS,1992). The difference in Pearsonχ2 is the amount(�χ2) by which the Pearsonχ2 decreases if theithcase were deleted. Values higher than 4 indicated sig-nificant change. Analogue to the Cook’sD statisticin Ordinary Least Square regression, a displacementdiagnostic was calculated to approximate the changein all regression coefficients when theith case wasdeleted. Changes in Pearsonχ2 were plotted againstprobability, with bubble sizes indicating the influenceof an observation on all regression coefficients.

2.6. Validation of the models

The models were used to compute predicted prob-abilities and to classify the 300 plots into one of theresponse levels. Threshold probabilities were deter-mined for each model on the basis of percentagescorrectly classified, false positive and false negativeobservations. For binary responses, a bias-adjustedclassification table was used to determine cut-offprobabilities (SAS, 1992). For multiple responses, aclassification table summarised the predicted versus


observed response probabilities. Based on Eq. (3) andthe parameter estimates, the cumulative probabilitieswere converted to probabilities for predicting eachtype of communal agricultural land use, according to

Pr(Y ≤ j |x) = eB ′ikxk

1 + eB ′ikxk

Pr(Y = j |x)

= Pr(Y ≤ j |x) − Pr(Y ≤ (j − 1)|x)

(4)

All 300 plots used to estimate the model parameterswere classified into the different communal agricul-tural land use types at different probability levels. Theprobability level at which a maximum percentage ofcorrectly classified observations was obtained, wasused to classify the validation dataset. Validation ofthe fitted models and respective cut-off probabilitieswas carried out by classifying the remaining 88 plots,according to the best performing multivariate mod-els. Predictors incorporated into the best performingmodels were regarded as suitable spatial land usedeterminants.

Table 2Frequency table of agricultural land use by landform and association tests for 388 plots at Ikem, southeastern Nigeriaa

Agricultural land use Landform (% frequency) Total (%)

FT AG MG EG

Near and compound fields (NC) 6 (1.6) 47 (12.1) 26 (6.7) 1 (0.3) 80 (20.6)Continuous cultivation (CC) 43 (11.1) 38 (9.8) 0 (0.0) 0 (0.0) 81 (20.9)Grass fallow (GF) 8 (2.1) 11 (2.8) 54 (13.9) 15 (3.9) 88 (22.7)Grass and bush fallow (GBF) 0 (0.0) 0 (0.0) 38 (9.8) 40 (10.3) 78 (20.1)Bush fallow (BF) 0 (0.0) 3 (0.8) 26 (6.7) 32 (8.3) 61 (15.7)

Total 57 (14.7) 99 (25.5) 144 (37.1) 88 (22.7) 388 (100.0)

Statistic Value P

Pearsonχ2 327 0.001Likelihood ratioχ2 374 0.001Mantel–Haenszelχ2 152 0.001Row mean scores difference 182 0.001General association 326 0.001

Association measures Value ASE

Contingency coefficient 0.676Somers’D row/column 0.556 0.026γ 0.653 0.029Spearman correlation 0.654 0.026Pearson correlation 0.626 0.025

a FT: floodplain and terrace; AG: accumulation glacis; MG: mixed glacis; EG: erosion glacis; ASE: asymptotic standard error;P:probability.

3. Results

3.1. Spatial predictors associated withagricultural land use

All plots under continuous cultivation (CC,n = 81)were located on the fertile soils of the floodplain andterrace and accumulation glacis (Fig. 2, Table 2). Plotsunder grass fallow (GF,n = 88) were mainly situatedon the mixed glacis. Fields under grass and bush fal-low (GBF,n = 78) were spread over the mixed glacisand erosion glacis (Fig. 2, Table 2), whereas fieldsunder bush fallow (BF,n = 61) mainly occurred onthe less fertile soils of the erosion glacis. Most of thenear-and-compound fields (NC,n = 80) were foundon the accumulation glacis. The association analysisbetween landform and agricultural land use showedsignificantχ2-tests and demonstrated a linear asso-ciation between landform and agricultural land use(Table 2). Conditional association tests showed thatthere was a significant (P = 0.001) difference be-tween the mean score of the different land use types


(value for the test is 182). Pearson (0.626± 0.025)and Spearman (0.654±0.026) correlation coefficientsconfirmed a positive linear relationship. Values forγ (0.653± 0.029) and Somers’D (0.556± 0.026)indicated that local agricultural land use could bepredicted on the basis of landform (Table 2).

Accessibility to features of socio-economic impor-tance was expressed in Euclidean and/or least-costdistances. As a result of the calculation procedure,least-cost distances were higher than Euclidean dis-tances (Table 3). The ANOVA showed significant dif-ferences between the agricultural land use systems forEuclidean distance to the nearest track (P = 0.0026),settlement (P < 0.0001), stream (P < 0.0001) andmain river (P < 0.0001). Significant differences be-tween agricultural land use systems (P < 0.0001)were also recorded for least-cost distance to the mainroad, market, settlement, stream and river. Since theEuclidean distance and least-cost distance were cor-related for the same feature, either was selected forfurther analysis on the basis of its power to signifi-cantly discern between the different agricultural landuses of the plots.

The Euclidean distance to the nearest track wassmallest for the NC-fields and highest for GF-fields(Table 3). The distance to the nearest settlement,where the density of tracks was highest, explainedthe small value for the NC-fields. The distances tothe nearest settlement varied significantly and gen-erally increased with decreasing intensity of fallowmanagement (Table 3). However, farmers’ decisionsfor locating CC-fields depended on the soil fertility,

Table 3Accessibility to selected features expressed as Euclidean (E) or least-cost (lc) distances (m) for 388 field plotsa

Variable NC (n = 80)x̄ ± S.E. (DW)

CC (n = 81)x̄ ± S.E. (DW)

GF (n = 88)x̄ ± S.E. (DW)

GBF (n = 78)x̄ ± S.E. (DW)

BF (n = 61)x̄ ± S.E. (DW)

Track (E) 112 ± 11 (c) 168± 17 (ab) 189± 13 (a) 167± 17 (ab) 135± 17 (bc)Settle (E) 59 ± 6 (d) 382± 25 (b) 162± 11 (c) 333± 23 (b) 540± 37 (a)Stream (E) 386 ± 29 (a) 153± 13 (d) 411± 28 (a) 238± 18 (c) 315± 21 (b)River (E) 821 ± 64 (c) 239± 26 (d) 1631± 117 (ab) 1734± 122 (a) 1432± 119 (b)Road (lc) 605± 86 (d) 2228± 108 (a) 1847± 146 (bc) 1768± 121 (c) 2138± 120 (ab)Market (lc) 2113± 115 (c) 3122± 115 (b) 3572± 180 (a) 3887± 120 (a) 3918± 138 (a)Settle (lc) 111± 11 (e) 705± 46 (b) 309± 21 (d) 573± 41 (c) 903± 57 (a)Stream (lc) 659± 42 (a) 270± 22 (c) 740± 46 (a) 447± 36 (b) 536± 33 (b)River (lc) 1188± 75 (c) 421± 41 (d) 2317± 137 (a) 2310± 132 (a) 1851± 137 (b)

a x̄: mean, S.E.: standard error, DW: Duncan–Waller grouping at the 5% significance level shown as letters in alphabetical orderaccording to the magnitude of the class mean. Variables in bold were selected for further analysis based on DW. NC: near-and-compoundfields; CC: continuous cultivation; GF: grass fallow; GBF: grass and bush fallow and BF: bush fallow (Table 2).

which was highest on the terraces and accumulationglacis, and was therefore, reflected in the Euclideandistance to the nearest stream and the least-cost dis-tance to the main river. Least-cost distances to themarket were lowest for the NC-fields (x̄ = 2113) andsignificantly different from the CC-fields (x̄ = 3122)and the fields under fallow management. On aver-age, the NC-fields were located closer to the majorroads (̄x = 605), followed by the GF and GBF-plots(Table 3), whereas the CC-fields were significantlyfarthest away from the main roads (x̄ = 2228).

3.2. Logistic models for agricultural land use

In a first step, the probability of private agriculturalland use (private ALU) was modelled using Eq. (1)(Fig. 3). The predictor variables were screened ontheir ability to predict private ALU. A comparison ofAIC and −2lnL between different univariate modelsshowed that the distance to the settlement was the bestvariable to predict private ALU (Table 4), closely fol-lowed by the distance to the main roads. This was alsoreflected in a high value forγ (0.866). Although ac-cessibility to the market produced a statistically bettermodel than landform (Table 4), the association of pre-dicted values and observed responses was higher forlandform (γ = 0.712) than for market accessibility(γ = 0.647). Models based on spatial accessibility tothe stream (γ = 0.264) or river (γ = 0.115) were notvery successful in predicting the probability of privateALU (Table 4). Collinearity was diagnosed betweenthe distance to the settlement and distances to the


Table 4Summary statistics for predicting the probability of private agricultural land usea

Variable AIC SC −2lnL P > χ2 γ

Intercept only 304.993 308.697 302.993

Univariate:D to settlement (LC) 159.340 166.748 155.340 0.0001 0.866D to main roads (LC) 167.155 174.563 163.155 0.0001 0.866D to market (LC) 236.231 243.639 232.231 0.0001 0.647Landform 255.607 266.718 249.607 0.0001 0.712D to main river (LC) 295.409 302.816 291.409 0.0007 0.115D to stream (E) 298.651 306.059 294.651 0.0039 0.264

Multivariate 99.887 114.702 91.887 0.0001 0.951

a AIC: Akaike’s information criterion; SC: Chwarz criterion;−2lnL: −2 × Ln likelihood; P > χ2 = P(−2lnL > χ2); γ : rankcorrelation index;D: distance in meters; LC: distance according to least-cost calculation;E: Euclidean distance.

market, tracks and major roads. Distance to the settle-ment was retained as the best predictor variable.

The multivariate model based on landform and dis-tance to the settlement was the best performing model(AIC = 100; −2lnL = 92; P < 0.0001) and hada high value for the association between predictedand observed responses (γ = 0.951). The maximumlikelihood estimates for the parameters (β) were allsignificantly different from 0 (P < 0.0001). The oddswere negatively associated with landform and dis-tance from the settlement (odds ratio< 1, Table 5).The original landform classes mixed glacis and ero-sion glacis were collapsed into a combined categoryto avoid convergence problems due to quasi-completeseparation in the dataset. Quasi-complete separationis often caused by a categorical predictor variable thathas the same value for most observations of one levelof the response variable (SAS, 1992). The changein Pearsonχ2 versus estimated probability (Fig. 4,left panel) showed two curves sloping upward. The

Table 5Analysis of maximum likelihood estimates for the multivariate logistic model predicting the probability of private (as opposed to communal)agricultural land usea

Variable β S.E. (β) Wald χ2 P > χ2 Odds ratio 95% CI

Intercept 6.0932 1.1375 28.6951 0.0001Landform (FT) −4.0544 0.9610 17.8004 0.0001 0.017 0.003–0.114Landform (MG and EG) −4.9628 0.9475 27.4335 0.0001 0.007 0.001–0.045D to settlement (LC) −0.0193 0.00324 35.5009 0.0001 0.824 0.773–0.878

a D: least-cost distance (LC),β: estimated parameter, S.E. (β): standard error of estimated parameter and CI: Wald confidence limitsfor the odds ratio. FT: coded 1 for floodplain and terraces, MG and EG: coded 1 if the landform is either mixed glacis (MG) or erosionglacis (EG). The reference landform: accumulation glacis (AG). Odds ratio:eβ for landform,e100×β for distance to settlement.

curve sloping upward to the right corresponded toobservations of fields not under private ALU (i.e.fields under communal ALU), whereas the downwardsloping curve showed observations of fields underprivate ALU. Considering that the bubble size repre-sented the overall change in regression coefficients,observation 213 was regarded as an outlier (Fig. 4,left panel). The multivariate model was presented aslog it versus settlement distance for the three differ-ent landform classes (Fig. 4, right panel). Per 10 mdistance (Euclidean) away from the settlement, theprobability of locating a field under private ALU re-duced with 21.3%. The odds that a particular field onthe floodplain and terraces was under private ALUwere 0.017 smaller than the odds of a location on theaccumulation glacis. Similarly, the odds for a locationon mixed and erosion glacis were 0.007 smaller.

The four communal agricultural land use systemswere predicted using an ordinal response model ac-cording to Eq. (3) (Fig. 3). The univariate model based


Fig. 4. Left panel: changes inχ2 vs. predicted probability (bubble size is proportional to the influence of each case on the estimatedcoefficients). Right panel: model for predicting the log it of private agricultural land use.

on landform showed the best performance, followedby the model based on distance to the river (Table 6).Since distance to the river was collinear with land-form, it was not included in the multivariate model.The variables distance to the major roads and dis-tance to the stream did not produce significant models(P > 0.01). Although the model based on distanceto the market was statistically better than distance tothe settlement (Table 6), farmers repeatedly reporteddistance to the settlement as important ALU determi-nant. Stepwise multiple regression selected landformand distance to settlement into the multivariate ordinalmodel (Table 7). Floodplain, terrace and accumula-tion glacis were combined into one class to avoidconvergence problems due to quasi-complete separa-tion. Farmers preferred the landforms included intothis combined class for agricultural purposes. Thecombined class was, therefore, taken as the referencelandform class. The odds for increased agricultural

Table 6Summary statistics for predicting the probabilities of communal agricultural land usea

Variable AIC SC −2lnL P > χ2 γ

Intercept only 663.161 673.590 657.161

UnivariateLandform 442.238 459.621 432.238 0.0001 0.816D to main river (LC) 617.881 631.787 609.881 0.0001 0.466D to market (LC) 650.840 664.746 642.840 0.0002 0.230D to settlement (LC) 656.725 670.631 648.725 0.0037 0.217D to stream (E) 658.818 672.724 650.818 0.0118 0.129D to main roads (LC) 664.020 677.926 656.020 0.2856 0.047

Multivariate 399.830 424.166 385.830 0.0001 0.851

a Notes see Table 4.

land use (i.e. shorter fallow periods) on either themixed glacis or the erosion glacis were as low as0.001 times the odds on the other landform class(Table 7). The ordinal model was graphically pre-sented as log it versus distance to the settlement forthe mixed glacis, erosion glacis and the combinedlandform class (Fig. 5). The negative slopes related tothe odds of a less intensive agricultural land use withlonger fallow periods. The odds for longer fallow pe-riods increased with 21.8% per 100 m distance awayfrom the settlement (Table 7, Fig. 5).

3.3. Validation and determinants inagricultural land use

A bias-adjusted classification table (SAS, 1992) wasconstructed based on the multivariate model for pre-dicting the probability of private agricultural land use.The percentage of correctly classified fields (95.7%)


Table 7Analysis of maximum likelihood estimates for multivariate ordinal models predicting the probability of communal land use as classifiedaccording to a decreasing level of intensificationa

Variable β S.E. (β) Wald χ2 P > χ2 Odds ratio 95% CI

Intercept (π1) 3.0004 0.4172 51.7284 0.0001Intercept (π1 + π2) 6.9361 0.8296 69.9099 0.0001Intercept (π1 + π2 + π3) 8.9764 0.8787 104.3464 0.0001Landform (MG) −6.5465 0.7990 67.1396 0.0001 0.001 0.000–0.005Landform (EG) −6.9543 0.8059 74.4710 0.0001 0.001 0.000–0.003D to settlement (LC) −0.00197 0.000345 32.6438 0.0001 0.821 0.767–0.878

a D: distance, LC: least-cost distance,β: estimated parameter, S.E. (β): standard error of estimated parameter and CI: Wald confidencelimits for the odds ratio.π1: probability of continuous cultivation (CC);π2: probability of CC and grass fallow cultivation (GF);π3: theprobability of CC, GF and grass and bush fallow cultivation (GBF). MG: coded 1 for mixed glacis, EG: coded 1 for erosion glacis. Thereference landform class combines floodplain, terraces and accumulation glacis. Odds ratio:eβ for landform, ande100×β for distance tosettlement.

was maximum at a threshold probability of 0.5. Atthe same probability, four fields were false positiveand nine fields were false negative. The model and therespective threshold probability of 0.5 were appliedto the validation set of 88 fields. Correctly classifiedfields amounted to 89.9% with three false positive andsix false negative classified fields.

Fig. 5. Log it plots for communal agricultural land use types (see Table 2 for agricultural land use codes).

Based on Eq. (3) and the parameter estimates(Table 7), all 300 plots were classified into the differ-ent communal agricultural land use types at differentthresholds (Table 8). A maximum of 93.3% correctlyclassified observations was obtained at threshold 0.4for continuous cultivation; for grass fallow this was76.5%. A balance between correctly classified, false


Table 8Classification and validation of the multivariate ordinal model (Table 6)a

Prob-level CC GF GBF BF

Correct Falsepositive

Falsenegative


Falsenegative


Falsenegative


Falsenegative

0.3 93.3 6.7 0.0 70.7 0.0 8.4 74.5 21.8 0.8 85.4 9.6 5.00.35 93.3 6.7 0.0 74.5 0.0 9.2 74.5 21.8 2.5 87.9 6.3 5.90.4 93.3 6.7 0.0 76.2 11.3 12.6 74.5 21.8 7.1 87.0 5.4 7.50.45 92.9 6.7 0.4 76.2 6.3 17.6 74.5 7.1 15.9 86.6 5.0 8.40.5 90.8 6.7 2.5 75.3 3.3 21.3 74.5 0.0 25.5 84.9 3.3 11.7

Validation0.35 91.3 8.7 0.0 75.4 13.0 11.6 50.7 46.4 2.9 79.7 13.0 7.20.40 91.3 8.7 0.0 76.8 8.7 14.5 69.6 23.2 7.2 82.6 4.3 13.00.45 91.3 8.7 0.0 72.5 1.4 26.1 75.4 0.0 24.6 79.7 4.3 15.9

a NC: near-and-compound fields; CC: continuous cultivation; GF: grass fallow; GBF: grass and bush fallow, and BF: bush fallow(Table 2).

negative and false positive classification was obtainedat probability levels 0.45 for grass bush fallow and0.4 for bush fallow (Table 8). An overall 83.3% of300 observations was correctly classified. The valuesfor the threshold probabilities were confirmed on thevalidation dataset (Table 8). Overall, 78.3% of 88 plotswere correctly classified.

4. Discussion

There is a clear paradigm shift in land use models.Density gradients and concentric zones are the coreideas of the classic bid-rent model of Von Thunen,which forms the basis of several models in urban/ruraleconomics, ecology and geography. These modelshave highlighted the importance of the relationship be-tween location, land value and land use. However, thefundamental concepts of an equilibrium between de-clining land price gradients and increasing transporta-tion costs and of the landscape as a featureless plainmake the model increasingly irrelevant, especially tonon-economists or to areas where economic values aredifficult to determine. Social, cultural, economic andecological influences on agricultural land use are de-scribed in a large and diverse literature. Determinantsof agricultural land use include access (Skole et al.,1994), rural population density (Walsh et al., 1999),labour (Dvorak, 1992) and ownership (Turner et al.,1996). Environmental factors that interact with landuse include land cover (Lagemann, 1977; Gobin et al.,

2000a,b), soil type (Sanchez, 1976; Turner and Meyer,1991; Gobin et al., 1998a,b), physiography (Schreieret al., 1994) and biodiversity (Dale et al., 1993).

This study converted factors that farmers use todetermine agricultural land use into spatial variables,and demonstrated that landform and least-cost dis-tance to the settlements are influencing local agricul-tural land use (ALU). The response variable ALU isintrinsically related to land cover and biodiversity asdemonstrated for the region by Gobin et al., (2000a,b).The nested modelling strategy (Fig. 3) enabled a dis-tinction between different ownership types of ALUand showed that the determinants had different effectson different types of land use. The effect of settle-ment location was higher on the multivariate modelfor private ALU than on the multivariate model forcommunal ALU. For each of the multivariate models,a different reference group was chosen for the cate-gorical variable landform, and landform classes werecombined in a different manner. The landforms mixedglacis and erosion glacis had to be combined into oneclass when modelling private ALU (Table 5), whereasthe accumulation glacis, terraces and floodplain werecombined when modelling communal ALU (Table 7).

The strong association between ALU and least-costdistance to the settlement (Tables 5 and 7) reflectsthe impact of settlement location on agricultural landuse intensity. This is consistent with findings fromparticipatory rural appraisals (Gobin et al., 1997) andwith studies of similar farming systems in the re-gion (Lagemann, 1977; Okafor and Fernandes, 1987;


Omotayo and Musa, 1999). Intensity of agriculturalcultivation in terms of agricultural inputs and cropdensity decreases with increasing distance to the set-tlement. The overall importance of settlement locationand the multi-collinearity among predictor variablessuggests that a separate logistic model could be set-upfor deriving spatial determinants of settlement loca-tion. The spatial organisation of settlements, however,does not follow a density gradient from a central point(Fig. 2), and reflects the coexistence of governmentalplanning, market-oriented activities and the traditionalsettlement system, which was also observed by Njoh(2000). This spatial pattern together with the numberof settlements provides an indication of rural popula-tion density. The least-cost distance to the settlementincorporates the access to the fields along tracks andrural paths.

The spatial determinant landform includes phys-iography and soil type. The pronounced associa-tion between landform and ALU was reflected inquasi-complete separation within the datasets whenmodelling ALU. Recoding the particular predic-tor variable through combining classes solved theproblem, but also accounted for a potential loss ininformation. The disadvantage inherent of using cat-egorical predictor variables is unlikely to occur withcontinuous data. Improvements to the current modelscould therefore focus on incorporating raster-basedlandform attributes, derived from digital elevationmodels, instead of the categorical variable landform.More accurate information on terrain would alsoupgrade distance calculations to settlements.

Distances to streams and rivers (water resources,in general) were mentioned as land use determinantsby some villagers, whereas other villagers were re-luctant to cultivate near permanent waterbodies dueto increased risks of flood damage, mosquitoes andwaterborne diseases. The statistical analysis demon-strated that distances to streams and rivers were notsignificantly related to agricultural land use. How-ever, wet season rice (Oryza sativa) followed byirrigated vegetable and hot pepper (Capsicum an-nuum) cultivation represents a growing practice onthe floodplain (Gobin et al., 1998a,b). Accessibilityto the rivers will become increasingly important toagricultural land use, although the variable landformmay be equally suitable to express the nearness tothe river.

The developed models are useful tools in ecologicalmodelling and land use planning at the local govern-ment level. Since the models allow for incorporatinglikely responses in ALU to changes in the deter-minants, they provide important means to performscenario analyses and impact assessments. Spatial de-terminants and models for the location of settlementscould therefore further refine scenario analysis andimpact assessment. In addition, tracking and mod-elling land use changes would introduce temporal dy-namics into the land use models, which in turn supportenvironmental monitoring and sustainable planning.When new settlement areas are being built, land coverand local agricultural land use are affected. Higherpopulation densities cause an increased number ofsettlements with more private lands, and hence, morepalm dominated woodlots (Gobin et al., 1998a,b). Inthe communal lands, a higher population causes fal-low periods to shorten such that woody species canno longer establish (Gobin et al., 2000a,b).

5. Conclusions

An integrated approach of participatory rural ap-praisal and scientific analysis resulted in land usemodels that effectively simulate probabilities of localagricultural land use. Successful local land use de-terminants are predictor variables incorporated in thebest performing logistic models. The two most im-portant land use determinants for agricultural land useare landform and distance to the settlement calculatedalong the track/road network. The models could beincorporated into a land use framework for planningpurposes, environmental monitoring, scenario analysisand impact assessment at the local government level.

Acknowledgements

Funding for this research was provided by the Bel-gian Agency for Development Co-operation (BADC)through the Inter-University Project on ‘Water Re-sources Development for domestic use and small scaleirrigation in the rural areas of southeastern Nigeria’.Special appreciation is extended to the project staffand farmers of Ikem who contributed to this particularstudy.


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