Spatial residual analysis of six modeling techniques

In recent years alternative modeling techniques have been used to account for spatial autocorrelations among data observations. They include linear mixed model (LMM), generalized additive model (GAM), multi-layer perceptron (MLP) neural network, radial basis function (RBF) neural network, and geographically weighted regression (GWR). Previous studies show these models are robust to the violation of model assumptions and flexible to nonlinear relationships among variables. However, many of them are non-spatial in nature. In this study, we utilize a local spatial analysis method (i.e., local Moran coefficient) to investigate spatial distribution and heterogeneity in model residuals from those modeling techniques with ordinary least-squares (OLS) as the benchmark. The regression model used in this study has tree crown area as the response variable, and tree diameter and the coordinates of tree locations as the predictor variables. The results indicate that LMM, GAM, MLP and RBF may improve model fitting to the data and provide better predictions for the response variable, but they generate spatial patterns for model residuals similar to OLS. The OLS, LMM, GAM, MLP and RBF models yield more residual clusters of similar values, indicating that trees in some sub-areas are either all underestimated or all overestimated for the response variable. In contrast, GWR estimates model coefficients at each location in the study area, and produces more accurate predictions for the response variable. Furthermore, the residuals of the GWR model have more desirable spatial distributions than the ones derived from the OLS, LMM, GAM, MLP and RBF models.     

Imputing Unmeasured Explanatory Variables in Environmental Epidemiology With Application to Health Impact Analysis of Air Pollution

This paper presents the results of a reconsideration of earlier work that finds an association between daily hospital admissions for respiratory distress and daily concentrations of sulphate (lag 1) as well as daily maximum concentrations of ozone (lags 1 and 3). These associations are found even after clustering the data by hospital of admission and accounting for the effects of temperature. We use an adaptation of their generalized estimating equation technique for clustered data, that daily data being for southern Ontario summers from 1983 to 1988. Like them, we adjust for daily maximum temperatures. However, unlike the earlier work returned to ours includes daily average humidity as a potential explanatory variable in our model. Our analysis also differs from theirs in that we cluster the data by census subdivision to reduce the risk of confounding pollutant levels with population size within regions. Moreover, we log-transform the explanatory variables and then high-pass filter the resulting data. We also deviate from the earlier analysis by taking account of measurement error incurred in using surrogate measures of the explanatory variables. To do so we use new methodology designed for our study but of potential value in other applications. That methodology requires a spatial predictive distribution for the unmeasured explanatory variables. Each day about 700 missing measurements for each of these variables can then be imputed over the geographical domain of the study. With these imputations we get a measure of imputation error through the covariance of the predictive distribution. Along with the predictive distribution we require an impact model to link-up with the predictive distribution. We describe that model and show how it uses the imputed measurements of the missing values of the explanatory variables. We also show how through that model, uncertainty about these values is reflected in our analysis and in commensurate uncertainties in the inferences made. Apart from its substantive objectives, our analysis serves to test the new methods with the earlier results serving as a foil. The reassuring qualitative agreement between our findings and the earlier results seems encouraging.     

Are existing vegetation maps adequate to predict bird distributions?

Bird species are selective on the vegetation types in which they are found but predictive models of bird distribution based on variables derived from land-use/land-cover maps tend to have limited success. It has been suggested that accuracy of existing maps used to derive predictors is in part responsible for the limited success of bird distribution models. In two areas of 4900 km² of Western Andalusia, Spain, we compared the predictive ability of bird distribution models derived from two existing general-purpose land-use/land-cover maps, which differ in their resolution and accuracy: a coarse scale vegetation map of Europe, the CORINE land-cover map, and a detailed regional map, the 1995 land-use/land-cover map of Andalusia from the SINAMBA (Consejerı́a de Medio Ambiente, Junta de Andalucı́a). We compared the bird distribution models derived from these general-purpose vegetation maps with models derived from two more accurate structural vegetation maps built considering directly variables that influence bird habitat selection, one built from satellite images for this study and another obtained by improving the resolution and accuracy of the SINAMBA map with satellite data. We sampled the presence/absence of bird species at 857 points using 15-min point surveys. Predictive models for 54 bird species were built with generalised additive models (GAMs), using as potential predictors the same set of landscape and vegetation structure variables measured on each map. We compared for each bird species the predictive accuracy of the best model derived from each map. Vegetation structure measured at bird sample points was used as ground-truth for comparing the accuracy of vegetation maps. Although maps differed in their resolution and accuracy, the results show that all of them produced similarly accurate bird distribution models, with a mixed map produced with both thematic and satellite information being the best. The models derived from the more accurate vegetation structure maps obtained from satellite data were not more accurate than those derived directly from the SINAMBA or CORINE maps. Our results suggest that some general-purpose land-use/land-cover maps are accurate enough to derive bird distribution models. There is a certain limit to improve vegetation maps above which there is no effect in their power to predict bird distribution.     

Fine-scale habitat modeling of a top marine predator: do prey data improve predictive capacity?

Predators and prey assort themselves relative to each other, the availability of resources and refuges, and the temporal and spatial scale of their interaction. Predictive models of predator distributions often rely on these relationships by incorporating data on environmental variability and prey availability to determine predator habitat selection patterns. This approach to predictive modeling holds true in marine systems where observations of predators are logistically difficult, emphasizing the need for accurate models. In this paper, we ask whether including prey distribution data in fine-scale predictive models of bottlenose dolphin (Tursiops truncatus) habitat selection in Florida Bay, Florida, U.S.A., improves predictive capacity. Environmental characteristics are often used as predictor variables in habitat models of top marine predators with the assumption that they act as proxies of prey distribution. We examine the validity of this assumption by comparing the response of dolphin distribution and fish catch rates to the same environmental variables. Next, the predictive capacities of four models, with and without prey distribution data, are tested to determine whether dolphin habitat selection can be predicted without recourse to describing the distribution of their prey. The final analysis determines the accuracy of predictive maps of dolphin distribution produced by modeling areas of high fish catch based on significant environmental characteristics. We use spatial analysis and independent data sets to train and test the models. Our results indicate that, due to high habitat heterogeneity and the spatial variability of prey patches, fine-scale models of dolphin habitat selection in coastal habitats will be more successful if environmental variables are used as predictor variables of predator distributions rather than relying on prey data as explanatory variables. However, predictive modeling of prey distribution as the response variable based on environmental variability did produce high predictive performance of dolphin habitat selection, particularly foraging habitat.     

A global evaluation of metabolic theory as an explanation for terrestrial species richness gradients

We compiled 46 broadscale data sets of species richness for a wide range of terrestrial plant, invertebrate, and ectothermic vertebrate groups in all parts of the world to test the ability of metabolic theory to account for observed diversity gradients. The theory makes two related predictions: (1) In-transformed richness is linearly associated with a linear, inverse transformation of annual temperature, and (2) the slope of the relationship is near -0.65. Of the 46 data sets, 14 had no significant relationship; of the remaining 32, nine were linear, meeting prediction 1. Model I (ordinary least squares, OLS) and model II (reduced major axis, RMA) regressions then tested the linear slopes against prediction 2. In the 23 data sets having nonlinear relationships between richness and temperature, split-line regression divided the data into linear components, and regressions were done on each component to test prediction 2 for subsets of the data. Of the 46 data sets analyzed in their entirety using OLS regression, one was consistent with metabolic theory (meeting both predictions), and one was possibly consistent. Using RMA regression, no data sets were consistent. Of 67 analyses of prediction 2 using OLS regression on all linear data sets and subsets, two were consistent with the prediction, and four were possibly consistent. Using RMA regression, one was consistent (albeit weakly), and four were possibly consistent. We also found that the relationship between richness and temperature is both taxonomically and geographically conditional, and there is no evidence for a universal response of diversity to temperature. Meta-analyses confirmed significant heterogeneity in slopes among data sets, and the combined slopes across studies were significantly lower than the range of slopes predicted by metabolic theory based on both OLS and RMA regressions. We conclude that metabolic theory, as currently formulated, is a poor predictor of observed diversity gradients in most terrestrial systems.     

Hierarchical Bayesian scaling of soil properties across urban, agricultural, and desert ecosystems.

Ecologists increasingly use plot-scale data to inform research and policy related to regional and global environmental change. For soil chemistry research, scaling from the plot to the region is especially difficult due to high spatial variability at all scales. We used a hierarchical Bayesian model of plot-scale soil nutrient pools to predict storage of soil organic carbon (oC), inorganic carbon (iC), total nitrogen (N), and available phosphorus (avP) in a 7962-km2 area including the Phoenix, Arizona, USA, metropolitan area and its desert and agricultural surroundings. The Bayesian approach was compared to a traditional approach that multiplied mean values for urban mesic residential, urban xeric residential, nonresidential urban, agricultural, and desert areas by the aerial coverage of each land-use type. Both approaches suggest that oC, N, and avP are correlated with each other and are higher (in g/m2) in mesic residential and agricultural areas than in deserts or xeric residential areas. In addition to traditional biophysical variables, cultural variables related to impervious surface cover, tree cover, and turfgrass cover were significant in regression models predicting the regional distribution of soil properties. We estimate that 1140 Gg of oC have accumulated in human-dominated soils of this region, but a significant portion of this new C has a very short mean residence time in mesic yards and agricultural soils. For N, we estimate that 130 Gg have accumulated in soils, which explains a significant portion of "missing N" observed in the regional N budget. Predictions for iC differed between the approaches because the Bayesian approach predicted iC as a function of elevation while the traditional approach employed only land use. We suggest that Bayesian scaling enables models that are flexible enough to accommodate the diverse factors controlling soil chemistry in desert, urban, and agricultural ecosystems and, thus, may represent an important tool for ecological scaling that spans land-use types. Urban planners and city managers attempting to reduce C emissions and N pollution should consider ways that landscape choices and impervious surface cover affect city-wide soil C, N, and P storage.     

Effects of Land Use on Threatened Species

Abstract:  There is widespread agreement that biodiversity loss must be reduced, yet to alleviate threats to plant and animal species, the forces driving these losses need to be better understood. We searched for explanatory variables for threatened-species data at the country level through land-use information instead of previously used socioeconomic and demographic variables. To explain the number of threatened species in one country, we used information on land-use patterns in all neighboring countries and on the extent of the country's sea border. We carried out multiple regressions of the numbers of threatened species as a function of land-use patterns, and we tested various specifications of this function, including spatial autocorrelation. Most cross-border land-use patterns had a significant influence on the number of threatened species, and land-use patterns explained the number of threatened species better than less proximate socioeconomic variables. More specifically, our overall results showed a highly adverse influence of plantations and permanent cropland, a weaker negative influence of permanent pasture, and, for the most part, a beneficial influence of nonarable lands and natural forest. Surprisingly, built-up land also showed a conserving influence on threatened species. The adverse influences extended to distances between about 250 km (plants) and 2000 km (birds and mammals) away from where the species threat was recorded, depending on the species. Our results highlight that legislation affecting biodiversity should look beyond national boundaries.     

Robust ridge regression for estimating the effects of correlated gene expressions on phenotypic traits

Statistical packages such as edgeR and DESeq are intended to detect genes that are relevant to phenotypic traits and diseases. A few studies have also modeled the relationships between gene expressions and traits. In the presence of multicollinearity and outliers, which are unavoidable in genetic data, the robust ridge regression estimator can be applied with the trait value as the response variable and the gene expressions as explanatory variables. In some simulation scenarios, the robust ridge estimator is resistant to outliers and less susceptible to multicollinearity than the ordinary least-squares (OLS) estimator. This study investigated the reliability of the robust ridge estimator, in a scenario where the explanatory variables have tail-dependence and negative binomial distributions, by comparing its performance to that of OLS using vine copula to model the tail-dependence among gene expressions. The robust ridge estimator and OLS were both applied to an ecological dataset. First, statistical analysis was used to compare RNA sequencing data between two treatments; then, 15 differentially expressed genes were selected. Next, the regression parameter estimates of robust ridge and OLS for the effects of the 15 contigs (explanatory variables) on trait values (response variables) were compared. Robust ridge regression was found to detect fewer positive and negative slopes than OLS regression. These results indicate that robust ridge regression can be successfully applied for RNA sequencing analysis to estimate the effect of trait-associated genes using real data, and holds great promise as a tool for modeling the association between RNA expression and phenotypic traits.     

Modelling the productivity of naturalised pasture in the North Island,New Zealand: a decision tree approach

Decision tree, one of the data mining methods, has been widely used as a modelling approach and has shown better predictive ability than traditional approaches (e.g. regression). However, very little is known from the literature about how the decision tree performs in predicting pasture productivity. In this study, decision tree models were developed to investigate and predict the annual and seasonal productivity of naturalised hill-pasture in the North Island, New Zealand, and were compared with regression models with respect to model fit, validation and predictive accuracy. The results indicated that the decision tree models for annual and seasonal pasture productivity all had a smaller average squared error (ASE) and a higher percentage of correctly predicted cases than the corresponding regression models. The decision tree model for annual pasture productivity had an ASE which was only half of that of the regression model, and correctly predicted 90% of the cases in the model validation which was 10.8 percentage points higher than that of the regression model. Furthermore, the decision tree models for annual and seasonal pasture productivity also clearly revealed the relative importance of environmental and management variables in influencing pasture productivity, and the interaction among these variables. Spring rainfall was the most significant factor influencing annual pasture productivity, while hill slope was the most significant factor influencing spring and winter pasture productivity, and annual P fertiliser input and autumn rainfall were the most significant factors influencing summer and autumn pasture productivity. One limitation of using the decision tree to predict pasture productivity was that it did not generate a continuous prediction, and thus could not detect the influence of small changes in environmental and management variables on pasture productivity.     

Effects of sample survey design on the accuracy of classification tree models in species distribution models

We evaluated the effects of probabilistic (hereafter DESIGN) and non-probabilistic (PURPOSIVE) sample surveys on resultant classification tree models for predicting the presence of four lichen species in the Pacific Northwest, USA. Models derived from both survey forms were assessed using an independent data set (EVALUATION). Measures of accuracy as gauged by resubstitution rates were similar for each lichen species irrespective of the underlying sample survey form. Cross-validation estimates of prediction accuracies were lower than resubstitution accuracies for all species and both design types, and in all cases were closer to the true prediction accuracies based on the EVALUATION data set. We argue that greater emphasis should be placed on calculating and reporting cross-validation accuracy rates rather than simple resubstitution accuracy rates. Evaluation of the DESIGN and PURPOSIVE tree models on the EVALUATION data set shows significantly lower prediction accuracy for the PURPOSIVE tree models relative to the DESIGN models, indicating that non-probabilistic sample surveys may generate models with limited predictive capability. These differences were consistent across all four lichen species, with 11 of the 12 possible species and sample survey type comparisons having significantly lower accuracy rates. Some differences in accuracy were as large as 50%. The classification tree structures also differed considerably both among and within the modelled species, depending on the sample survey form. Overlap in the predictor variables selected by the DESIGN and PURPOSIVE tree models ranged from only 20% to 38%, indicating the classification trees fit the two evaluated survey forms on different sets of predictor variables. The magnitude of these differences in predictor variables throws doubt on ecological interpretation derived from prediction models based on non-probabilistic sample surveys.     

Dealing with collinearity in behavioural and ecological data: model averaging and the problems of measurement error

There has been a great deal of recent discussion of the practice of regression analysis (or more generally, linear modelling) in behaviour and ecology. In this paper, I wish to highlight two factors that have been under-considered, collinearity and measurement error in predictors, as well as to consider what happens when both exist at the same time. I examine what the consequences are for conventional regression analysis (ordinary least squares, OLS) as well as model averaging methods, typified by information theoretic approaches based around Akaike’s information criterion. Collinearity causes variance inflation of estimated slopes in OLS analysis, as is well known. In the presence of collinearity, model averaging reduces this variance for predictors with weak effects, but also can lead to parameter bias. When collinearity is strong or when all predictors have strong effects, model averaging relies heavily on the full model including all predictors and hence the results from this and OLS are essentially the same. I highlight that it is not safe to simply eliminate collinear variables without due consideration of their likely independent effects as this can lead to biases. Measurement error is also considered and I show that when collinearity exists, this can lead to extreme biases when predictors are collinear, have strong effects but differ in their degree of measurement error. I highlight techniques for dealing with and diagnosing these problems. These results reinforce that automated model selection techniques should not be relied on in the analysis of complex multivariable datasets.     

The value of disappearing beaches: A hedonic pricing model with endogenous beach width

Beach nourishment is a policy used to rebuild eroding beaches with sand dredged from other locations. Previous studies indicate that beach width positively affects coastal property values, but these studies ignore the dynamic features of beaches and the feedback that nourishment has on shoreline retreat. We correct for the resulting attenuation and endogeneity bias in a hedonic property value model by instrumenting for beach width using spatially varying coastal geological features. We find that the beach width coefficient is nearly five times larger than the OLS estimate, suggesting that beach width is a much larger portion of property value than previously thought. We use the empirical results to parameterize a dynamic optimization model of beach nourishment decisions and show that the predicted interval between nourishment projects is closer to what we observe in the data when we use the estimate from the instrumental variables model rather than OLS. As coastal communities adapt to climate change, we find that the long-term net value of coastal residential property can fall by as much as 52% when erosion rate triples and cost of nourishment sand quadruples.     

Functional autoregressive forecasting of long-term seabed evolution

There is a need for decadal predictions of the seabed evolution, for example to inform resurvey strategies when maintaining navigation channels. The understanding of the physical processes involved in morphological evolution, and the viability of process models to accurately model evolution over these time scales, are currently limited. As a result, statistical approaches are used to supply long-term forecasts. In this paper, we introduce a novel statistical approach for this problem: the autoregressive Hilbertian model (ARH). This model naturally assesses the time evolution of spatially-distributed measurements. We apply the technique to a coastal area in the East Anglian coast over the period 1846 to 2002, and compare with two other statistical methods used recently for seabed prediction: the autoregressive model and the EOF model. We evaluate the performance of the three methods by comparing observations and predictions for 2002. The ARH model enables a reduction of 10% of the root mean squared errors. Finally, we compute the variability in the predictions related to time sampling using the jackknife, a method that uses subsamples to quantify uncertainties.     

Nutrient criteria for lakes,ponds, and reservoirs: A Bayesian TREED model approach

We develop regional-scale eutrophication models for lakes, ponds, and reservoirs to investigate the link between nutrients and chlorophyll-a. The Bayesian TREED (BTREED) model approach allows association of multiple environmental stressors with biological responses, and quantification of uncertainty sources in the empirical water quality model. Nutrient data for lakes, ponds, and reservoirs across the United States were obtained from the Environmental Protection Agency (EPA) National Nutrient Criteria Database. The nutrient data consist of measurements for both stressor variables (such as total nitrogen and total phosphorus), and response variables (such as chlorophyll-a), used in the BTREED model. Markov chain Monte Carlo (McMC) posterior exploration guides a stochastic search through a rich suite of candidate trees toward models that better fit the data. The Bayes factor provides a goodness of fit criterion for comparison of resultant models. We randomly split the data into training and test sets; the training data were used in model estimation, and the test data were used to evaluate out-of-sample predictive performance of the model. An average relative efficiency of 1.02 between the training and test data for the four highest log-likelihood models suggests good out-of-sample predictive performance. Reduced model uncertainty relative to over-parameterized alternative models makes the BTREED models useful for nutrient criteria development, providing the link between nutrient stressors and meaningful eutrophication response.     

The influence of land use and climate change on forest biomass and composition in Massachusetts, USA

Land use and climate change have complex and interacting effects on naturally dynamic forest landscapes. To anticipate and adapt to these changes, it is necessary to understand their individual and aggregate impacts on forest growth and composition. We conducted a simulation experiment to evaluate regional forest change in Massachusetts, USA over the next 50 years (2010-2060). Our objective was to estimate, assuming a linear continuation of recent trends, the relative and interactive influence of continued growth and succession, climate change, forest conversion to developed uses, and timber harvest on live aboveground biomass (AGB) and tree species composition. We examined 20 years of land use records in relation to social and biophysical explanatory variables and used regression trees to create "probability-of-conversion" and "probability-of-harvest" zones. We incorporated this information into a spatially interactive forest landscape simulator to examine forest dynamics as they were affected by land use and climate change. We conducted simulations in a full-factorial design and found that continued forest growth and succession had the largest effect on AGB, increasing stores from 181.83 Tg to 309.56 Tg over 50 years. The increase varied from 49% to 112% depending on the ecoregion within the state. Compared to simulations with no climate or land use, forest conversion reduced gains in AGB by 23.18 Tg (or 18%) over 50 years. Timber harvests reduced gains in AGB by 5.23 Tg (4%). Climate change (temperature and precipitation) increased gains in AGB by 17.3 Tg (13.5%). Pinus strobus and Acer rubrum were ranked first and second, respectively, in terms of total AGB throughout all simulations. Climate change reinforced the dominance of those two species. Timber harvest reduced Quercus rubra from 10.8% to 9.4% of total AGB, but otherwise had little effect on composition. Forest conversion was generally indiscriminate in terms of species removal. Under the naive assumption that future land use patterns will resemble the recent past, we conclude that continued forest growth and recovery will be the dominant mechanism driving forest dynamics over the next 50 years, and that while climate change may enhance growth rates, this will be more than offset by land use, primarily forest conversion to developed uses.     

Hierarchical Bayesian strategy for modeling correlated compositional data with observed zero counts

This article proposes a hierarchical multivariate conditional autoregressive model applied to a compositional response vector. We particularly focus on situations when the composition is discrete occurring when observations are based on small multinomial counts. We address drawbacks that exist in current modeling approaches for such data. Our hierarchical model will be demonstrated with data used to help manage a commercial sockeye salmon fishery in the Fraser River of British Columbia.     

Selecting pseudo-absence data for presence-only distribution modeling: How far should you stray from what you know?

An important decision in presence-only species distribution modeling is how to select background (or pseudo-absence) localities for model parameterization. The selection of such localities may influence model parameterization and thus, can influence the appropriateness and accuracy of the model prediction when extrapolating the species distribution across time and space. We used 12 species from the Australian Wet Tropics (AWT) to evaluate the relationship between the geographic extent from which pseudo-absences are taken and model performance, and shape and importance of predictor variables using the MAXENT modeling method. Model performance is lower when pseudo-absence points are taken from either a restricted or broad region with respect to species occurrence data than from an intermediate region. Furthermore, variable importance (i.e., contribution to the model) changed such that, models became increasingly simplified, dominated by just two variables, as the area from which pseudo-absence points were drawn increased. Our results suggest that it is important to consider the spatial extent from which pseudo-absence data are taken. We suggest species distribution modeling exercises should begin with exploratory analyses evaluating what extent might provide both the most accurate results and biologically meaningful fit between species occurrence and predictor variables. This is especially important when modeling across space or time—a growing application for species distributional modeling.     

Modelling algal blooms using vector autoregressive model with exogenous variables and long memory filter

Algal blooms (ABs), which commonly occur in urbanised coastal marine environments worldwide, often result in hypoxia and even fish kills. Understanding the mechanism and providing accurate prediction of ABs’ formation and occurrence is of foremost importance in relation to the protection of sensitive marine resources. In this paper, a multivariate time series model, namely the vector autoregressive model with exogenous variables (VARX) and the long memory filter is proposed to model and predict ABs. To evaluate the effectiveness of this VARX model, both daily and 2-h field monitoring data of chlorophyll fluorescence (CHL), dissolved oxygen (DO), total inorganic nitrogen (TIN), water temperature (TEMP), solar radiation (SR) and wind speed (WS) obtained at Kat O, Hong Kong, between February 2000 and March 2003 were employed. Unlike the other data driven approaches, this VARX model not only provides more interpretable effects of specific lags of environmental factors, but also sheds light on the feedback effects of AB on these variables. In general, daily CHL measurements up to 4 days can provide crucial information for predicting algal dynamics, while the VARX model is able to explicitly reveal ecological relationships between CHL and other environmental factors. In addition, the application of long-memory filter can further extract patterns of seasonal variations which is thought to be correspondent to the variation of algal species in Hong Kong water. With a view to providing an early warning signal of AB to fishermen and regulatory authorities, an alarming system was developed based on the VARX model; it could achieve 83% correct prediction of AB occurrences with a lead time of 2.5 days. Concerning the forecast performance of the VARX model, daily forecasting performance is comparatively better than that of artificial neural network models.     

Land-use choices: the case of conservation reserve program (CRP) re-enrollment in Kansas,USA

Among the important alternatives for land conservation is the US Conservation Reserve Program (CRP) that celebrated its 30th anniversary in 2015. This paper explores how landowners decide on alternative land-use choices made available by the expiration of CRP contracts in Kansas. The study uses survey data and multinomial Logit models to predict land-use choices. Two models were tested. The first model does not incorporate variables concerning farmer perceptions and attitudes about land-use choices, while the second model does. The results show that CRP re-enrollment depends on factors, such as years of experience in cropping and percent of cropland irrigated. However, when perception variables are added, the models become more robust in explaining other land choice alternatives. The results suggest that as the perception of unfairness of more inflexible environmental policy rises, these farmers may be more likely to re-enroll their marginal land in the CRP program.