Logistic Regression for LUCC Modelling

This post is my third contribution to JustScience week.

In Land Use/Cover Change (LUCC) studies, empirical (statistical) models use the observed relationship between independent variables (for example mean annual temperature, human population density) and a dependent variable (for example land-cover type) to predict the future state of that dependent variable. The primary limitation of this approach is the inability to represent systems that are non-stationary.

Non-stationary systems are those in which the relationships between variables are changing through time. The assumption of stationarity rarely holds in landscape studies – both biophysical (e.g. climate change) and socio-economic driving forces (e.g. agricultural subsidies) are open to change. Two primary empirical models are available for studying lands cover and use change; transition matrix (Markov) models and regression models. My research has particularly focused on the latter, particularly the logistic regression model.

Figure 1.

Figure 1 above shows observed land cover for 3 years (1984 – 1999) for SPA 56, with a fourth map (2014) predicted from this data. Models run for observed periods of change for SPA 56 were found to have a pixel-by-pixel accuracy of up to 57%. That is, only just over half of the map was correctly predicted. Not so good really…

Pontius and colleagues have bemoaned such poor performance of models of this type, highlighting that models are often unable to perform even as well as the ‘null model of no change’. That is, assuming the landscape does not change from one point in time to another is often a better predictor of the landscape (at the second point in time) than a regression model! Clearly, maps of future land cover from these models should be understood as a projection of future land cover given observed trends continue unchanged into the future (i.e. the stationarity condition is maintained).

Acknowledgement of the stationarity assumption is perhaps more important, and more likely to be invalid, from a socio-economic perspective than biophysical. Whilst biophysical processes might be assumed to be relatively constant over decadal timescales (climatic change aside), this will likely not be the case for many socio-economic processes. With regard to SPA 56 for example, the recent expansion of the European Union to 25 countries, and the consequent likely restructuring of the Common Agricultural Policy (CAP), will lead to shifts in the political and economic forces driving LUCC in the region. The implication is that where socio-economic factors are important contributors to landscape change regression models are unlikely to be very useful for predicting future landscapes and making subsequent ecological interpretation or management decisions.

Because of the shortcomings of this type of model, alternative methods to better understanding processes of change, and likely future landscape states, will be useful. For example, hierarchical partitioning is a method for using statistical modelling in an explanatory capacity rather than for predictive purposes. Work I did on this with colleagues was recently accepted for publication by Ecosystems and I’ll discuss it in more detail tomorrow. The main thrust of my PhD however, is the development of an integrated socio-ecological simulation model that considers agricultural decision-making, vegetation dynamics and wildfire regimes.

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Generative Landscape Science

A paper from the recent special issue of Professional Geographer (and discussed briefly here) of particular interest to me, as it examines and emphasises an approach and perspective similar to my own, was that by Brown et al. (2006). They suggest that a generative landscape science, one which considers the implications microscale processes for macroscale phenomena, offers a complementary approach to explanation via other methods. Such an approach would combine ‘bottom-up’ models of candidate processes, believed to give rise to observed patterns, with empirical observations, predominantly through individual-based modelling approaches such as agent-based models. There are strong parallels between modelling in a generative landscape science approach and the pattern-oriented modelling of agent-based systems in ecology discussed by Grimm et al. (1995). As a result of the theory-ladeness of data (Oreskes et al. 1994) and issues of equifinality (Beven 2002) landscape modellers often find themselves encountering an ‘interesting’ issue (as Brown et al. put it):

“we may understand well the processes that operate on a landscape, but still be unable to make accurate predictions about the outcomes of those processes.”

Thus, whilst pattern-matching of (model and observed) system-level properties from models of microscale interactions may be useful for examining and explaining system structure, it does not imply prediction is necessarily possible. There is a distinction between pattern-matching for validation (sensu Oreskes and Beven) and pattern-matching for understanding (via strong inference), but it is a fine line. If we say, “Model 1 uses structure A and Model 2 uses structure B, Model 1 reproduces observed patterns at multiple scales more accurately than Model 2, so Model 1 is more like reality, and therefore we understand reality better”, we’re still left with the problems of equifinality.

And so (rightly IMHO) in turn, Brown et al. suggest that whilst the use of pattern-matching exercises to evaluate and interpret models will be useful, we should wary of an over-emphasis on these techniques at the expense of intuition and deduction. This perspective partly contributed to my investigation of the use of ‘stakeholder assessment’ to evaluate the landscape change model I’ve been developing as part of my PhD.

In conclusion Brown et al. suggest a generative component (i.e. exploiting individual- and process-based modelling approaches) in landscape science will help;

  • develop and encode explanations that combine multiple scales
  • evaluate the implicaitons of theory
  • identify and structure needs for empirical investigation
  • deal with uncertainty
  • highlight when prediction may not be a reasonable goal

This modelling approach adopts perspective that is characteristic of recent attitudes toward the uses and interpretation of models arising recently in other areas of simulation modelling (e.g. Beven in hydrology and Moss and Edmonds in social science) and is also resonant with perspectives arising from critical realism (without explicitly discussing ontology). As such their discussion is illustrative of recent trends environmental and social simulation with some good modelling examples from Elk-Wolf population dynamics in Yellowstone National Park, and places the discussion in a context and forum in which individuals with backgrounds in Geography, GIScience and Landscape Ecology can all associate.

Daniel G. Brown, Richard Aspinall, David A. Bennett (2006)
Landscape Models and Explanation in Landscape Ecology—A Space for Generative Landscape Science?
The Professional Geographer 58 (4), 369–382.

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Generational Landscape Change: Montana and Madrid

It’a been out for a while (so there are several reviews available ) but I only just got and started reading Jared Diamond’s Collapse (How societies choose to fail or survive). I’ve only read the first part (Modern Montana) so far, but already I’ve come across several parallels between the socio-economic changes, and their potential ecological impacts, occuring in the landscapes under Montana’s Big Sky and Madrid’s Sun-Blessed Skies.

The broad similarity between the change Diamond describes in Montana and that occurring in my PhD study area (SPA 56, an EU protection area for endangered bird species to the west of Madrid, Spain) is the shift from an economy and landscape driven by agricultural activity to one driven by recreational activities. Such a shift reflects both the differing visions of multiple stakeholders within these landscapes, but also generational changes in attitude between older inhabitants and their children and grandchildren. In Montana’s Bitteroot Valley larger macroeconomic changes nationally and internationally have made previously profitable extractive industries (forestry, mining and agriculture) largely unsustainable economically. This has come about as land is now valued not according to resource and agricultural production but according to real-estate potential for incoming retirees, second-homers and tourists. Incoming (usually older) ‘out-of-staters’ arrive to enjoy the outdoor recreation (fishing, hiking, etc.), beauty and lifestyle opportunities, replacing the younger generation of Montanans going the other way to seek modern urban lifestyle opportunities and lifestyles;

“It’s a wonderful lifestyle to get up before dawn and see the sunrise, to watch fly hawks overhead, and to see deer jump through your hay field to avoid your haying equipment. … Occasionally I get up at 3 AM and work until 10 AM. This isn’t a 9 to 5 job. But none of our children will sign up for being a farmer if it is 3 AM to 10 PM every day.”

Dairy Farmer, Montana

Locals in SPA 56 have expressed similar feelings and ideas when I have visited over the last few years. Younger generations that would have previously continued the family farm that has passed through generation upon generation of farmers, are now seeking out employment in construction and service sectors to secure what is understood as a more ‘modern’ lifestyle. A lifestyle that affords leisure time at specified times of the week and at regular intervals (i.e. the weekends and paid holidays);

“Most farmers are part-time, maintaining the tradition agriculture. The children or grandchildren of those [farmers] do not have interest [in agriculture] because is it not profitable and requires a lot of dedication. The youths go or they seek other work.”

Local Development Official, Madrid (2006)

In Montana, Diamond describes the conflicts that have arisen between existing inhabitants and the new-comers, each with differing world-views, priorities and values. For example, contrast the attitudes of the third generation dairy farmer fighting to ensure the survival of his farm in the global economy vs. the lady who complained to him when she got manure on her white running shoes. Of course, these multiple perspectives within the landscape are inevitable in a changing world and tools and strategies must be found and employed to ensure appropriate decisions and compromises are made. In my simulation model of agricultural decision-making I have attempted to represent the influence of two differing world-views on landscape change (as have other modellers). I have termed the representative agents ‘commercial’ and ‘traditional’; the former behaving as a perfectly rational actor (in economic terms), the latter designed to reflect the importance of traditional cultural values in land-use decision-making;

“Whoever has a vineyard nowadays is like a gardener… they like to keep it, even if they lose money. They maintain vineyards because they have done it all their life and they like it, even having to pay for it. If owners were looking for profitability there would be not a singe vineyard… People here grow wine because of a matter of feeling, love for the land…”

Vinter, Madrid (2005)

As the primary thesis of his book Diamond highlights, for both contemporary and historical societies, the impacts of social, economic and technological change on the physical environment, and the sustainability of those changes. Of the several issues of concern in Montana, those related to forestry and water availability are likely to be of most concern in SPA 56. One particular interest of my PhD thesis is the importance of changes in the landscape for wildfire regimes, which Diamond discusses with reference to previous management strategies of the Unites States Forest Service (USFS). Commercial forestry has not been a widespread activity in SPA 56, the nature and human history of Mediterranean ecosystems restricting contemporary timber productivity. However, the problems of increased fuel loads due to the fire suppression policies of the USFS during the 20th century may be beginning to present themselves in SPA 56. If the agricultural sector continues to decline due to the social and economic trends just outlined, farmland will (continue to) be abanoned or converted to recreational uses (for example, hunting reservations). In turn this will leading to increased biomass and fuel loads in the landscape. As yet the consequences of such change on the frequency and magnitude of fires in the region is unclear due to spatial relationships and feedbacks between vegetation growth and burning. In the very near future the results of my simulation model will be able shed some light on this aspect of the region’s changing landscape and ecology.

Buy on Amazon

Diamond Reviews
Ecological Economics

Ecosystems Paper

In an effort not to become one of the estimated 200 million blogs that have now been abandoned, I thought it about time I let the blogosphere know that the paper I submitted to Ecosystems with Dr. George Perry and Dr. Raul Romero-Calcerrada has been accepted for publication. The paper arose out of the initial statistical modelling of the SPA I did for my PhD thesis (also used in Millington 2005) and examines the use of statistical techniques for explaining causes of land use and cover changes versus techniques for projecting change.

Here’s the abstract:

In many areas of the northern Mediterranean Basin the abundance of forest and scrubland vegetation is increasing, commensurate with decreases in agricultural land use(s). Much of the land use/cover change (LUCC) in this region is associated with the marginalisation of traditional agricultural practices due to ongoing socioeconomic shifts and subsequent ecological change. Regression-based models of LUCC have two purposes: (i) to aid explanation of the processes driving change and/or (ii) spatial projection of the changes themselves. The independent variables contained in the single ‘best’ regression model (i.e. that which minimises variation in the dependent variable) cannot be inferred as providing the strongest causal relationship with the dependent variable. Here, we examine the utility of hierarchical partitioning and multinomial regression models for, respectively, explanation and prediction of LUCC in EU Special Protection Area 56, ‘Encinares del río Alberche y Cofio’ (SPA 56) near Madrid, Spain. Hierarchical partitioning estimates the contribution of regression model variables, both independently and in conjunction with other variables in a model, to the total variance explained by that model and is a tool to isolate important causal variables. By using hierarchical partitioning we find that the combined effects of factors driving land cover transitions varies with land cover classification, with a coarser classification reducing explained variance in LUCC. We use multinomial logistic regression models solely for projecting change, finding that accuracies of maps produced vary by land cover classification and are influenced by differing spatial resolutions of socioeconomic and biophysical data. When examining LUCC in human-dominated landscapes such as those of the Mediterranean Basin, the availability and analysis of spatial data at scales that match causal processes is vital to the performance of the statistical modelling techniques used here.

Look out for it during 2007:

MILLINGTON, J.D.A., Perry, G.L.W. and Romero-Calcerrada, R. (In Press) Regression techniques for explanation versus prediction: A case study of Mediterranean land use/cover change Ecosystems

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Stoic Bravery and the Bull Economy

The rain in Spain stays mainly on the plain? Not when I’m there it doesn’t, then it follows me about. In this case all the way up to Santa Maria de la Alameda in the Sierra de Guadarrama.

Santa Maria de la Alameda
Quite a gloomy picture. We were up there interviewing the president of a local cattle farming organisation for some work related to my PhD. Earlier in the week we had been talking about bullfighting, and Raul had pointed out the large stones found in each corner of town squares, one on either side of the road, with large holes cut through them. The purpose of these holes is to hold wooden poles across the road, closing the square for the corrida de toros. As we waited for el presidente to arrive we sheltered from the rain in the porch of the ayuntamiento. Looking at the bullring’s cornerstones and the balconies that would allow spectators to overlook the confrontation, the town square reminded me of a story retold in Hemingway’s For Whom the Bell Tolls. On that occasion it wasn’t a bullfight, it was a civil war a massacre.

Hemingway’s leading characters display stoic bravery becoming, in Lawrence Broer’s view, “manifestations of the Spanish matador”;

The bull was on him as he jumped back and as he tripped on a cushion he felt the horn go into him, into his side. He grabbed the horn with his two hands and rode backward, holding tight onto the place. The bull tossed him and he was clear. He lay still. It was all right. The bull was gone.

He got up coughing and feeling broken and gone. The dirty bastards!

“Give me the sword”, he shouted. “Give me the stuff.”

Fuentes came up with the muleta and the sword.

Hernandez put his arm around him.

“Go on to the infirmary, man”, he said. “Don’t be a damn fool.”

“Get away from me”, Manuel said. “Get to hell away from me.”

He twisted free. Hernandez shrugged his shoulders. Manuel ran toward the bull.

There was the bull standing, heavy, firmly planted.

All right, you bastard! Manuel drew his sword out of the muleta, sighted with the same movement, and flung himself onto the bull. He felt the sword go in all the way. Right up to the guard. Four fingers and his thumb into the bull. The blood was hot on his knuckles, and he was on top of the bull.

The bull lurched with him as he lay on, and seemed to sink; then he was standing clear. He looked at the bull going down slowly over on his side, then suddenly four feet in the air.

Then he gestured at the crowd, his hand warm from the bull blood.

[from Ernest Hemingway, The Undefeated]

Down on the plains of Madrid below Santa Maria, the rain has stopped and the attitude seems more ‘spirited optimism’ than ‘stoic bravery’. The Spanish economy is booming, with GDP steadily rising year on year.

The environs of Madrid feel positive, the attitude is ‘go-ahead’. Cranes are everywhere, more than in London probably. Apartments being thrown up rapidly. New roads and motorways being constructed apace. It’s been like that the last few years I’ve been visiting.

Further out, within range of the commuters (going into Madrid) and the day-trippers (coming out), economic change is modifying the landscape. The agricultural sector is in decline and as the younger generation seeks out employment in manufacturing, construction and service sectors. Talking to people in my study area it seems such employment is desired as it brings more stable working hours, more benefits, greater leisure time and a more ‘modern’ lifestyle. The environmental consequences of these shifts are still playing themselves out however. For example, such a lifestyle is likely to require more water, a precious resource in the Mediterranean. Environmentalists still campaign against large dam projects and the environmental impacts of tourism along the Costa del Sol and the Balearic Isles are well known. Maybe James ‘The Bringer of Rain’ Millington should spend more time in those places…

My particular interest is the impact of agricultural change on wildfire regimes; will the spirited optimism have to be tempered by some stoic bravery in the face of increasing wildfire risk? I’m nearing the end of my PhD research now so I hope to be able to comment on that with more authority in the near future.

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Stakeholder Model Assessment

This last week I have been undertaking the final piece of fieldwork for my PhD thesis in my study area, EU Special Protection Area number 56, ‘Encinares del rio Alberche y Cofio’ (SPA56). The aim of this fieldwork is what I have been terming ‘Stakeholder Model Assessment’ and involved interviews with several actors and stakeholders within the study area to assess the credibility and potential utility of my integrated socio-ecological simulation model of land use and cover change (LUCC).

Specifically, two questions guiding these meetings were;

  1. from a technical/modelling standpoint, how can we utilise local stakeholder knowledge and understandings of LUCC better in our simulation models?
  2. if we understand that often science does not move fast enough to deal with pressing environmental and political problems, how can we use socio-ecological models (incorporating local knowledge) to speed the process of decision-making and consensus building in the face of incomplete knowledge about a system?

The simulation model I have developed is a tangible manifestation of my ‘mental model’ (i.e. understanding) of processes of change in SPA56. This research aimed to develop an understanding of how well this manifestation corresponds with a (hypothetical) simulation model that would be produced using the ‘mental model’ of the stakeholder.

I embarked on this fieldtrip with a certain amount of trepidation as I was laying myself and my model open to a degree of criticism from a source of knowledge not often tapped. That is, whilst LUCC models developed in an academic setting are routinely exposed to academic peer review they are infrequently reviewed by those actors which they attempt to represent. I was quite prepared to be told that the results and model structure I had developed were not realistic or largely irrelevant.

I was pleasantly surprised to be proven wrong as much of the feedback received was positive, both about model results (maps of land cover for 25 years hence – i.e. 2026) and model structure (i.e. model rules and assumptions). I’m just about to start writing this all up for my thesis but the findings can be outlined as follows;

1. Interviewees were very accepting of the results but focused on the results of individual scenarios that fitted most closely with their projections of future change. They did not seem to have any problems with model output for the scenario that matched their perception of future change, suggesting that the model accurately reflects the expected change for that scenario. (Spatial) criticism of results was rather weak however and their analysis was rather broad.

2. Interviewees confirmed model rules and assumptions, with some caveats;

  1. Distance between fields and farmstead were not deemed important for farmer decision-making
  2. Some interviewees suggested land tenure was not important, others that size of land parcels would dictate what land was changed to
  3. Agent types (i.e. ‘Traditional’ vs. ‘Commercial’ farmers) were deemed sensible. Greater variation is present in SPA56 farmer behaviour but generally this dichotomy is accurate

3. All interviewees commented that the model was lacking consideration of urban development and change (i.e. expansion)

4. Individual agricultural actors (i.e. farmers) were generally apathetic towards model (linked I suggest with their generally pessimistic view of future state of agriculture in the study area). Higher-level, institutional stakeholders (i.e. local development officials and planners) were much more interested in potential uses of the model for planning.

5. Interviews suggest the model is realistic/credible enough to act as a focus around which discussion about future change can proceed (‘model as mediator’ or ‘model as discussant’). Interview discussion followed the presentation of model assumptions and allowed the stakeholder to reflect on the processes causing change.

6. Interviewees’ ‘mental models’ were little influenced by the process of model assessment and discussion for two main reasons;

  1. they are apathetic towards the model and sceptical about what it can do for them
  2. presentation of model structure (and the model structure itself) is not as detailed or nuanced as their understanding of processes and change.

7. Related to point six, some interviewees were positive about the model because it confirmed their understanding of future change. That is, they envisaged opportunities to use the model as a rhetorical tool to further their interests. [More thoughts on this important point to follow soon…]

All-in-all a useful and interesting trip. These are my initial thoughts, more in-depth analysis and reflection is ongoing – I’ll post something more permanent on a page on my main website in the near future.

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dreaming code

George said it would happen. Last week I woke up one morning and realised I’d been dreaming code. I can’t say whether I was dreaming in code, or dreaming about code. Hard to tell the difference. I’m not very good at remembering what happens in my dreams – other people seem to be quite good at it though. Either way, it was a mixture of C++ and HTML. A mixture of simulation model and website I guess.

This reminded me of the title of a book that inspired a hollywood movie. “Do Androids Dream of Electric Sheep?” is apparently quite different from the movie Blade Runner, but I haven’t time for that right now so had to settle with watching the director’s cut. No time for post-modernism here (apparently the movie is, like, totally post-modern. I’ll leave Post-Normal Science to another blog) I’ll concentrate on some musings arising from my late night veiwing.

What’s the difference between a dream and a memory?” Dreams can feel immensly real, more real than memories I’d argue. They can feel so real you wake up in a cold sweat. Once you’re awake you realise it’s a dream and remember that bad dreams can happen sometimes and have happened before (but what about if you’re still asleep eh? That film Existenz). So you disregard the dream, relying on your memory that ‘it’s only a dream’. But if the dream can feel more real, why isn’t it trusted as much as the memory? Because we were unconscious when we had the dream? It wasn’t ‘real’?

So how ‘real’ are memories? What’s the relationship between the memory when it happened to the memory when it’s remembered? How has it changed? It can’t be exactly the same memory surely? I’m sure there’s a ton of literature out there on the relationship of dreams, reality, memory but I don’t know anything about that.

What I’m thinking about is the reliability of memories. We use memories to make decisions everyday. We use our memories of the past to make decisions now about the future. For someone trying to understand and simulate the decision-making process, this is quite an interesting question. Do we have some built-in understanding that sits with a memory giving us an idea about how ‘good’ (accurate) it is? If it feels vague, less vivid, if it feels less real, (if it feels less ‘real’ like a dream feels ‘real’) then this it’s not as reliable? Or is it about repetition – if we drive the same route to work everyday we remember it better than one we don’t drive often (but what about the details of that daily journey?).

Anyway, I think that’s all a little too detailed for me. It’s something interesting to think about and seemingly a popular topic for movie-makers. This guy Michel Gondry seems quite interested. Eternal Sunshine of the Spotless Mind was good – memories are more than just in your head, they’re part of you, they and the experiences that produced them make you who you are and that can’t be ignored. He’s got a new one out soon – The Science of Sleep. Looks quite fun.

I doubt it will help answer any of my questions though. I’m not going to be able to represent memories as a part of the decision-making process in my simulation model. I reckon it would be pretty ambitious for anyone to try that for a while. I’ll stick with some more general observations and mechanisms and keep dreaming code for a while longer.

[PS BAWA 1 – 3 Warmley Saints. Millington opened his scoring account in the first pre-season friendly today. A glorious 1 yard tap in, steaming in from central midfield, after the ‘keeper fumbled.]

Crisis Relief

In the midst of writing a PhD thesis crises of confidence are like those Routemaster buses I was talking about the other day (but on a different temporal scale); days and weeks without a worry and then a couple come along on the same day. Sometimes the end feels infintely far away. Today has been such a day.

However, I’ve found by writing down my specific aims and objectives and then reviewing my progress toward them I can calm myself down before any lasting damage is done. So here’s what I wrote today:


  1. Examine the impacts of human land use/cover change upon wildfire regimes in a Mediterranean landscape
  2. Explore and evaluate novel methods to ‘validate’ simulation models (and processes of modelling) of environmental change considering human activity

To achieve aim i): Develop a spatially-explicit computer simulation model to examine:

  1. impacts of change in land use/cover configuration (specifically fragmentation) on future wildfire regime (spread component)
  2. impacts of change in vegetation (land cover) composition on future wildfire regime (spread and ignition risk components)
  3. impacts of change in human population (size and ‘type’ of inhabitant) on future wildfire regime (ignition risk component)

To achieve aim ii):

  1. Explore ways of using local stakeholder input to ‘validate’ (or assess the ‘warrantability’ of) the construction of the model (emphasis on the ‘realism’ of the model rather than dynamics
  2. Discuss potential uses of narrative approaches to present processes of model construction and interpretation of results
  3. Examine use of ‘table of inductions’ as proposed by W. Whewell
  4. Think about discussion of potential of online tools for collaborative/participatory approaches to environmental modelling

Ahhhh. That’s better…

(And England won the cricket! GET IN!)