SystemDynamics Archives - Page 6 of 22

Aging is unnatural

Larry Yeager and I submitted a paper to the SD conference, proposing dynamic cohorts as a new way to model aging populations, vehicle fleets, and other quantities. Cohorts aren’t new*, of course, but Ventity makes it practical to allocate them on demand, so you don’t waste computation and attention on a lot of inactive zeroes.

The traditional alternative has been aging chains. Setting aside technical issues like dispersion, I think there’s a basic conceptual problem with aging chains: they aren’t a natural, intuitive operational representation of what’s happening in a system. Here’s why.

Consider a model of an individual. You’d probably model age like this:

Here, age is a state of the individual that increases with aging. Simple. Equivalently, you could calculate it from the individual’s birth date:

Ideally, a model of a population would preserve the simplicity of the model of the individual. But that’s not what the aging chain does:

This says that, as individuals age, they flow from one stock to another. But there’s no equivalent physical process for that. People don’t flow anywhere on their birthday. Age is continuous, but the separate stocks here represent an arbitrary discretization of age.

Even worse, if there’s mortality, the transition time from age x to age x+1 (the taus on the diagram above) is not precisely one year.

You can contrast this with most categorical attributes of an individual or population:

When cars change (geographic) state, the flow represents an actual, physical movement across a boundary, which seems a lot more intuitive.

As we’ll show in the forthcoming paper, dynamic cohorts provide a more natural link between models of individuals and groups, and make it easy to see the lifecycle of a set of related entities. Here are the population sizes of annual cohorts for Japan:

I’ll link the paper here when it’s available.

* This was one of the applications we proposed in the original Ventity white paper, and others have arrived at the same idea, minus the dynamic allocation of the cohorts. Demographers have been doing it this way for ages, though usually in statistical approaches with no visual representation of the system.

Data science meets the bottom line

A view from simulation & System Dynamics

I come to data science from simulation and System Dynamics, which originated in control engineering, rather than from the statistics and database world. For much of my career, I’ve been working on problems in strategy and public policy, where we have some access to mental models and other a priori information, but little formal data. The attribution of success is tough, due to the ambiguity, long time horizons and diverse stakeholders.

I’ve always looked over the fence into the big data pasture with a bit of envy, because it seemed that most projects were more tactical, and establishing value based on immediate operational improvements would be fairly simple. So, I was surprised to see data scientists’ angst over establishing business value for their work:

One part of solving the business value problem comes naturally when you approach things from the engineering point of view. It’s second nature to include an objective function in our models, whether it’s the cash flow NPV for a firm, a project’s duration, or delta-V for a rocket. When you start with an abstract statistical model, you have to be a little more deliberate about representing the goal after the model is estimated (a simulation model may be the delivery vehicle that’s needed).

You can solve a problem whether you start with the model or start with the data, but I think your preferred approach does shape your world view. Here’s my vision of the simulation-centric universe:

The more your aspirations cross organizational silos, the more you need the engineering mindset, because you’ll have data gaps at the boundaries – variations in source, frequency, aggregation and interpretation. You can backfill those gaps with structural knowledge, so that the model-data combination yields good indirect measurements of system state. A machine learning algorithm doesn’t know about dimensional consistency, conservation of people, or accounting identities unless the data reveals such structure, but you probably do. On the other hand, when your problem is local, data is plentiful and your prior knowledge is weak, an algorithm can explore more possibilities than you can dream up in a given amount of time. (Combining the two approaches, by using prior knowledge of structure as “free data” constraints for automated model construction, is an area of active research here at Ventana.)

I think all approaches have a lot in common. We’re all trying to improve performance with systems science, we all have to deal with messy data that’s expensive to process, and we all face challenges formulating problems and staying connected to decision makers. Simulations need better connectivity to data and users, and purely data driven approaches aren’t going to solve our biggest problems without some strategic context, so maybe the big data and simulation worlds should be working with each other more.

Cross-posted from LinkedIn

Remembering Jay Forrester

I’m sad to report that Jay Forrester, pioneer in servo control, digital computing, System Dynamics, global modeling, and education has passed away at the age of 98.

I’ve only begun to think about the ways Jay influenced my life, but digging through the archives here I ran across a nice short video clip on Jay’s hope for the future. Jay sounds as prescient as ever, given recent events:

“The coming century, I think, will be dominated by major social, political turmoil. And it will result primarily because people are doing what they think they should do, but do not realize that what they’re doing are causing these problems. So, I think the hope for this coming century is to develop a sufficiently large percentage of the population that have true insight into the nature of the complex systems within which they live.”

I delve into the roots of this thought in Election Reflection (2010).

Here’s a sampling of other Forrester ideas from these pages:

The Law of Attraction

Forrester on the Financial Crisis

Self-generated seasonal cycles

Deeper Lessons

Servo-chicken

Models

Market Growth

Urban Dynamics

Industrial Dynamics

World Dynamics

Dead buffalo diagrams

I think it was George Richardson who coined the term “dead buffalo” to refer to a diagram that surrounds a central concept with a hail of inbound causal arrows explaining it. This arrangement can be pretty useful as a list of things to think about, but it’s not much help toward solving a systemic problem from an endogenous point of view.

I recently found the granddaddy of them all:

Early economic dynamics: Samuelson's multiplier-accelerator

Paul Samuelson’s 1939 analysis of the multiplier-accelerator is a neat piece of work. Too bad it’s wrong.

Interestingly, this work dates from a time in which the very idea of a mathematical model was still questioned:

Contrary to the impression commonly held, mathematical methods properly employed, far from making economic theory more abstract, actually serve as a powerful liberating device enabling the entertainment and analysis of ever more realistic and complicated hypotheses.

Samuelson should be hailed as one of the early explorers of a very big jungle.

The basic statement of the model is very simple:

In quasi-System Dynamics notation, that looks like:

A caveat:

The limitations inherent in so simplified a picture as that presented here should not be overlooked. In particular, it assumes that the marginal propensity to consume and the relation are constants; actually these will change with the level of income, so that this representation is strictly a marginal analysis to be applied to the study of small oscillations. Nevertheless it is more general than the usual analysis.

Samuelson hand-simulated the model (it’s fun – once – but he runs four scenarios): Samuelson then solves the discrete time system, to identify four regions with different behavior: goal seeking (exponential decay to a steady state), damped oscillations, unstable (explosive) oscillations, and unstable exponential growth or decline. He nicely maps the parameter space:

So where’s the problem?

The first is not so much of Samuelson’s making as it is a limitation of the pre-computer era. The essential simplification of the model for analytic solution is;

This is fine, but it’s incredibly abstract. Presented with this equation out of context – as readers often are – it’s almost impossible to posit a sensible description of how the economy works that would enable one to critique the model. This kind of notation remains common in econometrics, to the detriment of understanding and progress.

At the first SD conference, Gil Low presented a critique and reconstruction of the MA model that addressed this problem. He reconstructed the model, providing an operational description of the economy that remains consistent with the multiplier-accelerator framework.

The mere act of crafting a stock-flow description reveals problem #1: the basic multiplier-accelerator doesn’t conserve stuff.

Non-conservation of stuff leads to problem #2. When you do implement inventories and capital stocks, the period of multiplier-accelerator oscillations moves to about 2 decades – far from the 3-7 year period of the business cycle that Samuelson originally sought to explain. This occurs in part because the capital stock, with a 15-year lifetime, introduces considerable momentum. You simply can’t discover this problem in the original multiplier-accelerator framework, because too many physical and behavioral time constants are buried in the assumptions associated with its 2 parameters.

Low goes on to introduce labor, finding that variations in capacity utilization do produce oscillations of the required time scale.

I think there’s a third problem with the approach as well: discrete time. Discrete time notation is convenient for matching a model to data sampled at regular intervals. But the economy is not even remotely close to operating in discrete annual steps. Moreover a one-year step is dangerously close to the 3-year period of the business cycle phenomenon of interest. This means that it is a distinct possibility that some of the oscillatory tendency is an artifact of discrete time sampling. While improper oscillations can be detected analytically, with discrete time notation it’s not easy to apply the simple heuristic of halving the time step to test stability, because it merely compresses the time axis or causes problems with implicit time constants, depending on how the model is implemented. Halving the time step and switching to RK4 integration illustrates these issues:

It seems like a no-brainer, that economic dynamic models should start with operational descriptions, continuous time, and engineering state variable or stock flow notation. Abstraction and discrete time should emerge as simplifications, as needed for analysis or calibration. The fact that this has not become standard operating procedure suggests that the invisible hand is sometimes rather slow as it gropes for understanding.

The model is in my library.

See Richardson’s Feedback Thought in Social Science and Systems Theory for more history.

Parameter Distributions

Answering my own question, here’s the distribution of all 12,000 constants from a dozen models, harvested from my hard drive. About half are from Ventana, and there are a few classics, like World3. All are policy models – no physics, biology, etc.

The vertical scale is magnitude, ABS(x). Values are sorted on the horizontal axis, so that negative values appear on the left. Incredibly, there were only about 60 negative values in the set. Clearly, unlike linear models where signs fall where they may, there’s a strong user preference for parameters with a positive sense.

Next comes a big block of 0s, which don’t show on the log scale. Most of the 0s are not really interesting parameters; they’re things like switches in subscript mapping, though doubtless some are real.

At the right are the positive values, ranging from about 10^-15 to 10^+15. The extremes are units converters and physical parameters (area of the earth). There are a couple of flat spots in the distribution – 1s (green arrow), probably corresponding with the 0s, though some are surely “interesting”, and years (i.e. things with a value of about 2000, blue arrow).

If you look at just the positive parameters, here’s the density histogram, in log10 magnitude bins:

Again, the two big peaks are the 1s and the 2000s. The 0s would be off the scale by a factor of 2. There’s clearly some asymmetry – more numbers greater than 1 (magnitude 0) than less.

One thing that seems clear here is that log-uniform (which would be a flat line on the last two graphs) is a bad guess.

What's the empirical distribution of parameters?

Vensim‘s answer to exploring ill-behaved problem spaces is either to do hill-climbing with random restarts, or MCMC and simulated annealing. Either way, you need to start with some initial distribution of points to search.

It’s helpful if that distribution is somehow efficient at exploring the interesting parts of the space. I think this is closely related to the problem of selecting uninformative priors in Bayesian statistics. There’s lots of research about appropriate uninformative priors for various kinds of parameters. For example,

If a parameter represents a probability, one might choose the Jeffreys or Haldane prior.
Indifference to units, scale and inversion might suggest the use of a log uniform prior, where nothing else is known about a positive parameter

However, when a user specifies a parameter in Vensim, we don’t even know what it represents. So what’s the appropriate prior for a parameter that might be positive or negative, a probability, a time constant, a scale factor, an initial condition for a physical stock, etc.?

On the other hand, we aren’t quite as ignorant as the pure maximum entropy derivation usually assumes. For example,

All numbers have to lie between the largest and smallest float or double, i.e. +/- 3e38 or 2e308.
More practically, no one scales their models such that a parameter like 6.5e173 would ever be required. There’s a reason that metric prefixes range from yotta to yocto (10^24 to 10^-24). The only constant I can think of that approaches that range is Avogadro’s number (though there are probably others), and that’s not normally a changeable parameter.
For lots of things, one can impose more constraints, given a little more information,
- A time constant or delay must lie on [TIME STEP,infinity], and the “infinity” of interest is practically limited by the simulation duration.
- A fractional rate of change similarly must lie on [-1/TIME STEP,1/TIME STEP] for stability
- Other parameters probably have limits for stability, though it may be hard to discover them except by experiment.
- A parameter with units of year is probably modern, [1900-2100], unless you’re doing Mayan archaeology or paleoclimate.

At some point, the assumptions become too heroic, and we need to rely on users for some help. But it would still be really interesting to see the distribution of all parameters in real models. (See next …)

Self-generated seasonal cycles

This time of year, systems thinkers should eschew sugar plum fairies and instead dream of Industrial Dynamics, Appendix N:

Self-generated Seasonal Cycles

Industrial policies adopted in recognition of seasonal sales patterns may often accentuate the very seasonality from which they arise. A seasonal forecast can lead to action that may cause fulfillment of the forecast. In closed-loop systems this is a likely possibility. The analysis of sales data in search of seasonality is fraught with many dangers. As discussed in Appendix F, random-noise disturbances contain a broad band of component frequencies. This means that any effort toward statistical isolation of a seasonal sales component will find some seasonality in the random disturbances. Should the seasonality so located lead to decisions that create actual seasonality, the process can become self-regenerative.

Self-induced seasonality appears to occur many places in American industry. Sometimes it is obvious and clearly recognized, and perhaps little can be done about it. An example of the obvious is the strong seasonality in items such as cameras sold in the Christmas trade. By bringing out new models and by advertising and other sales promotion in anticipation of Christmas purchases, the industry tends to concentrate its sales at this particular time of year.

Other kinds of seasonality are much less clear. Almost always when seasonality is expected, explanations can be found to justify whatever one believes to be true. A tradition can be established that a particular item sells better at a certain time of year. As this “fact” becomes more and more widely believed, it may tend to concentrate sales effort at the time when the customers are believed to wish to buy. This in turn still further heightens the sales at that particular time.

Retailer sales & e-commerce sales, from FRED

Announcing Leverage Networks

Leverage Networks is filling the gap left by the shutdown of Pegasus Communications:

We are excited to announce our new company, Leverage Networks, Inc. We have acquired most of the assets of Pegasus Communications and are looking forward to driving its reinvention. Below is our official press release which provides more details. We invite you to visit our interim website at leveragenetworks.com to see what we have planned for the upcoming months. You will soon be able to access most of the existing Pegasus products through a newly revamped online store that offers customer reviews, improved categorization, and helpful suggestions for additional products that you might find interesting. Features and applications will include a calendar of events, a service marketplace, and community forums

As we continue the reinvention, we encourage suggestions, thoughts, inquiries and any notes on current and future products, services or resources that you feel support our mission of bringing the tools of Systems Thinking, System Dynamics, and Organizational Learning to the world.

Please share or forward this email to friends and colleagues and watch for future emails as we roll out new initiatives.

Thank you,

Kris Wile, Co-President

Rebecca Niles, Co-President

Kate Skaare, Director

As we create the Leverage Networks platform, it is important that the entire community surrounding Organizational Learning, Systems Thinking and System Dynamics be part of the evolution. We envision a virtual space that is composed both archival and newly generated (by partners, community members) resources in our Knowledge Base, a peer-supported Service Marketplace where service providers (coaches, graphic facilitators, modelers, and consultants) can hang a virtual “shingle” to connect with new projects, and finally a fully interactive Calendar of events for webinars, seminars, live conferences and trainings.

If you are interested in working with us as a partner or vendor, please email partners@leveragenetworks.com

ISDC 2013 Capen quiz results

Participants in my Vensim mini-course at the 2013 System Dynamics Conference outperformed their colleagues from 2012 on the Capen Quiz (mean of 5 right vs. 4 last year).

5 right is well above the typical performance of the public, but sadly this means that few among us are destined to be CEOs, who are often wildly overconfident (console yourself – abject failure on the quiz can make you a titan of industry).

Take the quiz and report back!