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Haggerstrand’s Model: Introduction
The study of diffusion processes has engaged the attention of many geographers in recent years. While these ideas were originally discussed in qualitative terms by anthropologists Clark Wissler and A.L. Kroeber, it was Haggerstrand who combined the depth of research and originality of content.
Torsten Haggerstrand published his work “Innovation Diffusion as a Spatial Process” in 1953, in which he described the spatial stages in the spread of a number of new ideas and techniques. Haggerstrand constructed a series of Monte Carlo simulation models of the spread. In simulation procedures, the researcher sets up a model of the real situation and a closer approximation to it in the output of the model.
The Monte Carlo technique of simulation incorporates a chance element. Haggerstrand was the first geographer to introduce the random element or chance into the study of geography. Both the aim and methods of his work were relatively new to geography.
Haggerstrand’s Assumptions
In his theoretical models, Haggerstrand made the familiar initial assumptions.
1. An even population density on a uniform plain, and
2. The information about the innovation was received in the same form by everyone. People were either informed or not.
Haggerstrand’s initial interest was in developing a theoretical explanation of the spread of innovations. In order to test his ideas, he needed data giving both the times and places at which an innovation was accepted as it spread from its point of origin. In searching for such sets of data he became interested in the spread of Swedish government subsidy programmes for farmers throughout rural Sweden.
These included the acceptance of government pasture subsidies by farmers who were willing to fence in their land in order to protect forests from grazing animals and the use of tests to detect bovine tuberculosis. His efforts to understand the processes by which use of pasture subsidies spread from farm to farm, provides an introduction of his work in general. By accepting such subsidies, farmers received money to fence in and improve their pasture lands. It may seem that such should be immediately accepted by all eligible farmers in the area but this was not true.
The acceptance was at first slow and spatially irregular. The western part of the area developed ahead of the eastern section that was relatively backward. The diffusion process was more complex, having a very strong spatial character. Many more acceptances occurred among farmers adjacent to neighbors, who already had the subsidy, and only few occurred in the more remote areas.
Haggerstrand reasoned that if he could simulate such a pattern of spatial diffusion using simplistic rules he would gain valuable insight into how development and change take place in a spatial context.
Haggerstrand’s Other assumptions
1. There is a single source of information or ‘knower”, located on
2. a homogeneous and isotropic plain, with
3. an evenly distributed population of potential acceptors, who are
4. informed about the innovation in the same form. They are either informed or not.
5. Information was spread only when two people exchanged messages. Such paired meetings would take place at constant intervals.
6. A knower or innovator would tell one neighbor after another and that once told, a neighbor would accept the subsidy without further persuasion.
Principles of Haggerstrand’s Model
The spatial extent of the contacts that a person has made in a given period of time is called a person’s information field. By analyzing short distance migration and telephone calls, Haggerstrand depicted indirectly, the structure of private information fields. He concluded that, on an average, the density of contacts included in a person’s private information field must decrease rapidly with increasing distance. Thus, the probability of information being transmitted from an adopter to a potential adopter declines with distance (Figure 1).
The generalization of these fields for a group of similar people is called the mean information field. The process whereby future adopting is more likely to occur around existing adopters is called the neighborhood effect. In his model Haggerstrand depicted the mean information field at Asby (Figure 2).
The some total of numbers in a cell divided by the total number of digits equals the cell probability for example 300 = 0.3 (note 0-999 is 1000 numbers) X1000
In his study of the Asby district, Haggerstrand divided a 25 X 25 km area into 25 squares or cells each one measuring 5 X 5 km. The distance decay values have had their point of origin set on the center cell and have been rotated through 360 degrees to give point values for the center of each cell.
These values were then multiplied by 25 since the distance decay values were based on the number of migrating households per square kilometer and each cell covers 25 km². The probability of contact for each cell with the center cell can now be calculated by dividing each cell value by the sum of all values (Figure 5.8).
Finally, the contact probability values are converted into a series of intervals, the sizes of which are determined by their respective probability values. The latter procedure makes possible the use of random numbers. The cell intervals are large near the center of the grid and there is a strong chance that a randomly drawn four figure number would fall within one of the intervals near the middle of the grid, whereas in the outer cells the interval is small and the chance of random number falling within one of these ranges is only slight.
Once constructed in this way, the mean information field can be used as an overlay or a floating grid to enable the stimulation of patterns of diffusion.
To activate the model, Haggerstrand at each time period floated the Mean Information Field (MIF) of Asby over every acceptor from the previous generation one at a time, and one new paired contact was chosen for each acceptor. The farmer contacted there upon became a knower or message sender in the next and all subsequent generations. As more and more farmers accepted the innovation, the contribution of the central cells to the spreading pattern became less important. At the same time in some subsequent generations, that effort was considered redundant and not counted.
The results of Haggerstrand’s initial efforts showed similarities to the actual distribution but they were, nevertheless, disappointing. Too much variation occurred between the model and reality and also between one run of the stimulation and another. In order to account for such variations, Haggerstrand introduced further modification into his model.
In his next effort, he weighed the MIF by underlying uneven distribution of population and also introduced barriers which either prevented or slowed communication. These barriers in large part represented the lakes which broke up the area in western Sweden.
Haggerstrand also began his diffusion with twenty-two original knowers rather than a single subsidized farm. Runs with the improved model were conducted much as were those with the original one. In the improved case, the MIF was floated over each of the 22 knowers in turn. The MIF was then weighed according to the underlying population distribution (Figure 3).
After that one paired contact was randomly chosen for each innovator. In the next time period, or generation, the original innovators again were allowed paired meetings, but so were those with whom they had come in contact the previous time. The simulation was stopped when the number of acceptors approximately matched the actual number.
This method of choosing locations randomly, but according to an overlying set of probabilities (shown by MIF), is called the Monte Carlo Method. The simulation at four different time periods shows remarkable similarity between the actual and simulated final patterns.
The model has a very improved power of prediction but it did not take into account the influence that mass media, such as newspapers, radio, TV, and government agencies might have; only word of mouth contact has been considered. The success of the simulation indicates that such contacts are extremely important in spreading ideas and innovations.
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