# Bird’s-eye view of the IBM for complex « interaction » cases

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## Searching for a working place

The question for the individual is now to decide where to search for a job. If the leader of the household has already found a job far (further than the proximity attribute) from the place of residence and the household is trying to move close the leader’s place of work, then the other household members, waiting for a change of residence, do not try to change job since they do not know where they will be living. Until the household finds out a new residence place, nobody is going to change jobs.
In the other cases, if the individual is searching for a job, she looks from the closest offer to the furthest considering successive rings of distance relevant to describe the average space between municipalities, for example 3 in France, starting from her place of residence.
Indeed, she considers at first the job offer located in her place of residence and at most at distance 3 in our example from this place. If she can’t find a job, she continues looking from a distance 3 to a distance 6 (in our example) from her place of residence. She continues the procedure until finding a not empty list of possible jobs or considering the ring at the maximum distance far from her place of residence. She can also search for a job outside the set. This depends on the parameterisation. For example, in France, as presented in (Huet, Lenormand et al. 2012), she decides to commute outside using the probability to commute outside knowing her place of living since the searching procedure finished and only if she had not found out a job in her place of residence and found one elsewhere (to be coherent with the data available for parameterisation). Finally, if she does not commute outside the set of municipalities, she chooses at random a municipality as a place of work in the list of the possible job offer she has collected.
Parameters: length of a ring; maximum distance to search for a job inside the set; probability to commute outside for an inhabitant of every municipality (example for France).

Become a retiree

At a given age, the individual becomes a retiree. We assume, for sake of simplicity, that a retiree does not search for a job. Parameter: probability law to decide the individual’s retirement age.

Demographic dynamics

A new household can be created when an individual becomes an adult or when a new household comes to live in the set of municipality (i.e. in-migration). The main reasons for household elimination are out-migration and death. Three main dynamics change the household type (single, couple, with or without children and complex4): makeCouple; splitCouple and givingBirth. These processes have to be parameterised depending on the case study and its available data. We describe them using an example of implementation for a French region allowing the reader to form a clearer idea about them. Moreover this implementation is described and discussed in chapter 1.4.

Household migration and mobility

In changing residence process, we include both residential migration and mobility without making a difference, between short and long distance move, as it is often the case (Coulombel 2010) in the literature. The submodel we propose directly manages both types of moving. However, it turned out easier for us to distinguish two categories of migration: the migration of people coming from outside to live inside the set; the migration of people who already live inside the set.
The immigration into the set is an external forcing. Each year, a number of potential immigrants from outside the set are added to the municipalities of the set. These potential immigrants can really become inhabitants of the set if they find a residence by themselves or by being chosen as a partner by someone already living in the set in case they are single (with or without children). Thus, looking for a place or a partner of residence are the only action they execute until they become an inhabitant of the set. Until the potential immigrant becomes a real inhabitant, she cannot search for a job. Indeed, the job occupied by people living outside the municipality set are already taken into account through the scenario and allowing potential immigrants to find a job directly would be redundant. The definition of who are potential immigrants, how numerous they are, and when they are introduced is specified exogenously. Since they are created, the potential immigrants are temporarily located into a municipality from which they can find a residence or being chosen as a partner. They are placed in a municipality following a probability to be chosen, which is computed for each municipality depending on the population size of the municipality and its distance to the frontier of the set. A particular attraction of young people for larger municipalities is also taken into account.

An iterative algorithm avoiding to generate all possible households

The principle of the algorithm is to build progressively the household, by picking its member(s) according to the previously described probabilities, and, for each new member, to test if there is an individual of this age in the list of individuals I. If not, we stop the process for this household and begin to build another one.
This process is equivalent to pick one household according to its evaluated probability, and keeping it if all the ages of its members are present in list I. Indeed, the process of picking the different members of the household leads to the same overall probability to pick a household, and since the attempt is cancelled as soon as one age is lacking in list I, it changes nothing to make these tests iteratively.
Moreover, we can constrain even more the process by considering the list of household sizes which is directly derived from the data. The rest of the process remains the same. Then we are sure to have the right number of households, even though when algorithm 3 stops, some void households remain in the list.
Indeed, the described algorithm should a priori be repeated until all the households of the list are filled with all the individuals of the availability vector. However, this situation is never reached and after the creation of almost all the households, the program reaches a point where no more households can be achieved given the remaining individuals. For this reason, when this situation is reached, the algorithm is stopped. The remaining households can be considered as “complex structures”, namely all the housing solutions that cannot be placed into the usual categorization of household type (single, couple, single-parent). A complex household can be, for example, a group of students occupying the same housing or two familiar groups sharing the same location. Therefore, since we do not have any information about these structures from the data sets, to conclude the generation of the artificial population, the complex households are filled randomly with the remaining individuals in the availability list.

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### Designing and parameterising the individual activity

This part focuses on the design and the parameterisation of the individual activity. The purpose is to illustrate how to model in a micro simulation approach individuals’ behaviour on a labour market utilising existing data. The European project that funded this work did not fund specific interviews or surveys for this purpose. But, even if such funding had been available, it would have been difficult to have a sufficiently large sample to ensure the statistical significance of the obtained attributes and behaviours. Therefore, it seemed better to use existing large database dedicating especially to the labour force, such as the labour force survey, which gives information on the labour force based on a very large sample and the weights for projection at various levels. Moreover these databases, developed by the National Statistical Office, have been built on a data collection model designed by experts.
They represent common knowledge, largely shared by every stakeholder since they are used as references in decisions and predictions.
We start from existing databases and the objectives of the modelling to characterise our agents and their attributes and behaviours. That is what we discuss in the following first subsection. The two following subsections give details on the initialisation of the attributes and on the parameterisation of the behaviours. The link between attributes and behaviours is guaranteed as this data is implemented to ensure its compatibility with the agent attribute modalities. Similarly, the projection of attributes and behaviour for the whole virtual population is easy: an innovative generation population algorithm builds directly a robust and significant population of individuals while the link between modalities of attributes and their evolving rules allows an automatic projection at the population level.

#### Data sources and main modelling choices

This is to identify the agent classes and the structure of agent behaviour in each class. The first steps have been:
· to collect all relevant data source regarding the region we want to simulate considering the exact problem (aim of the project) we need to address.
· to make a state-of-the art.
From the literature and the expertise coming mainly from economists, we identify two complementary groups of dynamics to take into account to model the evolution of a local labour market:
· Job offers and corresponding dynamics.
· Job demand and occupation, and corresponding dynamics.
We identify two possible databases to help us conceptualising and parameterizing the model:
· The Census: it gives indications about the situation of individual when being student, retired, or active and also who is occupied and who is not occupied, what occupations individual have aggregated in socio-professional categories and activity sectors; Census data are available at the municipality level for three different dates 1990, 1999 and 2006. We can also benefit from the mobility tables of the Census giving, at least in 1999, an exhaustive description of the commuting flows between municipalities; French Census data are also available for 1982 but not electronically;
· Labour force survey (from 1990) and census data.

Overview
Data driven integrated modelling of social dynamics
Theoretical individual based models of social influence
Part 1. Data driven integrated modelling of social dynamics
Chapter 1.1 The SimMunicipality model
Main entities, state variables and scales
Process overview and scheduling
Chapter 1.2 Generating the initial population
Materials and Methods
Results
Conclusion
Chapter 1.3 Parametrisation of the individual activity dynamics
Designing and parameterising the individual activity
Lessons / Experience
Acknowledgements
References
Chapter 1.4 Parametrisation of the unknown laws of demography
The Cantal and its demography
How to model couple and birth dynamics in Cantal
How to model moving
Conclusion
Acknowledgements
Part 2. Theoretical individual based models of social influence
Chapter 2.1 Disregarding information – a model exhibiting the primacy bias
The models
Diffusion of a two-feature object
Diffusion of more than two features
Discussion
Chapter 2.2 Disregarding information – a double modelling approach
The individual based model (IBM)
Bird’s-eye view of the IBM for complex « interaction » cases
The aggregated model helping to predict the IBM
Conclusion, discussion
Chapter 2.3 Attraction-Rejection – designed from theories
1 Introduction
2 Overview of the model
3 Analysis of several examples
4 Systematic analysis of the number of clusters
Discussion and conclusion
Acknowledgement
References
Chapter 2.4 Attraction-rejection – a double modelling approach
Number of clusters in the ABM when the uncertainty varies
Aggregate model at the limit of infinite population
Discussion and conclusion
References
Chapter 2.5 Attraction-Rejection – designed from experiments
1 Introduction
2 The Dynamical Model of Interacting Individuals
3 Typical Evolutions of the population
4 Systematic experiments
5 Discussion and conclusion
Conclusions and perspectives
A methodological point of view on data and design