Page 210 - DCAP601_SIMULATION_AND_MODELING

Simulation and Modelling

Notes In what follows we want to discuss the use of quantitative and qualitative computational models
to make quantitative and qualitative predictions or rather to draw conclusions from complex
antecedents and discuss different types of explanation and prediction (and the relation between
these two) and close with an overview of topics in validity and validation.

Task Analyze the difference between validity and validation.

12.2.1 Qualitative and Quantitative Simulation

Although most simulation uses quantitative procedures — doing calculations with numbers,
often real valued, which make believe that the properties of the target system are quantitative,
metric properties —, most of our mental models and verbal theories which are the predecessors
of most of our simulation programmes do not talk about numbers and numerical values, but
rather of properties which are categorical or, at best, ordinal. “However we claim that the use of
numbers in this way is often simply a result of laziness — we often use numbers as a stand-in for
qualitative aspects that we do not know how to program or have not the time to program.”
(Edmonds and Hales 2003: 3)

Example: Gender desegregation among staffs of schools
The following example — which is taken from (Gilbert and Troitzsch 1999: 108–114) and earlier
papers — tries to “explain” how the process of overcoming gender segregation in German
schools went on in the 1950s and 1960s. The modeling process started from a large collection of
empirical data showing the proportion of male and female teachers in all grammar schools in
the federal state of Rhineland-Palatinate (approximately 150 in number) from 1950 to 1990.
The model reproducing the empirical distribution of this proportion over time quite well was
designed as parsimonious as possible, just assuming three hypotheses:
1. That all teachers leaving their jobs are replaced by men and women with equal overall
probability (Article 2 linea 2 of the German Basic Law),

2. That men stay in their jobs approximately twice as long as women (an empirical
observation), and
3. That new women are assigned to an individual school with probability P(W|) = (t)exp()
according to the percentage  of women among its teachers (a theoretical assumption); ??is
0.5 in this simulation run, and ?(t) is such that at all times men and women have the same
overall probability of replacing retired teachers, to comply with hypothesis 1.
The simulation is initialized with a gender distribution close to the empirical distribution of
1950.

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