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DDMA Level IIQuantitative Modelling Skills
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Chapter 1

Quantitative modelling concepts

Last updated November 2026about 4 min read

Key takeaways

  • A model is a simplified representation of a real system, built to understand, predict or optimise its behaviour; a quantitative model expresses it in numbers, variables and equations.
  • Building one runs through model type selection, definition and formulation, the target expression type, and the key mathematical functions it relies on.
  • A linear model gives one deterministic answer; a probabilistic (stochastic) model builds in randomness and gives a distribution of possible outcomes.
  • Quantitative modelling makes assumptions explicit and testable, supports objective comparison of alternatives, and allows what-if analysis without changing the real system.
  • The types range from simple analysis and econometric estimation to systems of equations, input-output analysis and partial modelling.
Model
A simplified representation of a real system, built to understand, predict or optimise its behaviour.
Quantitative model
A model expressed in mathematical terms, using numbers, variables and equations rather than qualitative description.

Modelling methodology, the steps a quantitative model is built through:

  • Model type selection, choosing an approach that fits the problem (the chapters on regression, linear programming and simulation cover the main types this paper addresses)
  • Definition and formulation, stating precisely what the model represents and its variables
  • Target expression type, deciding what form the model's output takes (a single number, an equation, a set of decisions)
  • Key mathematical functions, the specific relationships (linear, exponential, etc.) the model relies on

Examples of models:

Linear models
Represent a relationship as a straight-line function of the inputs.
Probabilistic (stochastic) models
Incorporate randomness explicitly, producing a distribution of possible outcomes rather than one fixed answer.
Regression models
Estimate the relationship between a dependent variable and one or more predictors (see the chapter on regression modelling).
Multiple regression
Regression with more than one predictor variable.
Line fitting
Finding the line that best represents a set of data points, the basis of simple linear regression.

Advantages of quantitative modelling: makes assumptions explicit and testable, supports objective comparison of alternatives, and allows what-if analysis without needing to change the real system.

Mathematical modelling paradigms include differential equations, ordinary differential equations in particular describe how a quantity changes continuously with respect to another variable, commonly time, and underpin models of growth, decay and dynamic systems.

Types of quantitative modelling:

Simple analysis
Direct calculation from known relationships, without a formal statistical or optimisation model.
Econometric estimation
Applying statistical methods (often regression) to economic data to estimate relationships.
Systems of equations
Modelling several interacting relationships together, solved simultaneously.
Input-output analysis
Models how outputs of one part of a system become inputs to another, common in economic sector analysis.
Partial modelling
Models one part of a system in detail while treating the rest as fixed or simplified.

Exam tip

Linear versus probabilistic models is a useful lens for the whole paper, a linear model gives one deterministic answer, a probabilistic model (simulation in particular, which has its own chapter) gives a range of possible outcomes and their likelihoods.

Test Your Knowledge

3 questions on this chapter
Question 1 of 3An analyst at a Mombasa logistics firm wants a model that shows the range of possible delivery times and how likely each is, rather than one fixed figure. Which type of model fits?
Pick an option first
Question 2 of 3A Treasury economist wants to model how the output of Kenya's agricultural sector becomes an input to its food-processing sector. Which type of quantitative modelling is this?
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Question 3 of 3Which mathematical modelling paradigm describes how a quantity changes continuously with respect to another variable, commonly time, and underpins models of growth and decay?
Pick an option first