What is Modeling?

Simplifying Complex Phenomena v We live in a complex world v Most of the scientific relationships we study are very complex v Understanding the relationships can be improved by simplification to represent the major relationships v Simplified views of such systems called “models”

Types of Models v Want to skip a lot of definitions v Categories not mutually exclusive v Some simple divisions –Physical models - some scale representation of the system –Mathematical models - use mathematical equations to represent relationships –Simulation models - uses variations in math relationships to explore many “what-if” situations

Creating a Model v Difficult for most people to do - beyond their formal experience v Needs to be explained conceptual terms first v People actually do this but informally

Example v How long will it take me to get to work? –During rush hours? –During off-peak hours? –Using alternative routes because of congestion or construction v What are the components, cause and effect variables in this conceptual model?

Conceptual Model v Have formed a conceptual model of relationships –When traffic is light, take the most direct route –Driving on freeways is faster in low congestion conditions –When traffic is heavy, the freeway backs up –In high traffic conditions, take secondary roads. –Even if the distance is farther, the time will be less

Conceptual Model Definitions v What objects in the system are important v What are the relationships in terms of cause - condition - effect? v How do they vary? –In qualitative terms - direct or indirect; higher or lower; –In quantitative terms - additive; multiplicative; with a particular formula relationship

Visualization v As we try to build models, graphical tools can help us to see patterns and relationships v Kinds of patterns to look for depend on the nature of the system v Spatial systems - patterns in the form of map distributions; locational v Aspatial systems - mathematical relationships

Tabular Data Hard to Interpret

Spatial Cause and Effect

Deriving Mathematical Relationships v Can use simple formulations –Curve fitting –Simple statistical models - linear regression or correlation v Can draw on models produced by others v Adjust the approach relative to capabilities of students