Modeling Behavior

Psychology 891C

Agenda

• Syllabus• Introductions• Modeling

– What is a model?– Why use

mathematical models?

– How to evaluate a model.

• Octave– Installation– Tutorial – Assignment 1

• Readings for week 2– Go over math– Choose a presenter

• Auditors

Modeling

• What is a model?

• Why use mathematical models?

• How to evaluate a model.

Braking Distance

• d = V2/(2g(f + G))

• Where:– d = Braking Distance (ft)– g = Acceleration due to gravity (32.2 ft/sec2)– G = Roadway grade as a percentage; for 2% use

0.02– V = Initial vehicle speed (ft/sec)– f = Coefficient of friction between the tires and the

roadway

A Blue Beetle

• Step on the gas pedal and the vehicle accelerates.

• Step on the brake and the vehicle decelerates.

• Turn the wheel left/right the front wheel turn left/right.

A Model is an Analogy that

• represents certain aspects of complex systems.

• in some way resemble the thing being modeled.

• is made up of a set of assumptions about the thing being modeled together with implications drawn from those assumptions.

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As the plane angle rate increases, the plane angle increases, which in turn increases the pitch depth and therefore pitch and depth increases.

All of this is shown in the display which the planesman can use to control plane angle rate…

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∫∫∫ ⊕ χ ⋅ ′ ′ ˆ ξ

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ANOVA

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Models of Theory

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(Rec

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Time

P(Recall)=a exp(-b*Time)

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Angle

A Model is Not

• any equation.

• a theory.

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Modeling

• What is a model?

• Why use mathematical models?

• How to evaluate a model.

What’s Wrong With Verbal Models?

• Implications can be difficult to derive.

Dissonance Theory Example"The amount of dissonance

experienced by the person depends on the ratio of dissonant to consonant elements, where each element is weighted according to its importance to him... In sum, the magnitude of the dissonance experienced depends directly on the number and/or importance of consonant cognitions."

"Many derivations follow from the above formulation. For example ..., with the relative attractiveness of the two alternatives held constant, the more attractive they both are, the greater is the magnitude of the dissonance.”

Brem & Cohen, 1963

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Dissonance =Smoking- + Quit+

Smoking+ + Quit -

Total_Attractiveness = (Smoking+ + Quit+) - (Smoking- + Quit -)

Relative_Attractiveness = (Smoking+ + Quit -) − (Smoking- + Quit+)

so, (Smoking- + Quit+) = (Smoking+ + Quit -) - Relative_Attractiveness

so, Dissonance = 1 - Relative_Attractiveness

Smoking+ + Quit−

1) Increase Smoking+ & Quit+ by same amount.

Dissonance increases.

2) Decrease Smoking- & Quit - by same amount.

Dissonance decreases.

3) Increase Smoking+ & decrease Quit - by same amount.

Dissonance Stays the same.

Why Use Mathematical Models?

• To understand the behavior of a complex system.– Mechanical rat.– Broadbent’s model

of human attention.

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Why Use Mathematical Models?

• Must be precise– Cognitive dissonance example.– Check on compelling ideas

• Prototype enhancement effect.• Serial vs. parallel systems.• "While adultery rates for men and women may be

equalizing, men still have more partners than women do, and they are more likely to have one-night stands" (Leahey & Harris, 1985 and Hintzman, p 41).

Why Use Mathematical Models?

• More readily falsifiable– Better able to get rid of inadequate

models.– “All things that are stored in memory can

be retrieved; we never forget anything; apparent forgetting is really due to a lack of storage.”

Why Use Mathematical Models?

• Can derive implications– Especially unexpected implications.– Can be used to design new experiments.– Example: Prototype enhancement effect.

Why Use Mathematical Models?

• Helps avoid reasoning errors– Working memory capacity.– Confusion of similar concepts and

percepts.– Mapping of meanings to words is not 1-to-

1.– Humans are biased to accept familiar

ideas.– …

Why Use Mathematical Models?

• Practical applications

Why Use Mathematical Models?

• "One of the reasons why scientists and engineers spend so much time with [models] is that they are fun. They are fun to design, fun to build, and fun to look at" (Chapanis, p. 125).

• Scientists model "simply because it is the thing to do" (Chapanis, p 114).

Dangers of Modeling

• Poor communication.• Models can magnify the confirmation bias.• Models invite overgeneralization.• Models may constrain our research.• A->B, B, A?• Most psychological data is ordinal.• Model building takes away time from more

productive activities.

Modeling

• What is a model?

• Why use mathematical models?

• How to evaluate a model.

How Models are Used

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How NOT to Evaluate a Model

• Trying to prove the model correct.

• The sophistication of the math.

• Solely relying on the accuracy of the model.

How to Evaluate a Model

• DID THE MODEL HELP US LEARN ANYTHING?– Human judgment.– Evaluating assumptions of a model, not its

implementation.– Models don’t have to be true, just useful.

How to Evaluate a Model

• Goodness of fit– How well do

the model predictions match the data?

Trial Obs. Pr(E1)

Pred. Pr(E1)

1 .36 .37

2 .50 .51

3 .62 .63

4 .79 .70

5 .66 .66

How to Evaluate a Model

• Interpretability– How plausible and explicit are the

psychological assumptions of the model?

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How to Evaluate a Model

• Explanatory adequacy– One model or model class can handle

easily.– Another model class can only handle with

ad hoc assumptions.

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How to Evaluate a Model

• Simplicity– Whether the model’s description of the

observed data is achieved in the simplest possible manner.

– Easiest to judge relative to other models.

How to Evaluate a Model

• Falsifiability– Whether there exists potential observations

that are incompatible with the model.

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How to Evaluate a Model

• Faithfulness– Assumptions, not instantiation.

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How to Evaluate a Model

• Generalizability– How well does the

model generalize across different stimulus sets and configurations, different tasks, or response types and measures.

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