Modeling Behavior

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Modeling Behavior

• Psychology 891C

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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

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Modeling

• What is a model?
• Why use mathematical models?
• How to evaluate a model.

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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

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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.

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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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ANOVA
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Models of Theory
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P(Recall)a exp(-bTime)
P(Recall)
Time
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A
A
A
A
B
B
Height
A
B
B
Angle
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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.

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Whats Wrong With Verbal Models?

• Implications can be difficult to derive.

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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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Why Use Mathematical Models?

• To understand the behavior of a complex system.
• Mechanical rat.
• Broadbents 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).

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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.

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Why Use Mathematical Models?

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

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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.

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Why Use Mathematical Models?

• Practical applications

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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).

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Dangers of Modeling

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

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Modeling

• What is a model?
• Why use mathematical models?
• How to evaluate a model.

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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.

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How to Evaluate a Model

• DID THE MODEL HELP US LEARN ANYTHING?
• Human judgment.
• Evaluating assumptions of a model, not its
  implementation.
• Models dont have to be true, just useful.

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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
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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 models description of the observed
  data is achieved in the simplest possible manner.
• Easiest to judge relative to other models.

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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.