Quantitative Methods

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Quantitative Methods

• Random Effects

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Random Effects
What are random effects?
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Random Effects
What are random effects?
Criterion Fixed effects Random effects
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Random Effects
What are random effects?
RepetitionIf the experiment were repeated
Criterion Fixed effects Random effects
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Random Effects
What are random effects?
RepetitionIf the experiment were
repeated Same levels would be used
Criterion Fixed effects Random effects
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Random Effects
What are random effects?
RepetitionIf the experiment were
repeated Same levels would be used Different
levels would be used
Criterion Fixed effects Random effects
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Random Effects
What are random effects?
RepetitionIf the experiment were
repeated Same levels would be used Different
levels would be used
Criterion Fixed effects Random effects
Desired inferenceThe conclusions refer to
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Random Effects
What are random effects?
RepetitionIf the experiment were
repeated Same levels would be used Different
levels would be used
Criterion Fixed effects Random effects
Desired inferenceThe conclusions refer to The
levels used
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Random Effects
What are random effects?
RepetitionIf the experiment were
repeated Same levels would be used Different
levels would be used
Criterion Fixed effects Random effects
Desired inferenceThe conclusions refer to The
levels used A population from which the levels
used are just a (random) sample
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Random Effects
What are random effects?
RepetitionIf the experiment were
repeated Same levels would be used Different
levels would be used
Criterion Fixed effects Random effects
Desired inferenceThe conclusions refer to The
levels used A population from which the levels
used are just a (random) sample
Applying the criteria
Fixed or random?
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Random Effects
What are random effects?
RepetitionIf the experiment were
repeated Same levels would be used Different
levels would be used
Criterion Fixed effects Random effects
Desired inferenceThe conclusions refer to The
levels used A population from which the levels
used are just a (random) sample
Applying the criteria
Fixed or random?
Does one strain of barley grow faster than
another?
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Random Effects
What are random effects?
RepetitionIf the experiment were
repeated Same levels would be used Different
levels would be used
Criterion Fixed effects Random effects
Desired inferenceThe conclusions refer to The
levels used A population from which the levels
used are just a (random) sample
Applying the criteria
Fixed or random?
Does one strain of barley grow faster than
another?
The strain
The barley plant
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Random Effects
What are random effects?
RepetitionIf the experiment were
repeated Same levels would be used Different
levels would be used
Criterion Fixed effects Random effects
Desired inferenceThe conclusions refer to The
levels used A population from which the levels
used are just a (random) sample
Applying the criteria
Fixed or random?
Does one strain of barley grow faster than
another?
The strain
The barley plant
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Random Effects
What are random effects?
RepetitionIf the experiment were
repeated Same levels would be used Different
levels would be used
Criterion Fixed effects Random effects
Desired inferenceThe conclusions refer to The
levels used A population from which the levels
used are just a (random) sample
Applying the criteria
Fixed or random?
Does one strain of barley grow faster than
another?
The strain
The barley plant
Do guppies swim faster at higher temperatures?
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Random Effects
What are random effects?
RepetitionIf the experiment were
repeated Same levels would be used Different
levels would be used
Criterion Fixed effects Random effects
Desired inferenceThe conclusions refer to The
levels used A population from which the levels
used are just a (random) sample
Applying the criteria
Fixed or random?
Does one strain of barley grow faster than
another?
The strain
The barley plant
Do guppies swim faster at higher temperatures?
Temperature
Guppy
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Random Effects
What are random effects?
RepetitionIf the experiment were
repeated Same levels would be used Different
levels would be used
Criterion Fixed effects Random effects
Desired inferenceThe conclusions refer to The
levels used A population from which the levels
used are just a (random) sample
Applying the criteria
Fixed or random?
Does one strain of barley grow faster than
another?
The strain
The barley plant
Do guppies swim faster at higher temperatures?
Temperature
Guppy
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Random Effects
What are random effects?
RepetitionIf the experiment were
repeated Same levels would be used Different
levels would be used
Criterion Fixed effects Random effects
Desired inferenceThe conclusions refer to The
levels used A population from which the levels
used are just a (random) sample
Applying the criteria
Fixed or random?
Does one strain of barley grow faster than
another?
The strain
The barley plant
Do guppies swim faster at higher temperatures?
Temperature
Guppy
Do starlings learn faster with higher rewards?
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Random Effects
What are random effects?
RepetitionIf the experiment were
repeated Same levels would be used Different
levels would be used
Criterion Fixed effects Random effects
Desired inferenceThe conclusions refer to The
levels used A population from which the levels
used are just a (random) sample
Applying the criteria
Fixed or random?
Does one strain of barley grow faster than
another?
The strain
The barley plant
Do guppies swim faster at higher temperatures?
Temperature
Guppy
Do starlings learn faster with higher rewards?
Starling
Reward
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Random Effects
What are random effects?
RepetitionIf the experiment were
repeated Same levels would be used Different
levels would be used
Criterion Fixed effects Random effects
Desired inferenceThe conclusions refer to The
levels used A population from which the levels
used are just a (random) sample
Applying the criteria
Fixed or random?
Does one strain of barley grow faster than
another?
The strain
The barley plant
Do guppies swim faster at higher temperatures?
Temperature
Guppy
Do starlings learn faster with higher rewards?
Starling
Reward
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Random Effects
What are random effects?
RepetitionIf the experiment were
repeated Same levels would be used Different
levels would be used
Criterion Fixed effects Random effects
Desired inferenceThe conclusions refer to The
levels used A population from which the levels
used are just a (random) sample
Applying the criteria
Fixed or random?
Does one strain of barley grow faster than
another?
The strain
The barley plant
Do guppies swim faster at higher temperatures?
Temperature
Guppy
Do starlings learn faster with higher rewards?
Starling
Reward
The problem is a random effect produces an extra
random term
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Random Effects
What are random effects?
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Random Effects
Why do random effects matter?
1. More than one random term 2. While the error
is different for each datapoint, a random effect
is not
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Random Effects
New concepts components of variance
Example 10 starlings, each set 5 different
foraging tasks and the time to learn was
measured. Model formula is LEARNTIME
STARLINGS There are 50 random error terms, but
10 random starling terms. The EMS measures the
size of the error variation. We also want to
measure the size of the starling variation
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Random Effects
New concepts expected mean square
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Random Effects
New concepts expected mean square
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Random Effects
New concepts nesting
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Random Effects
New concepts appropriate denominators
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Random Effects
New concepts appropriate denominators
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Random Effects
A one-way ANOVA with a random factor
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Random Effects
A one-way ANOVA with a random factor
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Random Effects
A one-way ANOVA with a random factor
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Random Effects
A one-way ANOVA with a random factor
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Random Effects
A one-way ANOVA with a random factor
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Random Effects
A one-way ANOVA with a random factor
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Random Effects
A one-way ANOVA with a random factor
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Random Effects
A one-way ANOVA with a random factor
(2) 4(1) 0.0107640.02072 0.09362
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Random Effects
A one-way ANOVA with a random factor
(2) 4(1) 0.0107640.02072 0.09362
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Random Effects
A one-way ANOVA with a random factor
(2) 4(1) 0.0107640.02072 0.09362
LEAF MS 0.09362
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Random Effects
A two-level nested ANOVA
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Random Effects
A two-level nested ANOVA
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Random Effects
A two-level nested ANOVA
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Random Effects
A two-level nested ANOVA
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Random Effects
A two-level nested ANOVA
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Random Effects
A two-level nested ANOVA
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Random Effects
A two-level nested ANOVA
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Random Effects
Mixing random and fixed effects
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Random Effects
Mixing random and fixed effects
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Random Effects
Mixing random and fixed effects
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Random Effects
Mixing random and fixed effects
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Random Effects
Last words

• Nested and crossed.
• Fixed or random? is a vital question. Tell by
  desired inference and repetition.
• Be prepared for the complications...

Categorical Data Read Chapter 13