What is a hierarchical model? Richard Erickson Quantitative - - PowerPoint PPT Presentation

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what is a hierarchical model

What is a hierarchical model? Richard Erickson Quantitative - - PowerPoint PPT Presentation

Sep 19, 2023 450 likes •721 views

DataCamp Hierarchical and Mixed Effects Models in R HIERARCHICAL AND MIXED EFFECTS MODELS IN R What is a hierarchical model? Richard Erickson Quantitative Ecologist DataCamp Hierarchical and Mixed Effects Models in R Why do we use a

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DataCamp Hierarchical and Mixed Effects Models in R

What is a hierarchical model?

HIERARCHICAL AND MIXED EFFECTS MODELS IN R

Richard Erickson

Quantitative Ecologist

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DataCamp Hierarchical and Mixed Effects Models in R

Why do we use a hierarchical model?

Data nested within itself Pool information across small sample sizes Repeated observations across groups or individuals

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DataCamp Hierarchical and Mixed Effects Models in R

Other names for hierarchical models

Hierarchical models: Nested models, Multi-level models Regression framework: "Pool" information, "Random-effect" versus a "fixed- effect", "Mixed-effect" (linear mixed-effect model; LMM), Linear mixed-effect regression (lmer) Repeated sampling: "Repeated-measures", "Paired-tests"

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DataCamp Hierarchical and Mixed Effects Models in R

School test scores

Meta-data: Gain in math scores for individual students from kindergarten to 1st grade Part of a national-level assessment in US Subset of data from West, Welch, and Galecki Student-level variables: Student ID: childid Math test-score gain: mathgain Math kindergarten score: mathdind Student's sex: sex Student's minority status: minority

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DataCamp Hierarchical and Mixed Effects Models in R

School test scores

Classroom-level variables: Classroom id: classid Teacher's math training: mathprep Teacher's math test knowledge test score: mathknow Teacher's years teaching: yearstea School-level variables: School ID: schoolid School's household poverty level:

housepov

School's socioeconomic status: ses

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DataCamp Hierarchical and Mixed Effects Models in R

Let's practice!

HIERARCHICAL AND MIXED EFFECTS MODELS IN R

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DataCamp Hierarchical and Mixed Effects Models in R

Parts of a regression

HIERARCHICAL AND MIXED EFFECTS MODELS IN R

Richard Erickson

Quantitative Ecologist

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DataCamp Hierarchical and Mixed Effects Models in R

An intercept

y = β + ϵ

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DataCamp Hierarchical and Mixed Effects Models in R

Multiple intercepts

y = β + β x + β x + ϵ y = β x + β x + β x + ϵ

2 2 3 3 1 1 2 2 3 3

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DataCamp Hierarchical and Mixed Effects Models in R

Linear models in R

lm( formula, data) lm( y ~ x, data = myData) anova(lm( y ~ x, data = myData))

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DataCamp Hierarchical and Mixed Effects Models in R

A simple linear regression with slopes

y ∼ β + β x + ϵ

1

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DataCamp Hierarchical and Mixed Effects Models in R

Multiple regression

y ∼ β + β x + β x + … + ϵ

1 1 2 2

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DataCamp Hierarchical and Mixed Effects Models in R

Multiple regression caveats

Independence of predictor variables "corrected for..." Simpson's paradox Only linear Interactions may be important

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DataCamp Hierarchical and Mixed Effects Models in R

Multiple regression in R tips

lm( y ~ x -1 ) estimates an intercept for each x

Numeric versus factors Scaling parameters and slopes

lm(y ~ x1 + x2 + x1:x2) can be written as lm(y ~ x1 * x2)

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DataCamp Hierarchical and Mixed Effects Models in R

Refresher of running and plotting a linear regression in R

regModel <- lm( response ~ predictor, data = regDemo) summary( regModel ) regModel regCoefPlot <- tidy(regModel) ggplot( regDemo, aes(x = predictor, y = response) ) + geom_point() + theme_minimal() + geom_abline( intercept = regCoefPlot$estimate[1], slope = regCoefPlot$estimate[2])

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DataCamp Hierarchical and Mixed Effects Models in R

Let's practice!

HIERARCHICAL AND MIXED EFFECTS MODELS IN R

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DataCamp Hierarchical and Mixed Effects Models in R

Random-effects in regressions

HIERARCHICAL AND MIXED EFFECTS MODELS IN R

Richard Erickson

Quantitative Ecologist

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DataCamp Hierarchical and Mixed Effects Models in R

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Algebraic representation

y ∼ β x + ϵ β ∼ Normal(μ,σ)

i i

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R syntax

library(lme4) lmer( y ~ x + (1|randomGroup), data = myData) lmer( y ~ x + (randomSlope|randomGroup), data = myData)

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DataCamp Hierarchical and Mixed Effects Models in R

Let's practice!

HIERARCHICAL AND MIXED EFFECTS MODELS IN R

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DataCamp Hierarchical and Mixed Effects Models in R

School data

HIERARCHICAL AND MIXED EFFECTS MODELS IN R

Richard Erickson

Quantitative Ecologist

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DataCamp Hierarchical and Mixed Effects Models in R

Data questions

1. Does the sex of a student impact their knowledge gain?
2. Does the teacher's training impact the gain and does the teacher's math

knowledge impact the gain?

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DataCamp Hierarchical and Mixed Effects Models in R

Let's practice!

HIERARCHICAL AND MIXED EFFECTS MODELS IN R