Course notes for HDFS 523
1
About This Book
1.1
Why this book?
1.2
Code Folding
1.3
Acknowledgements
2
Data Cleaning
2.1
Example Data
2.2
Reading in Repeated Measures Data
2.3
Familiarize Yourself with the Data
2.4
Look for Duplicated IDs
2.5
Using
table()
to Spot Irregularities
2.6
Missing Data
2.6.1
Generating Example Data
2.6.2
Recoding Values with
NA
2.6.3
Missing Data Visualization
2.7
Exporting Data
2.8
Reshaping Repeated Measures Data
2.8.1
Reshape Wide to Long
2.8.2
Reshape Long to Wide
3
Describing Longitudinal Data
3.1
Example Data
3.2
Describing Means and Variances
3.2.1
Verbal Ability (All Persons and Occasions)
3.2.2
Verbal Ability (Across Time)
3.3
Describing Covariances
3.4
Individual-Level Descriptives
3.5
References
4
Matrix Algebra
4.1
Types of matrices
4.1.1
Square
4.1.2
Symmetric
4.1.3
Diagonal
4.1.4
Identity
4.2
Operations on Matrices
4.2.1
Matrix Transpose
4.2.2
Matrix Trace
4.2.3
Addition
4.2.4
Subtraction
4.2.5
Matrix Multiplication
4.2.6
Matrix Division
4.3
References
5
Ordinary Least Squares
5.1
Linear Regression Model
5.2
Ordinary Least Squares (OLS)
5.3
Assumptions of OLS
5.3.1
Assumption 1.
\(\mathbb{E}(\epsilon_{i}) = 0\)
5.3.2
Assumption 2. Homoscedasticity
5.3.3
3.
\(\mathbb{E}(\epsilon_{i}\epsilon_{j}) = 0\)
5.3.4
4. No Perfect Collinearity
5.3.5
5.
\(\mathbb{C}(\epsilon_{i},x_{ki}) = 0\)
5.4
Properties of the OLS Estimator
5.4.1
1. Consistentcy of
\(\boldsymbol{{\beta}}\)
5.4.2
2. Asymptotic Normality
5.4.3
Variance of
\(\hat{\beta}\)
5.5
Failure to Meet Assumptions
5.5.1
Failure of Assumption 1.
5.5.2
Failure of Assumption 2 or 3.
5.5.3
Failure of Assumption 5.
5.6
Regression and Matrix Notation
5.6.1
An Intercept-Only Model
5.6.2
Intercept-Only Model in Matrix Form
5.6.3
Simple Regression in Matrix Form
5.6.4
Multiple Regression in Matrix Form
5.7
Solving the Regression Equation
5.7.1
Matrix Multiplication and Transpose
5.7.2
Matrix Inverse
5.8
The Linear Probability Model
5.8.1
Advantages of the LPM
5.8.2
Disadvantages of the LPM
6
Statistical Control
6.1
Statistical Control
6.2
Directed Acyclic Graphs (DAGs)
6.2.1
Introduction to DAGs
6.2.2
Introduction to DAGs: Paths
6.2.3
Introduction to DAGs: Chains
6.2.4
Introduction to DAGs: Descendants and Ancestors
6.2.5
Introduction to DAGs: Forks
6.2.6
Introduction to DAGs: Inverted Forks
6.2.7
Introduction to DAGs: Acyclicity
6.3
Statistical Control Done Right
6.3.1
Building a DAG
6.3.2
Building a DAG: Back-Door Paths
6.4
Statistical Control Gone Wrong
6.4.1
Collider Bias
6.4.2
Conditioning on a Collider
6.4.3
Avoiding Collider Bias
6.4.4
Variations on Collider Bias: Nonresponse Bias
6.4.5
Controlling for Mediators
7
Linear Regression
7.1
Example Data
7.2
Intercept-Only Model
7.2.1
Intercept-Only Equation
7.2.2
Intercept-Only Model in R
7.2.3
Intercept as Mean of Outcome
7.2.4
Intercept-Only Model
\(R^2\)
7.3
Simple Linear Regression
7.3.1
Regression Equation and Model Fitting
7.3.2
Path Diagram
7.3.3
Interpreting Model Parameters
7.3.4
Plotting Regression Line
7.4
Mean Centering Predictors
7.4.1
Interpreting Model Parameters
7.4.2
Plotting Regression Line
7.5
Multiple Linear Regression
7.5.1
Regression Equation
7.5.2
Fit Model in R
7.5.3
Path Diagram
7.5.4
A Note on Interpretation
7.6
Categorical Variable Interaction
7.6.1
Interaction as Moderation
7.6.2
Moderation by Categorical Variable
7.6.3
Interpretation
7.6.4
Fit Regression Model in R
7.6.5
Path Diagram
8
Logistic Regression
8.1
Categorical Data in the Social Sciences
8.1.1
Examples of Categorical Data
8.2
Introduction to GLMs
8.2.1
Linear Regression as GLM
8.2.2
Logistic Regression as GLM
8.2.3
Poisson Regression as GLM
8.2.4
Additional Remarks
8.3
Binary Logistic Regression
8.3.1
Overcoming LPM
8.3.2
Model
8.4
Example Data
8.4.1
Variables
8.5
Intercept-Only Model
8.5.1
Intercept-Only Model in R
8.5.2
Interpretation
8.6
Single Predictor Model
8.6.1
Overdispersion
8.6.2
Coefficients
8.7
Marginal Effects
8.7.1
A Definition of Marginal Effects
8.7.2
A Few Observations
8.7.3
Types of Marginal Effects
8.7.4
Example Model
8.7.5
Marginal Effects at Representative Values (MER)
9
Poisson Regression
9.1
Poisson Regression
9.1.1
Review of GLM
9.1.2
Poisson Regression as GLM
9.2
Poisson Distribution
9.3
Notes on Interpretation
9.3.1
One Predictor Model
9.3.2
Similarity to Logistic Regression
9.3.3
Percent Change
9.4
Example Data
9.4.1
Dependent variable
9.4.2
Explanatory Variables
9.5
Single Predictor Model
9.5.1
Read in Data
9.5.2
Single Predictor Model in GLM
9.5.3
Deviance and Goodness of Fit
9.5.4
Overdispersion?
9.5.5
Interpretation of Single Predictor Model
9.6
Multiple Predictor Model
9.7
Revisisting Overdispersion
9.7.1
Quassi-Poisson Family
9.7.2
Marginal Effects Examples
9.7.3
References
10
Marginal Effects
10.1
A Definition of Marginal Effects
10.2
Ferraro et al. (2016)
10.3
Quasi-Poisson Regression Model
10.4
marginaleffects: Predictions
10.5
References
11
Two-Occassion change
11.1
Introduction
11.1.1
A Thought Experiment
11.1.2
Equivalent Models in Psychology
11.1.3
Examples of Equivalent Models
11.2
Example Data I
11.3
Residualized Change
11.4
Raw Change
11.5
Autoregressive Models
11.5.1
Autoregressive Residuals
11.5.2
Autoregressive Model in R
11.6
Difference Score Model
11.6.1
Calculating Difference Scores
11.6.2
Comparison to Residualized Change
11.6.3
A Difference Score Regression Model
11.7
Critique of Residualized Change
11.8
Critique of Difference Scores
11.8.1
Alternative Interpretation
11.9
Comparing Models
11.10
Lord’s Paradox
11.11
Example Data II
11.11.1
Generate Some Data According to
(Castro-Schilo and Grimm 2018)
11.11.2
Plot Data
11.11.3
Fit Residualized Change Model
11.11.4
Fit Difference Score Model
11.12
Example Data III
11.12.1
Generate Some Data According to
(Castro-Schilo and Grimm 2018)
Example B
11.12.2
Plot Data
11.12.3
Fit Residualized Change Model
11.12.4
Fit Difference Score Model
11.13
Closing Thoughts
11.14
References
Published with bookdown
HDFS 523: Strategies for Data Analysis in Developmental Research
10.5
References