Multilevel modelling is a data analysis method that is frequently used to investigate hierarchal data structures in educational, behavioural, health, and social sciences disciplines. Multilevel data analysis exploits data structures that cannot be adequately investigated using single-level analytic methods such as multiple regression, path analysis, and structural modelling. This text offers a comprehensive treatment of multilevel models for univariate and multivariate outcomes. It explores their similarities and differences and demonstrates why one model may be more appropriate than another, given the research objectives.
New to this edition:
An expanded focus on the nature of different types of multilevel data structures (e.g., cross-sectional, longitudinal, cross-classified, etc.) for addressing specific research goals;
Varied modelling methods for examining longitudinal data including random-effect and fixed-effect approaches;
Expanded coverage illustrating different model-building sequences and how to use results to identify possible model improvements;
An expanded set of applied examples used throughout the text;
Use of four different software packages (i.e., Mplus, R, SPSS, Stata), with selected examples of model-building input files included in the chapter appendices and a more complete set of files available online.
This is an ideal text for graduate courses on multilevel, longitudinal, latent variable modelling, multivariate statistics, or advanced quantitative techniques taught in psychology, business, education, health, and sociology. Recommended prerequisites are introductory univariate and multivariate statistics.

lgli/An Introduction to Multilevel Modeling Techniques.pdf

lgrsnf/An Introduction to Multilevel Modeling Techniques.pdf

zlib/Mathematics/Ronald H. Heck, Scott L. Thomas/An Introduction to Multilevel Modeling Techniques: MLM and SEM Approaches_5524766.pdf

Heck, Ronald H., Thomas, Scott L.

Taylor & Francis Ltd

Psychology Press Ltd

CRC Press

Quantitative methodology series, Fourth edition, New York, NY, 2020

Taylor & Francis (Unlimited), New York, NY, 2020

United Kingdom and Ireland, United Kingdom

4, 2020-04-07

lg2525229

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Cover
Half Title
Series Information
Title Page
Copyright Page
Table of contents
Acknowledgments
Preface
1 Introduction
Providing a Conceptual Overview
Contrasting Linear Models
Univariate Analysis
Multiple Regression
Analysis of Variance
Multivariate Analysis
Multivariate Analysis of Variance
Structural Equation Modeling
Multilevel Data Structures
Multilevel Multivariate Model
Multilevel Structural Model
Summary
Appendix
References
2 Getting Started with Multilevel Analysis
Introduction
The Big Picture
From Single-level to Multilevel Analysis
Summarizing Some Differences between Single-level and Multilevel Analyses
Developing a General Multilevel Modeling Strategy
Step 1: Partitioning the Variance in an Outcome
Step 2: Adding Level-1 Predictors to Explain Variability in Intercepts
Step 3: Adding Level-2 Predictors to Explain Variability in Intercepts
Step 4: Examining Possible Variation in Level-1 Slopes
Step 5: Adding Predictors to Explain Variation in Slopes
Specifying the Basic Two-level Model with Path Diagrams
Model Estimation
Maximum Likelihood Estimation
Model Convergence and Fit
Considerations for ML Estimation
An ML Illustration
Bayesian Estimation
Bayesian and ML Estimation with a Limited Number of Groups
Summary
Appendix
References
3 Multilevel Regression Models
Introduction
Building a Model to Explain Employee Morale
Model 1: One-way ANOVA or Null Model
Model 2: Random-Intercept with Level-1 Predictors
Model 3: Specifying a Level-1 Random Slope
Model 4: Explaining Variation in the Level-2 Intercept and Slope
Model 4 Output
Examining Residuals
Centering Predictors
Centering Predictors in Models with Random Slopes
Summary
Appendix
Notes
References
4 Extending the Two-level Regression Model
Introduction
Three-level Univariate Model
Developing a Three-level Univariate Model
Research Questions
Data
Model 1: Null (No Predictors) Model
Model 2: Defining Predictors at Level 1
Model 3: Defining Predictors at Level 2
Model 4: Examining an Interaction at Level 2
Model 5: Examining a Randomly Varying Slope at Level 3
Model 6: Adding Level-3 Predictors
Accounting for Variance
Cross-classified Data Structures
Students Cross-classified in High Schools and Postsecondary Institutions
Research Questions
Model 1: Developing a Null Model
Model 2: Adding Within-cell (Level-1) Predictors
Model 3: Adding Between-cell Predictors
Model 4: Adding a Randomly Varying Level-1 Slope
Model 5: Explaining Variability in Random Slopes
Summary
Appendix
Note
References
5 Methods for Examining Individual and Organizational Change
Introduction
Analyzing Longitudinal Data
Repeated Measures ANOVA
Growth Modeling and Other Approaches
Random-coefficients Growth Modeling
Defining the Level-1 Model
Defining the Level-2 Model
Extending the Model to Examine Changes Between Groups
Examining Changes in Students’ Math Scores
Model 1: Unconditional Means Model
Model 2: Unconditional Growth Model
Model 3: Unconditional Growth Model with Random Time Parameter
Investigating Subsets of Individuals’ Trajectories
Model 4: Adding a Quadratic Polynomial Term
Model 5: Adding a Between-subjects Predictor
Model 6: Deciding on the Level-1 Covariance Structure
Building a Two-level Growth Model Using Age
Model 1: Unconditional Growth Model with Random Age Variable
Model 2: Final Growth Model with Between-subjects Predictor
Examining Changes in Institutions’ Graduation Rates
Model 1: Unconditional Means Model
Model 2: Unconditional Growth Model with Random Time Slope
Model 3: Adding a Time-varying Covariate
Model 4: Examining Whether Instructional Support Influences Growth in Graduation
Model 5: Testing a Random Effect for Instructional Support
Model 6: Adding Between-institution Covariates
Developing Piecewise Growth Models
Examining Student Growth in Literacy
Changes Due to a Policy
Fixed-effects Regression Models
Graduation Growth in One Higher Education System
Summary
Appendix
Notes
References
6 Multilevel Models with Categorical Variables
Introduction
Estimating the Models
Specifying Models for Binary, Ordinal, and Nominal Outcomes
Binary Outcome
Logit Link Function
Probit Link Function
Estimating the Intraclass Correlation
Ordinal Logit Outcome
Ordinal Probit Outcome
Mplus Latent Response Formulation
Unordered Categorical (Nominal) Outcome
Explaining Student Persistence
Binary Outcome
Null Model
Ordinal Outcome
Estimating Probabilities from Logit and Probit Coefficients
Dichotomous Outcome: Adding Level-1 and Level-2 Predictors
Ordinal Outcomes: Adding Level-1 and Level-2 Predictors
Examining a Cross-level Interaction with Continuous by Categorical Predictors
Examining a Cross-level Interaction with Two Continuous Variables
Count Data
Building a Level-1 and Level-2 Model
Summary
Appendix
Note
References
7 Multilevel Structural Equation Models
Multilevel Models with Latent Variables
Multilevel Measurement Models
Multilevel Factor Variance Components
Types of Multilevel Factors
Model 1: Individual-level Factor
Model 2: Within-cluster Factor
Model 3: Shared Cluster-level Factor
Model 4: Configural Factor Structure
Model 5: Shared and Configural Factors
Estimating MCFA Models
Developing a Two-level Model
Model 1 and Model 2 Results
Model 3 and Model 4 Results
Extending the CFA Model to Three Levels
Model 5: Defining a Configural Factor Model at Levels 1, 2, and 3
Model 6: Restricting Errors to Zero at Level 2
Multilevel CFA with Ordinal Observed Indicators
Developing a CFA Model
Multilevel Models with Latent Variables and Covariates
Model 1: Specifying a Two-level Latent Factor Model with Covariates
Model 2: Specifying a Random Level-1 Slope
Model 3: Adding a Latent Factor Between Groups
Model 4: Testing an Indirect (or Mediating) Effect
Summary
Appendix
Notes
References
8 Multilevel Latent Growth and Mixture Models
Introduction
Latent Growth Models
Intercept and Slope (IS) and Level and Shape (LS) Models
Defining the Latent Growth Model
Measurement Model
Structural Model
Multilevel Analysis of Growth
Examining Variables that Influence Student Growth in Science
Piecewise Latent Growth Model
Latent Variable Mixture Modeling
Defining Latent Profiles and Classes
An Example Latent Profile Analysis
Two-level Models
Examining Heterogeneity in Intercepts
Investigating Latent Classes for Random Slopes at Level 2
Alternative Model Specification
Growth Mixture Models
Examining Latent Classes in Students’ Growth in Science
Two-level GMM
Summary
Appendix
Notes
References
9 Data Considerations in Examining Multilevel Models
Complex Samples, Design Effects, and Sample Weights
An Example Using Multilevel Weights
Parameter Bias and Statistical Power
Parameter Bias
Power
An Example
Anticipated Effect Size and Power
Mplus Monte Carlo Study
Design Complexity
Missing Data
Missing Data at Level 2
Imputed Data Sets
Concluding Thoughts
Appendix
References
Index

2020-05-21