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Sem Paths to Networks Westland

In a sentence

A critical survey of the history, methods, and practical application of structural equation modeling, guiding researchers from the origins of path analysis to the future of network science.

This book provides a comprehensive and critical guide to the world of structural equation modeling (SEM) for researchers and doctoral students. It traces the evolution of path analysis methodologies from their roots in genetics with Sewall Wright, through the divergent developments of the Scandinavian school (PLS-PA, LISREL) and the Chicago school (systems of regression equations). The author demystifies the statistical underpinnings of each approach, highlighting their unique strengths, weaknesses, and the often-misrepresented controversies surrounding them. It offers indispensable practical advice on crucial research design aspects, including data collection, calculating adequate sample size, and the proper treatment of survey data, particularly the pitfalls of Likert scales. By equipping readers with a deep understanding of the assumptions and limitations of these powerful tools, the book aims to prevent common errors and elevate the quality of quantitative research, ultimately showing how the path-based thinking of SEM is merging into the broader, more powerful domain of network analysis.

The four lenses

  • Science
  • Statistics
  • Systems
  • Strategy

The model

This is an implicit meta-model derived from the book's central arguments. It outlines how a researcher's choices regarding methodology, data, and model specification influence the statistical properties of the analysis, which in turn determine the validity and defensibility of the research findings. The model posits that rigorous upfront choices lead to higher quality scientific outcomes.

Research Paradigm Choicedesign lever

The researcher's fundamental choice of research objective, primarily distinguishing between an exploratory/predictive paradigm (e.g., model building, specification search) and a confirmatory/descriptive paradigm (e.g., hypothesis testing, theory confirmation).

SEM Methodology Choicedesign lever

The researcher's selection of a specific SEM statistical method, such as Partial Least Squares Path Analysis (PLS-PA), Covariance-Based SEM (e.g., LISREL, AMOS), or Systems of Regression Equations (e.g., 2SLS, 3SLS).

Data Adequacydesign lever

The extent to which the collected data possesses sufficient information and appropriate characteristics for the intended analysis. Key components include sample size relative to model complexity, and measurement quality (e.g., accounting for information loss from Likert scales).

Model Specification Rigordesign lever

The degree of theoretical and empirical diligence applied to defining the structural model, including strong justification for paths, consideration of alternative models, and avoiding ad-hoc or data-driven specification in confirmatory research.

Statistical Powerpsychological state

The probability that the statistical test employed will correctly reject a false null hypothesis (i.e., avoid a Type II error). It is a function of significance level, effect size, and sample size.

Estimator Biaspsychological state

The degree to which the expected value of the estimated path coefficients diverges from the true population parameters. Certain methods, like PLS-PA with small samples, are prone to higher bias.

Model-Data Congruencepsychological state

The degree of alignment between the theoretically specified model and the empirical structure of the collected data. High congruence is indicated by good fit statistics and validated measurement models.

Validity of Findingsoutcome metric

The extent to which the conclusions of a research study are correct and free from statistical error, particularly Type I (false positive) and Type II (false negative) errors. This is the core measure of research quality.

Defensibility of Conclusionsoutcome metric

The ability of the research findings and the methodology used to generate them to withstand peer scrutiny and be accepted as a credible contribution to knowledge.

How they connect

  • research paradigm choice → influences sem methodology choice
  • data adequacy → predicts statistical power
  • data adequacy − predicts estimator bias
  • sem methodology choice → influences estimator bias
  • model specification rigor → predicts model data congruence
  • statistical power → predicts validity of findings
  • estimator bias − predicts validity of findings
  • model data congruence → predicts validity of findings
  • validity of findings → predicts defensibility of conclusions

A candidate measure

Sem Paths to Networks Westland — derived measurement candidates

Research Paradigm Choice

Binary code (0=exploratory, 1=confirmatory) based on reading the research objectives section of a paper

self-report suitability: none

SEM Methodology Choice

Nominal code for method used (e.g., 1=PLS-PA, 2=CB-SEM, 3=Systems of Regression)

self-report suitability: none

Data Adequacy

Ratio of actual sample size to minimum required sample size; Number of points on Likert scales used; Calculated information loss multiplier based on measurement type

self-report suitability: none

Model Specification Rigor

Count of alternative models tested; Score on a rubric for quality of theoretical justification

self-report suitability: none

Statistical Power

Post-hoc calculation of (1-β) based on reported sample size, alpha, and effect size

self-report suitability: none

Estimator Bias

Categorization of bias risk (low, medium, high) based on method and sample size combination

self-report suitability: none

Model-Data Congruence

Value of RMSEA; Value of CFI/TLI; Value of Cronbach's Alpha; Results of Harman's one-factor test

self-report suitability: none

Validity of Findings

Binary outcome of replication attempts (successful/failed); p-value of key hypothesis tests; Standardized path coefficient (beta) as effect size

self-report suitability: none

Defensibility of Conclusions

Journal Impact Factor or tier; Total number of citations

self-report suitability: none

Run the assessment

The story

The reader A quantitative social science researcher or doctoral student who needs to test complex theoretical models involving unobservable concepts like 'trust' or 'satisfaction'. They want to produce rigorous, defensible, and publishable findings.

External problem

The researcher is confronted with a confusing landscape of SEM methodologies (PLS-PA, LISREL, etc.) and software, each with conflicting claims, arcane assumptions, and inadequate guidance on critical issues like sample size calculation and handling survey data.

Internal problem

They feel uncertain about their methodological choices, anxious that their results might be invalid or rejected by reviewers, and fearful of inadvertently contributing to the proliferation of 'bad science'.

Philosophical problem

It's wrong that powerful statistical tools are often used as 'black boxes' without a deep understanding of their limitations, leading to a crisis of replicability and questionable research findings in the social sciences.

The plan

  1. Understand the historical context and statistical underpinnings of different SEM methods.
  2. Learn the specific strengths and weaknesses of PLS-PA, LISREL, and Systems of Regression to choose the right tool for your research.
  3. Master the principles of calculating adequate sample size and properly handling Likert scale data.
  4. Adopt a rigorous paradigm for model specification, testing, and interpretation.
  5. See how path modeling is evolving into the broader science of network analysis.

Success

  • The researcher confidently designs robust studies, justifies their methodological choices, and produces valid, defensible results.
  • Their work is published in high-impact journals and contributes meaningfully to their field.
  • They are recognized as a methodologically rigorous and thoughtful scholar.

At stake

  • The researcher continues to misuse SEM tools, producing underpowered studies with potentially false or biased results.
  • Their research is rejected or fails to withstand critical scrutiny.
  • They risk damaging their academic reputation and contributing to the body of non-replicable 'bad science'.

Chapter by chapter

  1. ch01An Introduction to Structural Equation Models

    Structural Equation Models (SEM) provide a robust and versatile framework for analyzing complex relationships among unobservable constructs, enhancing the scope of social science research by integrating latent variables into empirical analysis.

    • SEM empowers researchers to analyze relationships among unobservable constructs, significantly advancing social science research capabilities.
    • Understanding latent variables is crucial for building robust models that reflect complex social phenomena.
    • The choice of SEM methodology can impact the depth and validity of social science research, requiring careful consideration of fit statistics.
    • Sample size requirements in SEM are often misrepresented; researchers must adopt a more nuanced approach when planning studies.

  2. ch02p01A Brief History of Structural Equation Models (part 1/2)

    Structural equation modeling (SEM) evolved from early biological studies and statistical methods used to analyze complex genetic relationships, ultimately bridging natural and social sciences through path analysis.

    • Structural equation models emerged from a rich historical context spanning both genetic studies and social science research, reflecting the need for sophisticated analytical tools.
    • Sewall Wright’s path analysis was pivotal in linking genetics with statistical methodology, providing the groundwork for future developments in SEM.
    • The integration of latent variables into social science modeling transformed the ability to analyze abstract constructs, facilitating a deeper understanding of human behaviors.
    • Ongoing debates about the assumptions underlying SEM reveal the complexities of applying these models to real-world data, necessitating a careful consideration of each method’s contextual relevance.

  3. ch02p02A Brief History of Structural Equation Models (part 2/2)

    This chapter delves into the evolution and mathematical underpinnings of structural equation modeling (SEM), revealing how its complexity informs the intersection of statistical techniques and practical application in research.

  4. ch03p01Partial Least Squares Path Analysis (part 1/2)

    This chapter examines Partial Least Squares Path Analysis (PLS-PA), scrutinizing its methodology, practical applications, and the criticisms it faces regarding its statistical foundation and results validity.

  5. ch03p02Partial Least Squares Path Analysis (part 2/2)

    This chapter continues the discussion on Partial Least Squares (PLS) path analysis by detailing advanced estimation techniques, identification conditions, and contrasting PLS with other path analysis methods for robust modeling of latent variables.

  6. ch04p01LISREL and Its Progeny (part 1/2)

    This chapter explores the evolution of path analysis methods, focusing on the development and implications of LISREL software, highlighting the debates within the field regarding its limitations and alternative methodologies.

    • The evolution of LISREL marks a pivotal moment in path analysis, offering greater mathematical rigor but requiring stringent conditions for effective application.
    • Competing methodologies like PLS path analysis and AMOS present viable alternatives, each with unique strengths and weaknesses in modeling latent constructs.
    • Real-world data often does not meet LISREL's assumptions, raising significant concerns about empirical validity and drawing attention to the need for adaptable models.
    • Continuous critique of established practices in path analysis is critical for advancing methodological integrity in social science research.

  7. ch04p02LISREL and Its Progeny (part 2/2)

    This chapter argues that to build reliable structural equation models (SEMs), researchers must align their latent constructs with actual data rather than solely relying on theoretical frameworks, emphasizing the importance of data integrity and analysis methods in avoiding common biases.

  8. ch07, i.e., converges in distribution to a normal distribution with mean zero and variance σ G2 (this is from Schechtman and Yitzhaki (1987) applying methods developed by Hoeffding (1948)).

    This chapter explores the complexities and methodologies of survey and questionnaire data, highlighting the intricacies of designing effective instruments to measure public sentiment accurately.

    • Surveys are foundational to understanding public sentiment but require meticulous design to produce valid results.
    • Questionnaire design should prioritize clarity to ensure respondents understand the questions, reducing misinterpretation.
    • Likert scales, while ubiquitous, carry potential biases if not properly constructed—balanced designs are crucial.
    • The functionality of surveys is dependent not only on questions asked but also on how samples are selected and analyzed.

  9. ch08Research Structure and Paradigms

    This chapter critiques the hypothetico-deductive model of research in light of systemic failures and philosophical inquiries surrounding truth, causality, and model specification, particularly as they impact social sciences.

    • The 'Proteus phenomenon' reflects a painful truth in research: a significant proportion of findings are ultimately non-replicable, threatening the integrity of scientific knowledge.
    • Research incentives often prioritize rapid publication over meaningful validation, undermining the quality of academic contributions.
    • Truth in science is not merely objective; it reflects socially constructed narratives that researchers must navigate with care and ethical consideration.
    • Model specification is a complex yet essential aspect of hypothesis testing; simplifications can lead to misleading conclusions and require thorough validation.

  10. ch09From Paths to Networks: The Evolving Science of Networks

    This chapter explores the evolution of network science through various historical paradigms, highlighting the transition from path-based models to sophisticated network analysis, particularly in genetics and social sciences.

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