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STRUCTURAL EQUATION MODELING AND META-ANALYSIS: A MARRIAGE MADE IN ...

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### STRUCTURAL EQUATION MODELING AND META-ANALYSIS:A MARRIAGE MADE IN ...

Ronald S. Landis

Illinois Institute of Technology

1+1=??

- Peanut Butter & Chocolate
- Food & Wine
- Movies
- LeBron James & Dwayne Wade
- The Whole is More, Equal to, or Less than the Sum of Its Parts

Plan for Today

- Meta-Analysis (MA) FAQ
- Structural Equation Modeling (SEM) FAQ
- MASEM
- Research Questions & Focus
- Steps/Decisions/Frustrations
- Odds & Ends

MA FAQ

- Research Questions
- Summarize available (published & unpublished) evidence
- Estimate degree of relation between variables
- Identify conditions in which effect differs

MA FAQ

- Foundational Issues & Pragmatic Concerns
- Starting with a clear purpose
- Why not just collect and code everything?
- “HARK”ing
- Nature of available evidence
- Samples, research designs, measures
- When is there enough information?
- k’s and n’s
- Adequate construct development
- What am I looking for and how do I know if I have found it?
- File Drawers
- What if I’m missing something?

SEM FAQ

- Research Questions
- To what degree are a set of indicators associated with a given set of latent variables (CFA)?
- Are hypothesized causal relations between variables consistent with collected data (PA/Full SEM)?
- Are there systematic patterns of change across time (LCM)?

All require a priori specification of a particular model (or set of models)

SEM FAQ

- Foundational Issues & Pragmatic Concerns
- Starting with a clear purpose
- Why not just collect some data and start testing models?
- “HARK”ing
- Nature of available evidence
- Samples, research designs, measures
- When is there enough information?
- n’s and identification
- Adequate construct development
- What am I looking for and how do I know if I have found it?
- Everything relevant is included
- What if I have omitted some important variables?

MASEM

- Possible Combinations
- SEM used for MA (Cheung, 2008)
- MA as input for SEM [TODAY]
- Technical/Practical Focus
- What are the underlying mathematical/statistical elements?
- How do I undertake these analyses in my own work? [TODAY]
- Primary Questions
- Can I Integrate SEM and MA?
- YES
- How Do I Integrate SEM and MA?
- HOPEFULLY A CLEARER UNDERSTANDING
- Should I Integrate SEM and MA?
- THE $64,000 QUESTION – IT DEPENDS

General Steps Proposed by Viswesvaran & Ones (1995)

- ID Core Constructs and Relations
- ID Measures Used to Assess Each Construct
- Obtain Relevant Studies
- Conduct Meta-Analysis
- Test Measurement Model
- Estimate Construct Correlations
- Apply SEM to Test Specified Relations

Two-Stage Structural Equation Modeling (TSSEM)Proposed by Cheung & Chan (2005)

STEP 1

- Test for Homogeneity of Correlations/Covariances
- Using multiple groups CFA
- Calculate Pooled Correlation/Covariance Matrix
- Create Asymptotic Covariance Matrix

STEP 2

- Apply SEM to Test Specified Relations

BENEFIT

- Accounts for second order sampling error, leading to more accurate chi-square and fit indices

General Approach – Model Testing

- Confirmatory Factor Analysis
- Same measures/indicators across studies
- Covariances
- Path/Structural Models
- Different measures/indicators across studies
- Correlations

Logic

- First Step
- Test of homogeneity
- Build input matrix
- Second Step
- Model testing

An Example –Earnest, Allen, & Landis (2011)

- Student milestone project
- Interest in Realistic Job Previews (RJPs)
- How do we build on current MA’s?
- Increased number of studies
- Increased number of moderators
- Conducted Meta-Analysis
- Consideration of potential mediators via SEM

Example Matrix

Construct the correlation matrix

Issues in Constructing the Correlation Matrix

- What about blank cells?
- Listwise deletion?
- Previous meta-analyses
- Studies included in current meta-analysis
- Meta-analytic values from ‘outside’ studies
- Different sample sizes in cells
- Which one do we use?
- Illogical values/npd matrices
- What if my matrix can’t occur?
- Presence of moderators
- What do I do if I have heterogeneity in the correlation matrices?
- Correlations instead of covariances
- Can I still run SEM?

Odds & Ends

- But…
- Causality and MASEM make strange bedfellows
- Yes, but this is not unique to MASEM
- Lack of comfort with combining r’s from different studies into SEM analysis
- Why?
- What if latent variables differ across primary studies
- Problem with MA, not MASEM

A Few References

- Burke, M.J. & Landis, R.S. (2003). Methodological and conceptual challenges in conducting and interpreting meta-analyses. In K.R. Murphy (Ed.), Validity Generalization: A Critical Review (pp. 287-309). Mahwah, NJ: Erlbaum.
- Cheung, M.W.L. (2009). TSSEM: A LISREL syntax generator for two-stage structural equation modeling (Version 1.11) [Computer software and manual]. Retrieved from http://courses.nus.edu.sq/course/psycwlm/internet/tssem.zip.
- Cheung, M.W.L. & Chan, W. (2005). Meta-analytic structural equation modeling: A two-stage approach. Psychological Methods, 10, 40-64.
- Cheung, M.W.L. & Chan, W. (2009). A two-stage approach to synthesizing covariance matrices in meta-analytic structural equation modeling. Structural Equation Modeling, 16, 28-53.
- Christian, M. S., Bradley, J.C., Wallace, J.C., & Burke, M.J. (2009). Workplace safety: A meta-analysis of the roles of person and situation factors. Journal of Applied Psychology, 94, 1103-1127.

A Few References

- Colquitt, J. A., LePine, J. A., & Noe, R. A., toward an integrative theory of training motivation: A meta-analytic path analysis of 20 years of research. Journal of Applied Psychology, 85, 678-707.
- Earnest, D.R., Allen, D.G., & Landis, R.S. (2011). A meta-analytic path analysis of the mechanisms linking realistic job previews and turnover. Personnel Psychology, 64, 865-897.
- Klein, H.J., Wesson, M.J., Hollenbeck, J.R., Wright, P.M., & DeShon, R.P. (2001). The assessment of goal commitment: A measurement model meta-analysis. Organizational Behavior and Human Decision Processes, 85, 32-55.
- Robbins, S. B., Oh, I., Le, H., Button, C. (2009). Intervention effects on college performance as mediated by motivational, emotional, and social control factors: integrated meta-analytic path analyses. Journal of Applied Psychology, 94, 1163-1184.
- Viswesvaran, C. & Ones, D.S. (1995). Theory testing: Combining psychometric meta-analysis and structural equations modeling. Personnel Psychology, 48, 865-885.

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