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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.

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

Ronald S. Landis

Illinois Institute of Technology

• Peanut Butter & Chocolate

• Food & Wine

• Movies

• LeBron James & Dwayne Wade

• The Whole is More, Equal to, or Less than the Sum of Its Parts

• Meta-Analysis (MA) FAQ

• Structural Equation Modeling (SEM) FAQ

• MASEM

• Research Questions & Focus

• Steps/Decisions/Frustrations

• Odds & Ends

• Research Questions

• Summarize available (published & unpublished) evidence

• Estimate degree of relation between variables

• Identify conditions in which effect differs

• 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

• What am I looking for and how do I know if I have found it?

• File Drawers

• What if I’m missing something?

• 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)

• 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

• 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?

• 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

• 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

• Confirmatory Factor Analysis

• Same measures/indicators across studies

• Covariances

• Path/Structural Models

• Different measures/indicators across studies

• Correlations

• 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

Construct the correlation matrix

• 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?

• Can I still run SEM?

• 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

• 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.

• 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.