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Midwest Eco 2013 MSEM Presentation

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Midwest Eco 2013 MSEM Presentation

  1. 1. Testing Multilevel Theories Through Multilevel Structural Equation Modeling Christopher R. Beasley Midwest Eco 2013
  2. 2. Digital Copy of Slides crbeasley.info
  3. 3. Structural Equation Modeling Social Desirability Value Congruence Demands- Abilities Interpersonal Similarity Needs- Supplies Satisfaction Commitment OH TenureP-E Fit
  4. 4. Nesting • Dependence – Time – Complex Sampling
  5. 5. Study Design • Random sample by house • Oxford House residents – 95% of houses agreed to assist • nj = 82 – 48% individual response rate • ni = 296
  6. 6. Why Multilevel • Disaggregation of data (Byrne, 2012) – Biased estimates and standard errors • Aggregated data (Byrne, 2012) – Lack of individual variance may exaggerate group effects
  7. 7. MSEM • Extension of Multi-Group SEM – Covariance matrices at within and between level instead of for different groups • Assumptions – General Linear Model assumptions • Linearity • Normality • Homoscedasticity • Independence
  8. 8. MSEM Alternatives • Segregated Approach (Yuan & Bentler, 2007) – More established – Modification indices • Partially Saturated Approach (Ryu & West, 2009) – MLR – Random coefficients – 2-1-1, 2-1-2, 2-2-2, 1-1-2, 1-2-1, 1-1-1 – Better power for level 2 – Greater n at L1, so more influence on model fit statistics (Hox, 2002)
  9. 9. Software Packages • Mplus • LISREL • EQS • GLLAMM
  10. 10. Process (Stapleton, 2013) 1. Consider single-level model 2. Baseline models for w/i & b/t levels while saturating the other level 3. Theoretical w/i model with b/t saturated for model fit 4. Theoretical b/t model with w/i saturated for model fit 5. Combined w/i & b/t theoretical model for parameters 6. Evaluate random coefficients
  11. 11. 1. Consider Single Model • Consider single-level model – Null model for descriptives • Define ICC < 0.02 as within unless very large cluster sizes, then possibly lower threshold WITHIN ARE OHFITVC;
  12. 12. Between-Group Variance ANALYSIS: TYPE IS TWOLEVEL RANDOM; MODEL: %WITHIN% OHFITVC; %BETWEEN% OHFITVC; Observed Variables Null ICC Value Congruence 0.03 Commitment 0.11 Citizenship Behavior 0.04
  13. 13. 1.1 Multilevel Reliability ANALYSIS: TYPE IS TWOLEVEL; MODEL: %WITHIN% VCw@1; OHGEF3R OHGEF7R OHGEF15 (WR1- WR3); VCw BY OHGEF3R* (WL1) OHGEF7R (WL2) OHGEF15 (WL3); %BETWEEN% VCb@1; OHGEF3R OHGEF7R OHGEF15 (BR1- BR3); VCb BY OHGEF3R* (BL1) OHGEF7R (BL2) OHGEF15 (BL3); MODEL CONSTRAINT: NEW(NUMW DENOMW OMEGAW NUMB DENOMB OMEGAB); NUMW = (WL1+WL2+WL3)**2; DENOMW = NUMW+(WR1+WR2+WR3); OMEGAW = NUMW/DENOMW; NUMB = (BL1+BL2+BL3)**2; DENOMB = NUMB+(BR1+BR2+BR3); OMEGAB = NUMB/DENOMB; WR1 > 0; BR1 > 0; WR2 > 0; BR2 > 0; WR3 > 0; BR3 > 0; Geldhof, Preacher, & Zyhur (in press)
  14. 14. 1.1 Measurement Reliability Measures ωw ωb Satisfaction 0.77 0.92 Demands-Abilities Fit 0.78 0.97 Needs-Supplies Fit 0.79 0.92 Interpersonal Similarity 0.79 0.98 Social Desirability 0.88 0.96 Value Congruence 0.90 0.93 Tenure 0.91 0.93 Commitment 0.91 0.99
  15. 15. 1.2 Descriptive Statistics DEFINE: SDESIR=SDESIR/3; Observed Variables n Min Max Mean SD SE Social Desirability 292 0 13 6.67 3.23 0.19 Tenure 291 1 5 1.78 0.81 0.05 Commitment 292 2 7 5.26 1.10 0.06 Satisfaction 293 2 7 6.14 1.01 0.06 Interpersonal Similarity 291 1 5 3.42 0.96 0.06 Value Congruence 291 1 5 3.88 0.76 0.04 Demands-Abilities 293 1 5 3.96 0.80 0.05 Needs-Supplies Fit 293 1 5 4.01 0.70 0.04
  16. 16. 2. Baseline Models Baseline w/i Model MODEL: %WITHIN% OHFITVC with OHCit@0 OHCOM@0; OHCit with OHCOM@0; %BETWEEN% OHFITVC with OHCit OHCOM; OHCit with OHCOM; Baseline b/t Model MODEL: %WITHIN% OHFITVC with OHCit OHCOM; OHCit with OHCOM; %BETWEEN% OHFITVC with OHCit@0 OHCOM@0; OHCit with OHCOM@0;
  17. 17. Commitment 3. Theoretical w/i Model Value Congruence Citizenship Behavior Commitment Value Congruence Citizenship Behavior
  18. 18. 3. Theoretical w/i Model ANALYSIS: TYPE IS TWOLEVEL; MODEL: %WITHIN% OHCOM on OHFITVC; OHCOM on OHCit; %BETWEEN% OHCOM with OHFITVC OHCit; OHFITVC with OHCIT;
  19. 19. 3. Theoretical w/i Model Chi-Square Test of Model Fit Value 38.019* Degrees of Freedom 1 P-Value 0.0000 Scaling Correction Factor RMSEA Estimate 0.359 CFI/TLI CFI 0.895 TLI 0.373 SRMR Value for Within 0.169 Value for Between 0.010
  20. 20. Commitment 4. Theoretical b/t Model Value Congruence Citizenship Behavior Commitment Value Congruence Citizenship Behavior
  21. 21. 4. Theoretical b/t Model ANALYSIS: TYPE IS TWOLEVEL; MODEL: %WITHIN% OHCOM with OHFITVC OHCit; OHFITVC with OHCIT; %BETWEEN% OHCOM OHFITVC OHCit;
  22. 22. 4. Theoretical b/t Model Chi-Square Test of Model Fit Value 5.192* Degrees of Freedom 3 P-Value 0.1583 Scaling Correction Factor RMSEA Estimate 0.050 CFI/TLI CFI 0.994 TLI 0.988 SRMR Value for Within 0.022 Value for Between 0.693
  23. 23. Commitment 3. Theoretical Combined Model Value Congruence Citizenship Behavior Commitment Value Congruence Citizenship Behavior Commitment Value Congruence Citizenship Behavior
  24. 24. 5. Combined Model ANALYSIS: TYPE IS TWOLEVEL; MODEL: %WITHIN% OHCOM on OHFITVC; OHCOM on OHCit; %BETWEEN% OHCOM OHFITVC OHCit;
  25. 25. 5. Combined Model Two-Tailed Estimate S.E. Est./S.E. P-Value Within Level OHCOM ON OHFITVC 0.711 0.079 9.025 0.000 OHCIT 0.338 0.055 6.168 0.000 Between Level Means OHCOM 5.250 0.076 68.744 0.000 OHCIT 5.870 0.058 101.094 0.000 OHFITVC 3.887 0.046 83.593 0.000
  26. 26. Commitment 6. Random Coefficients Value Congruence Citizenship Behavior Commitment Value Congruence Citizenship Behavior Commitment Value Congruence Citizenship Behavior Random Slope
  27. 27. 6. Random Coefficients LISTWISE=ON; (or Monte Carlo integration) ANALYSIS: TYPE IS TWOLEVEL; MODEL: %WITHIN% OHCOM on OHFITVC; s1 | OHCOM ON OHCit; %BETWEEN% OHCOM OHFITVC OHCit;
  28. 28. 6. Random Coefficients LISTWISE=ON; ANALYSIS: TYPE IS TWOLEVEL; MODEL: %WITHIN% OHCOM on OHFITVC; s1 | OHCOM ON OHCit; %BETWEEN% OHCOM OHFITVC OHCit; s1 on OHFITVC;
  29. 29. 6. Random Coefficients Loglikelihood H0 Value -1074.838 H0 Scaling Correction Factor 0.9723 for MLR Information Criteria Akaike (AIC) 2175.675 Bayesian (BIC) 2223.249 Sample-Size Adjusted BIC 2182.024
  30. 30. 6. Random Coefficients Two-Tailed Estimate S.E. Est./S.E. P-Value Between Level S1 ON OHFITVC 0.327 0.112 2.905 0.004 Intercepts S1 -1.099 0.454 -2.421 0.015
  31. 31. Unresolved Issues • Sample & Power Estimation • Model Fit Approaches • Model Fit Statistics • MLR Performance in Multilevel Model • 3+ Levels • Balancing of Cluster Sizes
  32. 32. Unresolved Issues - Saturation • “In the MODEL command, the following variable is a y-variable (endogenous) on the BETWEEN level and an x-variable (exogenous) on the WITHIN level. • This variable will be treated as a y-variable on both levels: OHGEFIS” • Any discrepancy is treated as a y-variable on both levels
  33. 33. Other Models • Longitudinal Multilevel Models • Latent Models • Multilevel EFA • Multilevel CFA • 3+ Levels
  34. 34. Other Topics • Convergence Problems • Power Analysis & Sample Size • Alternative Estimators (MLR default) – MUML, Bayes • Random Starting Seeds • Interval Estimates – Bayes – Monte Carlo
  35. 35. Resources • Barbara Byrne Structural Equation Modeling with Mplus • Hancock & Mueller Structural Equation Modeling: A Second Course • Little, Bovarid, & Card Modeling Contextual Effects in Long. Studies • Kris Preacher http://www.quantpsy.org/pubs.htm • Steve Miller “Things Statistical” http://personalityandemotion.com/

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