PSY 9555A (Nov 13): SEM Approach to Multilevel Modeling with...
Transcript of PSY 9555A (Nov 13): SEM Approach to Multilevel Modeling with...
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PSY 9555A (Nov 13): SEM Approach to Multilevel Modeling with Mplus
• MLM in Mplus – Data structure and syntax
• Intercept only model
• Level 1 predictors
• Intercepts and slopes as outcomes
• Measures within persons
• LGM and MLM
• Multilevel CFA Additional resources Mplus manual (especially Chapter 9) Hox, J. J. (2010). Multilevel analysis. Techniques and applications. 2nd ed.
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Example (from Joop Hox book on Multilevel Analysis, 2010)
Data Level 1: pupils (2000 in total) Level 2: Classes (100 classes of approx 20 pupils each) Outcome variable: pupil popularity (scale 0-10) Predictor variables at pupil level (level 1) pupil gender (1=girl 0=boy) pupil extraversion (scale 1-10) Predictor variable(s) at class level (level 2) teacher experience (scale 2-25)
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Data Structure
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Scatterplot of Extraversion by Popularity for Each Class
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Intercepts and Slopes as Outcome Variables Model Mplus Diagram
EXTRAV
Teacher Experience
POPULAR
POPULAR (intercept)
S_Extrav
WITHIN
BETWEEN
S_Extrav
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Example: Intercept Only Model
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Intercept Only Model
0.695/(0.695 + 1.222) = .362
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Level-1 Predictor Fixed
Note: in this model, we are estimating random variation in the intercepts but not in the slopes
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Level-1 Predictor Fixed
EXTRAV
POPULAR
POPULAR (intercept)
WITHIN
BETWEEN
S_Extrav .498 .930
Mean = 5.078 Var = .710
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Level-1 Predictor Random
Note: in this model, we are estimating random variation in the intercepts and in the slopes (popularity regressed on extraversion)
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Level-1 Predictor Random
EXTRAV
POPULAR
POPULAR (intercept)
S_Extrav
WITHIN
BETWEEN
S_Extrav .892
Mean =5.078 Var = 0.711
Mean = 0.497 Var = .033
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Adding a Level-2 Predictor
Note: in this model, we add a Level-2 predictor. We regress both the intercepts and the slopes on this predictor. (I also included a correlation between the intercept and slope residuals)
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Adding a Level-2 Predictor
-.017
EXTRAV
Teacher Experience
POPULAR
POPULAR (intercept)
S_Extrav
WITHIN
BETWEEN
S_Extrav
-.027
Intercept = 5.076 Var = .547
.062
.888
Intercept =.499 Var = .002
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Replicating in SPSS Mixed Models
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Previous Model in SPSS Mixed Models
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Previous Model in SPSS Mixed Models
Note: model not exactly the same (level-1 predictor grand-mean centered instead of group-mean centered)
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Previous Model in SPSS Mixed Models
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Exact Same Model in Mplus (all predictors grand-mean centered)
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Measures within Persons
When your data file is structured in the conventional one line per subject with repeated measures on the same line
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Measures within Persons
Time (linear)
Drink
Drink (intercept)
Slope
WITHIN
BETWEEN
Slope 10.076
-0.139
Mean = -.118 Var = .782
Mean = 5.236 Var = 31.765
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Measures within Persons (Previous Model specified as LGM)
Back to the conventional data structure specification
IN LGM these residuals are usually not constrained to equality but they are in MLM. I constrained them here.
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Example: Measures within Persons (LGM and MLM)
LGM MLM
Same as in slide 13
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Example: Measures within Persons (LGM and MLM)
LGM MLM
0.00
M = -0.119 Var = .0776
M = 5.238 Var = 31.784
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Example: Measures within Persons (LGM and MLM)
MLM LGM
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Multilevel CFA
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Multilevel CFA (data from Joop Hox, 2010)
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Multilevel CFA (data from Joop Hox, 2010)
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Multilevel CFA (data from Joop Hox, 2010)