MATH 6643 Summer 2012 Applications of Mixed Models/Students/smithce/Model4

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Combined Model

mathach_{ij} = \underbrace{{\color{Red}\gamma_{00}} + {\color{Red}\gamma_{01}Sector_j} + {\color{Red}\gamma_{02}ses.m_j} + {\color{Blue}\gamma_{10}}ses_{ij} + {\color{Blue}\gamma_{11}Sector_j}ses_{ij}}_{Fixed} + \underbrace{{\color{Red}u_{0j}} + {\color{Blue}u_{1j}}ses.d_{ij} + r_{ij}}_{Random}


Fixed Portion of the Model Equivalent to FE model for Model 2 (LINK).

{\color{Red}\gamma_{00}} + {\color{Red}\gamma_{01}}Sector_j + {\color{Red}\gamma_{02}}ses.m_j + {\color{Blue}\gamma_{10}}ses_{ij} + {\color{Blue}\gamma_{11}}Sector_jses_{ij}


Random Portion of the Model Non-equivalent RE model as compared to Model 2 (LINK).

{\color{Red}u_{0j}} + {\color{Blue}u_{1j}}ses.d_{ij} + r_{ij}
{\color{Red}u_{0j}} + {\color{Blue}u_{1j}}(ses_{ij} - ses.m_{j}) + r_{ij}


fitca <- lme( mathach ~ ses * Sector + ses.m, dd, random = ~ 1 + ses.d | id )  #c# Model 4 #c#


Linear mixed-effects model fit by REML
Data: dd

AICBIClogLik
23889.7723945.66-11935.88


Random effects:
Formula: ~1 + ses.d | id
Structure: General positive-definite, Log-Cholesky parametrization

StdDevCorr
(Intercept)1.7465424(Intr)
ses.d0.64446230.398
Residual6.0649774


Fixed effects: mathach ~ ses * Sector + ses.m

ValueStd.ErrorDFt-valuep-value
(Intercept)13.8414590.3267406360242.362230.00E+00
ses1.5288620.24589536026.217540.00E+00
SectorPublic-1.8304170.457989577-3.996641.00E-04
ses.m3.0335310.5940779775.106290.00E+00
ses:SectorPublic1.3540430.324358536024.174530.00E+00


Correlation:

(Intr)sesSctrPbses.m
ses0.121
SectorPublic-0.734-0.114
ses.m-0.157-0.210.244
ses:SectorPublic-0.068-0.7280.1550.014


Standardized Within-Group Residuals:

MinQ1MedQ3Max
-3.10386562-0.733695520.022172220.750839422.85079637


Number of Observations: 3684
Number of Groups: 80


L <- list( 'Effect of ses' = rbind(
"Within-school" =  c( 0,1,0,0,0),
"Contextual"    =  c( 0,0,0,1,0),
"Compositional" =  c( 0,1,0,1,0)))
wald( fitca,L )


numDFdenDFF.valuep.value
Effect of ses27740.83481<.00001


EstimateStd.ErrorDFt-valuep-valueLower 0.95Upper 0.95
Within-school1.5288620.24589536026.217541<.000011.0467552.010969
Contextual3.0335310.594078775.106285<.000011.8505714.216492
Compositional4.5623940.593325777.68954<.000013.3809335.743854
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