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

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Line 44: Line 44:
| ||Value||Std.Error||DF||t-value||p-value
| ||Value||Std.Error||DF||t-value||p-value
|-
|-
-
| (Intercept)||13.841459||0.3267406||3602||42.36223||0.00E+00
+
| (Intercept)||13.841||0.327||3602||42.362||0.00E+00
|-
|-
-
| ses||1.528862||0.245895||3602||6.21754||0.00E+00
+
| ses||1.529||0.246||3602||6.218||0.00E+00
|-
|-
-
| SectorPublic||-1.830417||0.4579895||77||-3.99664||1.00E-04
+
| SectorPublic||-1.830||0.458||77||-3.997||1.00E-04
|-
|-
-
| ses.m||3.033531||0.5940779||77||5.10629||0.00E+00
+
| ses.m||3.034||0.594||77||5.106||0.00E+00
|-
|-
-
| ses:SectorPublic||1.354043||0.3243585||3602||4.17453||0.00E+00
+
| ses:SectorPublic||1.354||0.324||3602||4.175||0.00E+00
|}
|}
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| Min||Q1||Med||Q3||Max
| Min||Q1||Med||Q3||Max
|-
|-
-
| -3.10386562||-0.73369552||0.02217222||0.75083942||2.85079637
+
| -3.104||-0.734||0.022||0.751||2.851
|}
|}
Line 92: Line 92:
| ||numDF||denDF||F.value||p.value
| ||numDF||denDF||F.value||p.value
|-
|-
-
| Effect of ses||2||77||40.83481||<.00001
+
| Effect of ses||2||77||40.835||<.00001
|}
|}
Line 99: Line 99:
| ||Estimate||Std.Error||DF||t-value||p-value||Lower 0.95||Upper 0.95
| ||Estimate||Std.Error||DF||t-value||p-value||Lower 0.95||Upper 0.95
|-
|-
-
| Within-school||1.528862||0.245895||3602||6.217541||<.00001||1.046755||2.010969
+
| Within-school||1.529||0.246||3602||6.218||<.00001||1.047||2.011
|-
|-
-
| Contextual||3.033531||0.594078||77||5.106285||<.00001||1.850571||4.216492
+
| Contextual||3.034||0.594||77||5.106||<.00001||1.851||4.216
|-
|-
-
| Compositional||4.562394||0.593325||77||7.68954||<.00001||3.380933||5.743854
+
| Compositional||4.562||0.593||77||7.690||<.00001||3.381||5.744
|}
|}

Latest revision as of 10:51, 29 May 2012

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)13.8410.327360242.3620.00E+00
ses1.5290.24636026.2180.00E+00
SectorPublic-1.8300.45877-3.9971.00E-04
ses.m3.0340.594775.1060.00E+00
ses:SectorPublic1.3540.32436024.1750.00E+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
-3.104-0.7340.0220.7512.851


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 ses27740.835<.00001


EstimateStd.ErrorDFt-valuep-valueLower 0.95Upper 0.95
Within-school1.5290.24636026.218<.000011.0472.011
Contextual3.0340.594775.106<.000011.8514.216
Compositional4.5620.593777.690<.000013.3815.744
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