MATH 6643 Summer 2012 Applications of Mixed Models/Students/smithce/Model1
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< MATH 6643 Summer 2012 Applications of Mixed Models | Students | smithce(Difference between revisions)
(Created page with "=== Model 1 === <u> Level 1 Model </u> :<math>mathach_{ij} = {\color{Red}\beta_{0j}} + {\color{Blue}\beta_{1j}}ses_{ij} + r_{ij} </math> <u> Level 2 Model (Between School Model...") |
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Line 87: | Line 87: | ||
:1. <math>Var({\color{Red}u_{0}}) = 2.151^2</math> | :1. <math>Var({\color{Red}u_{0}}) = 2.151^2</math> | ||
:2. <math>Var({\color{Blue}u_{1}}) = 0.355^2</math> | :2. <math>Var({\color{Blue}u_{1}}) = 0.355^2</math> | ||
- | :3. <math> | + | :3. <math>Correlation({\color{Red}u_{0}},{\color{Blue}u_{1}}) = 0.973</math> |
:4. <math>Var({\color{Black}r_{ij}}) = 6.075^2</math> | :4. <math>Var({\color{Black}r_{ij}}) = 6.075^2</math> | ||
:5 <math>{\color{Red}\gamma_{00}} = 13.98</math> Intercept for Catholic schools | :5 <math>{\color{Red}\gamma_{00}} = 13.98</math> Intercept for Catholic schools |
Latest revision as of 14:27, 29 May 2012
Model 1
Level 1 Model
Level 2 Model (Between School Model)
Combined Model (by substitution)
Fixed Portion of the Model
Random Portion of the Model
fit <- lme( mathach ~ ses * Sector, dd, random = ~ 1 + ses | id, control = list(msMaxIter=200, msVerbose=T)) # Note that id refers to schools not students!
Linear mixed-effects model fit by REML
Data: dd
AIC | BIC | logLik |
23914 | 23964 | -11949 |
Random effects:
Formula: ~1 + ses | id
Structure: General positive-definite, Log-Cholesky parametrization
StdDev | Corr | |
(Intercept) | 2.151 ^{1} | (Intr) |
ses | 0.355 ^{2} | 0.973 ^{3} |
Residual | 6.075^{4} |
Fixed effects: mathach ~ ses * Sector
Value | Std.Error | DF | t-value | p-value | |
(Intercept) | 13.98^{5} | 0.387 | 3602 | 36.1 | 0 |
ses | 1.67^{6} | 0.228 | 3602 | 7.3 | 0 |
SectorPublic | -2.37^{7} | 0.526 | 78 | -4.5 | 0 |
ses:SectorPublic | 1.39^{8} | 0.307 | 3602 | 4.5 | 0 |
Correlation:
(Intr) | ses | SctrPb | |
ses | 0.204 | ||
SectorPublic | -0.736 | -0.15 | |
ses:SectorPublic | -0.152 | -0.744 | 0.252 |
Standardized Within-Group Residuals:
Min | Q1 | Med | Q3 | Max |
-3.0761 | -0.7378 | 0.0246 | 0.7565 | 2.7849 |
Number of Observations: 3684
Number of Groups: 80
Notes
- 1.
- 2.
- 3.
- 4.
- 5 Intercept for Catholic schools
- 6 Slope of ses for Catholic schools
- 7 Change in Intercept for Public schools (e.g. Intercept for Public = 13.98 - 2.37 = 11.61)
- 8 Change in Slope for Public schools (e.g. ses slope for Public = 1.67 + 1.39 = 3.06)