Newsom, USP 656 Multilevel Regression, Winter 20061
Intercept Only Model (ANOVA)
MIXED mathach
/METHOD = REML
/PRINT = SOLUTION TESTCOV
/FIXED = | SSTYPE(3)
/RANDOM = INTERCEPT | SUBJECT(schoolid) COVTYPE(UN).
Mixed Model Analysis
Fixed Effects
Covariance Parameters
One Level-1 Predictor (ANCOVA assuming homogenous slopes)
MIXED mathach WITH minority
/METHOD = REML
/PRINT = SOLUTION TESTCOV
/FIXED = minority | SSTYPE(3)
/RANDOM = INTERCEPT | SUBJECT(schoolid) COVTYPE(UN).
Mixed Model Analysis
Fixed Effects
Covariance Parameters
One Level-1 Predictor (ANCOVA with heterogeneous slopes)
MIXED mathach WITH minority
/METHOD = REML
/PRINT = SOLUTION TESTCOV
/FIXED = minority | SSTYPE(3)
/RANDOM = INTERCEPT minority | SUBJECT(schoolid) COVTYPE(UN).
Mixed Model Analysis
Fixed Effects
Covariance Parameters
Intercept Only Model (ANOVA)
****** ITERATION 4 *******
Sigma_squared = 39.14831
Tau
INTRCPT1,B0 8.61431
Tau (as correlations)
INTRCPT1,B0 1.000
------
Random level-1 coefficient Reliability estimate
------
INTRCPT1, B0 0.901
------
The value of the likelihood function at iteration 4 = -2.355840E+004
The outcome variable is MATHACH
Final estimation of fixed effects:
------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
------
For INTRCPT1, B0
INTRCPT2, G00 12.636972 0.244412 51.704 159 0.000
------
The outcome variable is MATHACH
Final estimation of fixed effects
(with robust standard errors)
------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
------
For INTRCPT1, B0
INTRCPT2, G00 12.636972 0.243628 51.870 159 0.000
------
Final estimation of variance components:
------
Random Effect Standard Variance df Chi-square P-value
Deviation Component
------
INTRCPT1, U0 2.93501 8.61431 159 1660.23259 0.000
level-1, R 6.25686 39.14831
------
Statistics for current covariance components model
------
Deviance = 47116.793477
Number of estimated parameters = 2
One Level-1 Predictor (ANCOVA assuming homogenous slopes)
******* ITERATION 4 *******
Sigma_squared = 37.77907
Tau
INTRCPT1,B0 6.46835
Tau (as correlations)
INTRCPT1,B0 1.000
------
Random level-1 coefficient Reliability estimate
------
INTRCPT1, B0 0.877
------
The value of the likelihood function at iteration 4 = -2.341198E+004
The outcome variable is MATHACH
Final estimation of fixed effects:
------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
------
For INTRCPT1, B0
INTRCPT2, G00 13.653248 0.222468 61.372 159 0.000
For MINORITY slope, B1
INTRCPT2, G10 -3.686667 0.211967 -17.393 7183 0.000
------
The outcome variable is MATHACH
Final estimation of fixed effects
(with robust standard errors)
------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
------
For INTRCPT1, B0
INTRCPT2, G00 13.653248 0.211216 64.641 159 0.000
For MINORITY slope, B1
INTRCPT2, G10 -3.686667 0.281096 -13.115 7183 0.000
------
Final estimation of variance components:
------
Random Effect Standard Variance df Chi-square P-value
Deviation Component
------
INTRCPT1, U0 2.54329 6.46835 159 1337.41109 0.000
level-1, R 6.14647 37.77907
------
Statistics for current covariance components model
------
Deviance = 46823.966240
Number of estimated parameters = 2
One Level-1 Predictor (ANCOVA with heterogeneous slopes)
******* ITERATION 11 *******
Sigma_squared = 37.40890
Tau
INTRCPT1,B0 5.62217 0.91054
MINORITY,B1 0.91054 3.25492
Tau (as correlations)
INTRCPT1,B0 1.000 0.213
MINORITY,B1 0.213 1.000
------
Random level-1 coefficient Reliability estimate
------
INTRCPT1, B0 0.770
MINORITY, B1 0.297
------
Note: The reliability estimates reported above are based on only 136 of 160
units that had sufficient data for computation. Fixed effects and variance
components are based on all the data.
The value of the likelihood function at iteration 11 = -2.339967E+004
The outcome variable is MATHACH
Final estimation of fixed effects:
------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
------
For INTRCPT1, B0
INTRCPT2, G00 13.675056 0.211071 64.789 159 0.000
For MINORITY slope, B1
INTRCPT2, G10 -3.753913 0.273932 -13.704 159 0.000
------
The outcome variable is MATHACH
Final estimation of fixed effects
(with robust standard errors)
------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
------
For INTRCPT1, B0
INTRCPT2, G00 13.675056 0.210347 65.012 159 0.000
For MINORITY slope, B1
INTRCPT2, G10 -3.753913 0.272473 -13.777 159 0.000
------
Final estimation of variance components:
------
Random Effect Standard Variance df Chi-square P-value
Deviation Component
------
INTRCPT1, U0 2.37111 5.62217 135 775.67156 0.000
MINORITY slope, U1 1.80414 3.25492 135 217.19186 0.000
level-1, R 6.11628 37.40890
------
Note: The chi-square statistics reported above are based on only 136 of 160
units that had sufficient data for computation. Fixed effects and variance
components are based on all the data.
Statistics for current covariance components model
------
Deviance = 46799.348858
Number of estimated parameters = 4