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Table 3.3 on page 48.
We will use imm10.sav and imm10_lev2.sav for this example. Variable schid is the ID variable that links the level-1 data file with the level-2 data file. We assume that an SSM file has been created based on these two files.
Sigma_squared = 43.07100
Tau INTRCPT1,B0 69.30426 -31.76171 HOMEWORK,B1 -31.76171 22.45254
Tau (as correlations) INTRCPT1,B0 1.000 -0.805 HOMEWORK,B1 -0.805 1.000
---------------------------------------------------- Random level-1 coefficient Reliability estimate ---------------------------------------------------- INTRCPT1, B0 0.920 HOMEWORK, B1 0.928 ----------------------------------------------------
The value of the likelihood function at iteration 6 = -8.819772E+002 The outcome variable is MATH
Final estimation of fixed effects:
----------------------------------------------------------------------------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 44.770591 2.743644 16.318 9 0.000
For HOMEWORK slope, B1
INTRCPT2, G10 2.040469 1.554194 1.313 9 0.222
----------------------------------------------------------------------------
The outcome variable is MATH
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 44.770591 2.602659 17.202 9 0.000
For HOMEWORK slope, B1
INTRCPT2, G10 2.040469 1.474242 1.384 9 0.200
----------------------------------------------------------------------------
The robust standard errors are appropriate for datasets having a moderate to large number of level 2 units. These data do not meet this criterion.
Final estimation of variance components:
-----------------------------------------------------------------------------
Random Effect Standard Variance df Chi-square P-value
Deviation Component
-----------------------------------------------------------------------------
INTRCPT1, U0 8.32492 69.30426 9 153.18126 0.000
HOMEWORK slope, U1 4.73841 22.45254 9 133.36740 0.000
level-1, R 6.56285 43.07100
-----------------------------------------------------------------------------
Statistics for current covariance components model -------------------------------------------------- Deviance = 1763.954337 Number of estimated parameters = 4
Table 3.4 on page 50.
Variable PUBLIC is included as level-2 predictor.
Sigma_squared = 42.96022
Tau INTRCPT1,B0 45.84914 -32.24989 HOMEWORK,B1 -32.24989 23.96176
Tau (as correlations) INTRCPT1,B0 1.000 -0.973 HOMEWORK,B1 -0.973 1.000
---------------------------------------------------- Random level-1 coefficient Reliability estimate ---------------------------------------------------- INTRCPT1, B0 0.885 HOMEWORK, B1 0.933 ----------------------------------------------------
The value of the likelihood function at iteration 11 = -8.710642E+002
Final estimation of fixed effects:
----------------------------------------------------------------------------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 58.040447 2.944241 19.713 8 0.000
MPUBLIC, G01 -14.660674 2.109003 -6.951 8 0.000
For HOMEWORK slope, B1
INTRCPT2, G10 1.952488 1.598905 1.221 9 0.253
----------------------------------------------------------------------------
The robust standard errors cannot be computed for this model.
Final estimation of variance components:
-----------------------------------------------------------------------------
Random Effect Standard Variance df Chi-square P-value
Deviation Component
-----------------------------------------------------------------------------
INTRCPT1, U0 6.77120 45.84914 8 81.98591 0.000
HOMEWORK slope, U1 4.89507 23.96176 9 133.96327 0.000
level-1, R 6.55440 42.96022
-----------------------------------------------------------------------------
Statistics for current covariance components model -------------------------------------------------- Deviance = 1742.128440 Number of estimated parameters = 4
Table 3.5 on page 51.
Variable PUBLIC is included as level-2 predictor for the slope of variable HOMEWORK, hence an interaction between the two.
Sigma_squared = 42.95762
Tau INTRCPT1,B0 51.85064 -36.71407 HOMEWORK,B1 -36.71407 27.26808
Tau (as correlations) INTRCPT1,B0 1.000 -0.976 HOMEWORK,B1 -0.976 1.000
---------------------------------------------------- Random level-1 coefficient Reliability estimate ---------------------------------------------------- INTRCPT1, B0 0.896 HOMEWORK, B1 0.940 ----------------------------------------------------
The value of the likelihood function at iteration 8 = -8.693684E+002
Final estimation of fixed effects:
----------------------------------------------------------------------------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 59.210218 7.408165 7.993 8 0.000
MPUBLIC, G01 -15.965966 7.830068 -2.039 8 0.075
For HOMEWORK slope, B1
INTRCPT2, G10 1.094640 5.242788 0.209 8 0.840
MPUBLIC, G11 0.951377 5.541947 0.172 8 0.868
----------------------------------------------------------------------------
The robust standard errors cannot be computed for this model.
Final estimation of variance components:
-----------------------------------------------------------------------------
Random Effect Standard Variance df Chi-square P-value
Deviation Component
-----------------------------------------------------------------------------
INTRCPT1, U0 7.20074 51.85064 8 81.54750 0.000
HOMEWORK slope, U1 5.22188 27.26808 8 129.57845 0.000
level-1, R 6.55421 42.95762
-----------------------------------------------------------------------------
Statistics for current covariance components model -------------------------------------------------- Deviance = 1738.736793 Number of estimated parameters = 4
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