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This chapter uses data file alcohol1_pp. You can download the SSM file ALCO.SSM for the data and use it directly from within HLM. To see how to use an SSM file in HLM, please see our FAQ page on it. The method we choose for estimating these models is ML. Estimation method is selected from Basic Specifications menu.
Table 4.1, pages 94-95
Model A:
Sigma_squared = 0.56175
Standard Error of Sigma_squared = 0.06203
Tau INTRCPT1,B0 0.56386
Standard Errors of Tau INTRCPT1,B0 0.11911
Tau (as correlations) INTRCPT1,B0 1.000
---------------------------------------------------- Random level-1 coefficient Reliability estimate ---------------------------------------------------- INTRCPT1, B0 0.751 ----------------------------------------------------
Final estimation of fixed effects:
----------------------------------------------------------------------------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 0.921955 0.095707 9.633 81 0.000
----------------------------------------------------------------------------
The outcome variable is ALCUSE
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 0.921955 0.095707 9.633 81 0.000
----------------------------------------------------------------------------
Final estimation of variance components:
-----------------------------------------------------------------------------
Random Effect Standard Variance df Chi-square P-value
Deviation Component
-----------------------------------------------------------------------------
INTRCPT1, U0 0.75091 0.56386 81 328.92616 0.000
level-1, R 0.74950 0.56175
-----------------------------------------------------------------------------
Statistics for current covariance components model -------------------------------------------------- Deviance = 670.155995 Number of estimated parameters = 3
Model B:
Sigma_squared = 0.33729
Standard Error of Sigma_squared = 0.05268
Tau INTRCPT1,B0 0.62436 -0.06844 AGE_14,B1 -0.06844 0.15120
Standard Errors of Tau INTRCPT1,B0 0.14806 0.07008 AGE_14,B1 0.07008 0.05647
Tau (as correlations) INTRCPT1,B0 1.000 -0.223 AGE_14,B1 -0.223 1.000
----------------------------------------------------
Random level-1 coefficient Reliability estimate
----------------------------------------------------
INTRCPT1, B0 0.690
AGE_14, B1 0.473
----------------------------------------------------
Final estimation of fixed effects:
----------------------------------------------------------------------------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 0.651304 0.105080 6.198 81 0.000
For AGE_14 slope, B1
INTRCPT2, G10 0.270651 0.062455 4.334 81 0.000
----------------------------------------------------------------------------
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 0.651304 0.105080 6.198 81 0.000
For AGE_14 slope, B1
INTRCPT2, G10 0.270651 0.062455 4.334 81 0.000
----------------------------------------------------------------------------
Final estimation of variance components:
-----------------------------------------------------------------------------
Random Effect Standard Variance df Chi-square P-value
Deviation Component
-----------------------------------------------------------------------------
INTRCPT1, U0 0.79016 0.62436 81 264.14675 0.000
AGE_14 slope, U1 0.38885 0.15120 81 155.51848 0.000
level-1, R 0.58077 0.33729
-----------------------------------------------------------------------------
Statistics for current covariance components model -------------------------------------------------- Deviance = 636.611086 Number of estimated parameters = 6
Model C:
Sigma_squared = 0.33729
Standard Error of Sigma_squared = 0.05268
Tau INTRCPT1,B0 0.48758 -0.05934 AGE_14,B1 -0.05934 0.15060
Standard Errors of Tau INTRCPT1,B0 0.12782 0.06573 AGE_14,B1 0.06573 0.05639
Tau (as correlations) INTRCPT1,B0 1.000 -0.219 AGE_14,B1 -0.219 1.000
----------------------------------------------------
Random level-1 coefficient Reliability estimate
----------------------------------------------------
INTRCPT1, B0 0.634
AGE_14, B1 0.472
----------------------------------------------------
Final estimation of fixed effects:
----------------------------------------------------------------------------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 0.315952 0.130695 2.417 80 0.016
COA, G01 0.743212 0.194566 3.820 80 0.000
For AGE_14 slope, B1
INTRCPT2, G10 0.292955 0.084228 3.478 80 0.001
COA, G11 -0.049430 0.125389 -0.394 80 0.693
----------------------------------------------------------------------------
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 0.315952 0.092525 3.415 80 0.001
COA, G01 0.743212 0.204789 3.629 80 0.001
For AGE_14 slope, B1
INTRCPT2, G10 0.292955 0.077620 3.774 80 0.000
COA, G11 -0.049430 0.127416 -0.388 80 0.698
----------------------------------------------------------------------------
Final estimation of variance components:
-----------------------------------------------------------------------------
Random Effect Standard Variance df Chi-square P-value
Deviation Component
-----------------------------------------------------------------------------
INTRCPT1, U0 0.69827 0.48758 80 224.24420 0.000
AGE_14 slope, U1 0.38807 0.15060 80 155.22430 0.000
level-1, R 0.58077 0.33729
-----------------------------------------------------------------------------
Statistics for current covariance components model -------------------------------------------------- Deviance = 621.202628 Number of estimated parameters = 8
Model D:
Sigma_squared = 0.33729
Standard Error of Sigma_squared = 0.05268
Tau INTRCPT1,B0 0.24091 -0.00612 AGE_14,B1 -0.00612 0.13911
Standard Errors of Tau INTRCPT1,B0 0.09259 0.05500 AGE_14,B1 0.05500 0.05481
Tau (as correlations) INTRCPT1,B0 1.000 -0.033 AGE_14,B1 -0.033 1.000
----------------------------------------------------
Random level-1 coefficient Reliability estimate
----------------------------------------------------
INTRCPT1, B0 0.462
AGE_14, B1 0.452
----------------------------------------------------
Final estimation of fixed effects:
----------------------------------------------------------------------------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 -0.316514 0.148062 -2.138 79 0.032
COA, G01 0.579165 0.162486 3.564 79 0.001
PEER, G02 0.694296 0.111533 6.225 79 0.000
For AGE_14 slope, B1
INTRCPT2, G10 0.429429 0.113689 3.777 79 0.000
COA, G11 -0.014032 0.124765 -0.112 79 0.911
PEER, G12 -0.149815 0.085641 -1.749 79 0.080
----------------------------------------------------------------------------
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 -0.316514 0.117611 -2.691 79 0.008
COA, G01 0.579165 0.168459 3.438 79 0.001
PEER, G02 0.694296 0.131544 5.278 79 0.000
For AGE_14 slope, B1
INTRCPT2, G10 0.429429 0.115458 3.719 79 0.000
COA, G11 -0.014032 0.127005 -0.110 79 0.912
PEER, G12 -0.149815 0.095926 -1.562 79 0.118
----------------------------------------------------------------------------
Final estimation of variance components:
-----------------------------------------------------------------------------
Random Effect Standard Variance df Chi-square P-value
Deviation Component
-----------------------------------------------------------------------------
INTRCPT1, U0 0.49082 0.24091 79 152.28049 0.000
AGE_14 slope, U1 0.37298 0.13911 79 149.63981 0.000
level-1, R 0.58077 0.33729
-----------------------------------------------------------------------------
Statistics for current covariance components model -------------------------------------------------- Deviance = 588.690655 Number of estimated parameters = 10
Model E:
Sigma_squared = 0.33729
Standard Error of Sigma_squared = 0.05268
Tau INTRCPT1,B0 0.24095 -0.00616 AGE_14,B1 -0.00616 0.13916
Standard Errors of Tau INTRCPT1,B0 0.09259 0.05501 AGE_14,B1 0.05501 0.05481
Tau (as correlations) INTRCPT1,B0 1.000 -0.034 AGE_14,B1 -0.034 1.000
----------------------------------------------------
Random level-1 coefficient Reliability estimate
----------------------------------------------------
INTRCPT1, B0 0.462
AGE_14, B1 0.452
----------------------------------------------------
Final estimation of fixed effects:
----------------------------------------------------------------------------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 -0.313821 0.146118 -2.148 79 0.032
COA, G01 0.571196 0.146228 3.906 79 0.000
PEER, G02 0.695183 0.111258 6.248 79 0.000
For AGE_14 slope, B1
INTRCPT2, G10 0.424687 0.105590 4.022 80 0.000
PEER, G11 -0.151377 0.084513 -1.791 80 0.073
----------------------------------------------------------------------------
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 -0.313821 0.117172 -2.678 79 0.008
COA, G01 0.571196 0.151710 3.765 79 0.000
PEER, G02 0.695183 0.131693 5.279 79 0.000
For AGE_14 slope, B1
INTRCPT2, G10 0.424687 0.111385 3.813 80 0.000
PEER, G11 -0.151377 0.093888 -1.612 80 0.107
----------------------------------------------------------------------------
Final estimation of variance components:
-----------------------------------------------------------------------------
Random Effect Standard Variance df Chi-square P-value
Deviation Component
-----------------------------------------------------------------------------
INTRCPT1, U0 0.49086 0.24095 79 152.28729 0.000
AGE_14 slope, U1 0.37305 0.13916 80 149.66517 0.000
level-1, R 0.58076 0.33729
-----------------------------------------------------------------------------
Statistics for current covariance components model -------------------------------------------------- Deviance = 588.703303 Number of estimated parameters = 9
Model F:
Sigma_squared = 0.33720
Tau
INTRCPT1,B0 0.25974 -0.01065
AGE_14,B1 -0.01065 0.14692
Tau (as correlations)
INTRCPT1,B0 1.000 -0.055
AGE_14,B1 -0.055 1.000
----------------------------------------------------
Random level-1 coefficient Reliability estimate
----------------------------------------------------
INTRCPT1, B0 0.480
AGE_14, B1 0.466
----------------------------------------------------
The value of the likelihood function at iteration 6 = -3.009300E+002
The outcome variable is ALCUSE
Final estimation of fixed effects:
----------------------------------------------------------------------------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 0.393570 0.105430 3.733 79 0.000
COA, G01 0.571193 0.149004 3.833 79 0.000
PEER, G02 0.695183 0.113244 6.139 79 0.000
For AGE_14 slope, B1
INTRCPT2, G10 0.270651 0.062030 4.363 80 0.000
PEER, G11 -0.151377 0.085566 -1.769 80 0.076
----------------------------------------------------------------------------
The outcome variable is ALCUSE
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 0.393570 0.098962 3.977 79 0.000
COA, G01 0.571193 0.151710 3.765 79 0.000
PEER, G02 0.695183 0.131693 5.279 79 0.000
For AGE_14 slope, B1
INTRCPT2, G10 0.270651 0.061268 4.418 80 0.000
PEER, G11 -0.151377 0.093888 -1.612 80 0.107
----------------------------------------------------------------------------
Final estimation of variance components:
-----------------------------------------------------------------------------
Random Effect Standard Variance df Chi-square P-value
Deviation Component
-----------------------------------------------------------------------------
INTRCPT1, U0 0.50965 0.25974 79 152.32552 0.000
AGE_14 slope, U1 0.38330 0.14692 80 149.70274 0.000
level-1, R 0.58069 0.33720
-----------------------------------------------------------------------------
Statistics for current covariance components model
--------------------------------------------------
Deviance = 601.859900
Number of estimated parameters = 4
Model G:
Sigma_squared = 0.33720
Tau
INTRCPT1,B0 0.25974 -0.01065
AGE_14,B1 -0.01065 0.14692
Tau (as correlations)
INTRCPT1,B0 1.000 -0.055
AGE_14,B1 -0.055 1.000
----------------------------------------------------
Random level-1 coefficient Reliability estimate
----------------------------------------------------
INTRCPT1, B0 0.480
AGE_14, B1 0.466
----------------------------------------------------
The value of the likelihood function at iteration 6 = -3.009300E+002
The outcome variable is ALCUSE
Final estimation of fixed effects:
----------------------------------------------------------------------------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 0.651303 0.081210 8.020 79 0.000
COA, G01 0.571193 0.149004 3.833 79 0.000
PEER, G02 0.695183 0.113244 6.139 79 0.000
For AGE_14 slope, B1
INTRCPT2, G10 0.270651 0.062030 4.363 80 0.000
PEER, G11 -0.151377 0.085566 -1.769 80 0.076
----------------------------------------------------------------------------
The outcome variable is ALCUSE
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 0.651303 0.079786 8.163 79 0.000
COA, G01 0.571193 0.151710 3.765 79 0.000
PEER, G02 0.695183 0.131693 5.279 79 0.000
For AGE_14 slope, B1
INTRCPT2, G10 0.270651 0.061268 4.418 80 0.000
PEER, G11 -0.151377 0.093888 -1.612 80 0.107
----------------------------------------------------------------------------
Final estimation of variance components:
-----------------------------------------------------------------------------
Random Effect Standard Variance df Chi-square P-value
Deviation Component
-----------------------------------------------------------------------------
INTRCPT1, U0 0.50965 0.25974 79 152.32552 0.000
AGE_14 slope, U1 0.38330 0.14692 80 149.70274 0.000
level-1, R 0.58069 0.33720
-----------------------------------------------------------------------------
Statistics for current covariance components model
--------------------------------------------------
Deviance = 601.859900
Number of estimated parameters = 4
Figure 4.3, page 99
Graph for Model E:
Page 123
Test of equation 4.18 using Model F:
After building model F, we can further specify optional hypothesis tests through Optional Specifications menu. For example, to test equation 4.18, we can specify as shown in the sequence of screen shots below. After the hypothesis test specification, we can run the model and the result of the test will be at the end of the output.
NOTE!!!!!!!
The results below do not match the book because these results use REML, while the book uses ML. We will fix this soon.
Results of General Linear Hypothesis Testing
-----------------------------------------------------------------------------
Coefficients Contrast
-----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 0.456443 1.000 0.000
COA, G01 0.571193 0.000 0.000
CPEER, G02 0.695183 0.000 0.000
For AGE_14 slope, B1
INTRCPT2, G10 0.256961 0.000 1.000
CPEER, G11 -0.151377 0.000 0.000
Chi-square statistic = 52.616211 Degrees of freedom = 2 P-value = 0.000000
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