### HLM Textbook Examples Multilevel Analysis Techniques and Applications by Joop Hox Chapter 4: Some Important Methodological and Statistical Issues

The data sets used Chapter 4 is the same as in Chapter 2 and we assume that an SSM file has been created based on these data files.
Part 1: The variable sex is not centered and is a fixed effect.
 Sigma_squared =      0.45992
Tau
INTRCPT1,B0      0.86222

Tau (as correlations)
INTRCPT1,B0  1.000
----------------------------------------------------
Random level-1 coefficient   Reliability estimate
----------------------------------------------------
INTRCPT1, B0                        0.974
----------------------------------------------------
The value of the likelihood function at iteration 3 = -2.246446E+003
Final estimation of fixed effects:
----------------------------------------------------------------------------
Standard             Approx.
Fixed Effect         Coefficient   Error      T-ratio   d.f.     P-value
----------------------------------------------------------------------------
For       INTRCPT1, B0
INTRCPT2, G00           4.897221   0.095295    51.390        99    0.000
For      SEX slope, B1
INTRCPT2, G10           0.843701   0.030963    27.248      1998    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           4.897221   0.098254    49.843        99    0.000
For      SEX slope, B1
INTRCPT2, G10           0.843701   0.059144    14.265      1998    0.000
----------------------------------------------------------------------------

Final estimation of variance components:
-----------------------------------------------------------------------------
Random Effect           Standard      Variance     df    Chi-square  P-value
Deviation     Component
-----------------------------------------------------------------------------
INTRCPT1,       U0        0.92856       0.86222    99    3788.54686    0.000
level-1,       R         0.67817       0.45992
-----------------------------------------------------------------------------

Statistics for current covariance components model
--------------------------------------------------
Deviance                       = 4492.892477
Number of estimated parameters = 2
Part 2: The variable sex is grand-mean centered and is a fixed effect.
Sigma_squared =      0.45992
Tau
INTRCPT1,B0      0.86222

Tau (as correlations)
INTRCPT1,B0  1.000
----------------------------------------------------
Random level-1 coefficient   Reliability estimate
----------------------------------------------------
INTRCPT1, B0                        0.974
----------------------------------------------------
The value of the likelihood function at iteration 3 = -2.246446E+003
Final estimation of fixed effects:
----------------------------------------------------------------------------
Standard             Approx.
Fixed Effect         Coefficient   Error      T-ratio   d.f.     P-value
----------------------------------------------------------------------------
For       INTRCPT1, B0
INTRCPT2, G00           5.308103   0.094098    56.410        99    0.000
For      SEX slope, B1
INTRCPT2, G10           0.843701   0.030963    27.248      1998    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           5.308103   0.093626    56.695        99    0.000
For      SEX slope, B1
INTRCPT2, G10           0.843701   0.059144    14.265      1998    0.000
----------------------------------------------------------------------------

Final estimation of variance components:
-----------------------------------------------------------------------------
Random Effect           Standard      Variance     df    Chi-square  P-value
Deviation     Component
-----------------------------------------------------------------------------
INTRCPT1,       U0        0.92856       0.86222    99    3788.54685    0.000
level-1,       R         0.67817       0.45992
-----------------------------------------------------------------------------

Statistics for current covariance components model
--------------------------------------------------
Deviance                       = 4492.892477
Number of estimated parameters = 2
Part 3: The variable sex is included as a random effect, not centered.
 Sigma_squared =      0.39244
Tau
INTRCPT1,B0      0.94027      -0.14100
SEX,B1     -0.14100       0.27252

Tau (as correlations)
INTRCPT1,B0  1.000 -0.279
SEX,B1 -0.279  1.000
----------------------------------------------------
Random level-1 coefficient   Reliability estimate
----------------------------------------------------
INTRCPT1, B0                        0.959
SEX, B1                        0.766
----------------------------------------------------
The value of the likelihood function at iteration 6 = -2.168157E+003
Final estimation of fixed effects:
----------------------------------------------------------------------------
Standard             Approx.
Fixed Effect         Coefficient   Error      T-ratio   d.f.     P-value
----------------------------------------------------------------------------
For       INTRCPT1, B0
INTRCPT2, G00           4.890086   0.099016    49.387        99    0.000
For      SEX slope, B1
INTRCPT2, G10           0.843106   0.059634    14.138        99    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           4.890086   0.098519    49.636        99    0.000
For      SEX slope, B1
INTRCPT2, G10           0.843106   0.059335    14.209        99    0.000
----------------------------------------------------------------------------

Final estimation of variance components:
-----------------------------------------------------------------------------
Random Effect           Standard      Variance     df    Chi-square  P-value
Deviation     Component
-----------------------------------------------------------------------------
INTRCPT1,       U0        0.96968       0.94027    99    2416.40514    0.000
SEX slope, U1        0.52204       0.27252    99     426.17652    0.000
level-1,       R         0.62645       0.39244
-----------------------------------------------------------------------------

Statistics for current covariance components model
--------------------------------------------------
Deviance                       = 4336.314651
Number of estimated parameters = 4
Part 4: The variable sex is included as a random effect and is also grand-mean centered.
 Sigma_squared =      0.39244
Tau
INTRCPT1,B0      0.86757      -0.00829
SEX,B1     -0.00829       0.27253

Tau (as correlations)
INTRCPT1,B0  1.000 -0.017
SEX,B1 -0.017  1.000
----------------------------------------------------
Random level-1 coefficient   Reliability estimate
----------------------------------------------------
INTRCPT1, B0                        0.976
SEX, B1                        0.766
----------------------------------------------------
The value of the likelihood function at iteration 6 = -2.168157E+003
Final estimation of fixed effects:
----------------------------------------------------------------------------
Standard             Approx.
Fixed Effect         Coefficient   Error      T-ratio   d.f.     P-value
----------------------------------------------------------------------------
For       INTRCPT1, B0
INTRCPT2, G00           5.300679   0.094243    56.245        99    0.000
For      SEX slope, B1
INTRCPT2, G10           0.843106   0.059636    14.138        99    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           5.300679   0.093770    56.529        99    0.000
For      SEX slope, B1
INTRCPT2, G10           0.843106   0.059335    14.209        99    0.000
----------------------------------------------------------------------------

Final estimation of variance components:
-----------------------------------------------------------------------------
Random Effect           Standard      Variance     df    Chi-square  P-value
Deviation     Component
-----------------------------------------------------------------------------
INTRCPT1,       U0        0.93143       0.86757    99    4277.32851    0.000
SEX slope, U1        0.52204       0.27253    99     426.17686    0.000
level-1,       R         0.62645       0.39244
-----------------------------------------------------------------------------

Statistics for current covariance components model
--------------------------------------------------
Deviance                       = 4336.314638
Number of estimated parameters = 4
Table 4.2 on page 60.
Part 1: No interaction, no centering.
 Sigma_squared =      0.39248
Tau
INTRCPT1,B0      0.41155       0.02093
SEX,B1      0.02093       0.27329

Tau (as correlations)
INTRCPT1,B0  1.000  0.062
SEX,B1  0.062  1.000
----------------------------------------------------
Random level-1 coefficient   Reliability estimate
----------------------------------------------------
INTRCPT1, B0                        0.911
SEX, B1                        0.767
----------------------------------------------------
The value of the likelihood function at iteration 6 = -2.137029E+003
Final estimation of fixed effects:
----------------------------------------------------------------------------
Standard             Approx.
Fixed Effect         Coefficient   Error      T-ratio   d.f.     P-value
----------------------------------------------------------------------------
For       INTRCPT1, B0
INTRCPT2, G00           3.339816   0.160775    20.773        99    0.000
For      SEX slope, B1
INTRCPT2, G10           0.843146   0.059689    14.126        99    0.000
For     TEXP slope, B2
INTRCPT2, G20           0.108363   0.010215    10.609      1997    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           3.339816   0.165505    20.180        99    0.000
For      SEX slope, B1
INTRCPT2, G10           0.843146   0.059388    14.197        99    0.000
For     TEXP slope, B2
INTRCPT2, G20           0.108363   0.011382     9.521      1997    0.000
----------------------------------------------------------------------------

Final estimation of variance components:
-----------------------------------------------------------------------------
Random Effect           Standard      Variance     df    Chi-square  P-value
Deviation     Component
-----------------------------------------------------------------------------
INTRCPT1,       U0        0.64152       0.41155    99    1125.84022    0.000
SEX slope, U1        0.52277       0.27329    99     426.12953    0.000
level-1,       R         0.62648       0.39248
-----------------------------------------------------------------------------

Statistics for current covariance components model
--------------------------------------------------
Deviance                       = 4274.057054
Number of estimated parameters = 4
Part 2: With interaction, but no centering.
 Sigma_squared =      0.39241
Tau
INTRCPT1,B0      0.41198       0.02342
SEX,B1      0.02342       0.22641

Tau (as correlations)
INTRCPT1,B0  1.000  0.077
SEX,B1  0.077  1.000
----------------------------------------------------
Random level-1 coefficient   Reliability estimate
----------------------------------------------------
INTRCPT1, B0                        0.911
SEX, B1                        0.731
----------------------------------------------------
The value of the likelihood function at iteration 6 = -2.134216E+003
Final estimation of fixed effects:
----------------------------------------------------------------------------
Standard             Approx.
Fixed Effect         Coefficient   Error      T-ratio   d.f.     P-value
----------------------------------------------------------------------------
For       INTRCPT1, B0
INTRCPT2, G00           3.313521   0.161014    20.579        98    0.000
MTEXP, G01           0.110235   0.010232    10.774        98    0.000
For      SEX slope, B1
INTRCPT2, G10           1.329594   0.133051     9.993        98    0.000
MTEXP, G11          -0.034035   0.008457    -4.024        98    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           3.313521   0.167064    19.834        98    0.000
MTEXP, G01           0.110235   0.011466     9.614        98    0.000
For      SEX slope, B1
INTRCPT2, G10           1.329594   0.108340    12.272        98    0.000
MTEXP, G11          -0.034035   0.007293    -4.667        98    0.000
----------------------------------------------------------------------------

Final estimation of variance components:
-----------------------------------------------------------------------------
Random Effect           Standard      Variance     df    Chi-square  P-value
Deviation     Component
-----------------------------------------------------------------------------
INTRCPT1,       U0        0.64186       0.41198    98    1126.47092    0.000
SEX slope, U1        0.47583       0.22641    98     367.94122    0.000
level-1,       R         0.62643       0.39241
-----------------------------------------------------------------------------

Statistics for current covariance components model
--------------------------------------------------
Deviance                       = 4268.431480
Number of estimated parameters = 4
Part 3: Centering, but no interaction.
 Sigma_squared =      0.39248
Tau
INTRCPT1,B0      0.49674       0.15400
SEX,B1      0.15400       0.27331

Tau (as correlations)
INTRCPT1,B0  1.000  0.418
SEX,B1  0.418  1.000
----------------------------------------------------
Random level-1 coefficient   Reliability estimate
----------------------------------------------------
INTRCPT1, B0                        0.960
SEX, B1                        0.767
----------------------------------------------------
The value of the likelihood function at iteration 6 = -2.137029E+003
Final estimation of fixed effects:
----------------------------------------------------------------------------
Standard             Approx.
Fixed Effect         Coefficient   Error      T-ratio   d.f.     P-value
----------------------------------------------------------------------------
For       INTRCPT1, B0
INTRCPT2, G00           5.296010   0.071925    73.633        99    0.000
For      SEX slope, B1
INTRCPT2, G10           0.843146   0.059693    14.125        99    0.000
For     TEXP slope, B2
INTRCPT2, G20           0.108358   0.010215    10.608      1997    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           5.296010   0.071189    74.394        99    0.000
For      SEX slope, B1
INTRCPT2, G10           0.843146   0.059388    14.197        99    0.000
For     TEXP slope, B2
INTRCPT2, G20           0.108358   0.011382     9.520      1997    0.000
----------------------------------------------------------------------------

Final estimation of variance components:
-----------------------------------------------------------------------------
Random Effect           Standard      Variance     df    Chi-square  P-value
Deviation     Component
-----------------------------------------------------------------------------
INTRCPT1,       U0        0.70480       0.49674    99    2433.70809    0.000
SEX slope, U1        0.52279       0.27331    99     426.13103    0.000
level-1,       R         0.62648       0.39248
-----------------------------------------------------------------------------

Statistics for current covariance components model
--------------------------------------------------
Deviance                       = 4274.057036
Number of estimated parameters = 4
Part 4: Centering and with interaction.
 Sigma_squared =      0.39241
Tau
INTRCPT1,B0      0.48850       0.13369
SEX,B1      0.13369       0.22643

Tau (as correlations)
INTRCPT1,B0  1.000  0.402
SEX,B1  0.402  1.000
----------------------------------------------------
Random level-1 coefficient   Reliability estimate
----------------------------------------------------
INTRCPT1, B0                        0.959
SEX, B1                        0.731
----------------------------------------------------
The value of the likelihood function at iteration 6 = -2.134216E+003
Final estimation of fixed effects:
----------------------------------------------------------------------------
Standard             Approx.
Fixed Effect         Coefficient   Error      T-ratio   d.f.     P-value
----------------------------------------------------------------------------
For       INTRCPT1, B0
INTRCPT2, G00           5.300373   0.071345    74.293        98    0.000
MTEXP, G01           0.093660   0.010851     8.631        98    0.000
For      SEX slope, B1
INTRCPT2, G10           0.842895   0.055619    15.155        98    0.000
MTEXP, G11          -0.034035   0.008458    -4.024        98    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           5.300373   0.070631    75.043        98    0.000
MTEXP, G01           0.093660   0.011275     8.307        98    0.000
For      SEX slope, B1
INTRCPT2, G10           0.842895   0.055066    15.307        98    0.000
MTEXP, G11          -0.034035   0.007293    -4.667        98    0.000
----------------------------------------------------------------------------

Final estimation of variance components:
-----------------------------------------------------------------------------
Random Effect           Standard      Variance     df    Chi-square  P-value
Deviation     Component
-----------------------------------------------------------------------------
INTRCPT1,       U0        0.69892       0.48850    98    2394.46566    0.000
SEX slope, U1        0.47585       0.22643    98     367.94224    0.000
level-1,       R         0.62643       0.39241
-----------------------------------------------------------------------------

Statistics for current covariance components model
--------------------------------------------------
Deviance                       = 4268.431481
Number of estimated parameters = 4
Figure 4.3 on page 61.
Use the model from Part 2 of Table 4.2, click on Graph Equations from File Menu and choose as follows. You can also add x-label and y-label and title for the graph by clicking the Range/Titles/Color option.
Table 4.3 on page 63.
Part 1: Intercept only
Sigma_squared =      0.63868
Tau
INTRCPT1,B0      0.87981

Tau (as correlations)
INTRCPT1,B0  1.000
----------------------------------------------------
Random level-1 coefficient   Reliability estimate
----------------------------------------------------
INTRCPT1, B0                        0.965
----------------------------------------------------
The value of the likelihood function at iteration 2 = -2.556874E+003
Final estimation of fixed effects:
----------------------------------------------------------------------------
Standard             Approx.
Fixed Effect         Coefficient   Error      T-ratio   d.f.     P-value
----------------------------------------------------------------------------
For       INTRCPT1, B0
INTRCPT2, G00           5.307603   0.095504    55.575        99    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           5.307603   0.095023    55.856        99    0.000
----------------------------------------------------------------------------

Final estimation of variance components:
-----------------------------------------------------------------------------
Random Effect           Standard      Variance     df    Chi-square  P-value
Deviation     Component
-----------------------------------------------------------------------------
INTRCPT1,       U0        0.93798       0.87981    99    2803.92595    0.000
level-1,       R         0.79917       0.63868
-----------------------------------------------------------------------------

Statistics for current covariance components model
--------------------------------------------------
Deviance                       = 5113.748909
Number of estimated parameters = 2
Part 2: The variable sex is included as a fixed effect.
 Sigma_squared =      0.45992
Tau
INTRCPT1,B0      0.86222

Tau (as correlations)
INTRCPT1,B0  1.000
----------------------------------------------------
Random level-1 coefficient   Reliability estimate
----------------------------------------------------
INTRCPT1, B0                        0.974
----------------------------------------------------
The value of the likelihood function at iteration 3 = -2.246446E+003
Final estimation of fixed effects:
----------------------------------------------------------------------------
Standard             Approx.
Fixed Effect         Coefficient   Error      T-ratio   d.f.     P-value
----------------------------------------------------------------------------
For       INTRCPT1, B0
INTRCPT2, G00           4.897221   0.095295    51.390        99    0.000
For      SEX slope, B1
INTRCPT2, G10           0.843701   0.030963    27.248      1998    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           4.897221   0.098254    49.843        99    0.000
For      SEX slope, B1
INTRCPT2, G10           0.843701   0.059144    14.265      1998    0.000
----------------------------------------------------------------------------

Final estimation of variance components:
-----------------------------------------------------------------------------
Random Effect           Standard      Variance     df    Chi-square  P-value
Deviation     Component
-----------------------------------------------------------------------------
INTRCPT1,       U0        0.92856       0.86222    99    3788.54686    0.000
level-1,       R         0.67817       0.45992
-----------------------------------------------------------------------------

Statistics for current covariance components model
--------------------------------------------------
Deviance                       = 4492.892477
Number of estimated parameters = 2
Part 3: The variable texp is also included.
Sigma_squared =      0.45992
Tau
INTRCPT1,B0      0.48596

Tau (as correlations)
INTRCPT1,B0  1.000
----------------------------------------------------
Random level-1 coefficient   Reliability estimate
----------------------------------------------------
INTRCPT1, B0                        0.954
----------------------------------------------------
The value of the likelihood function at iteration 4 = -2.221260E+003
Final estimation of fixed effects:
----------------------------------------------------------------------------
Standard             Approx.
Fixed Effect         Coefficient   Error      T-ratio   d.f.     P-value
----------------------------------------------------------------------------
For       INTRCPT1, B0
INTRCPT2, G00           3.560682   0.171477    20.765        99    0.000
For      SEX slope, B1
INTRCPT2, G10           0.844669   0.030951    27.291      1997    0.000
For     TEXP slope, B2
INTRCPT2, G20           0.093445   0.010854     8.609      1997    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           3.560682   0.163292    21.806        99    0.000
For      SEX slope, B1
INTRCPT2, G10           0.844669   0.059140    14.283      1997    0.000
For     TEXP slope, B2
INTRCPT2, G20           0.093445   0.011187     8.353      1997    0.000
----------------------------------------------------------------------------

Final estimation of variance components:
-----------------------------------------------------------------------------
Random Effect           Standard      Variance     df    Chi-square  P-value
Deviation     Component
-----------------------------------------------------------------------------
INTRCPT1,       U0        0.69711       0.48596    99    2156.96630    0.000
level-1,       R         0.67818       0.45992
-----------------------------------------------------------------------------

Statistics for current covariance components model
--------------------------------------------------
Deviance                       = 4442.520460
Number of estimated parameters = 2
Part 4: The variable sex is included as a random effect.
 Sigma_squared =      0.39248
Tau
INTRCPT1,B0      0.41155       0.02093
SEX,B1      0.02093       0.27329

Tau (as correlations)
INTRCPT1,B0  1.000  0.062
SEX,B1  0.062  1.000
----------------------------------------------------
Random level-1 coefficient   Reliability estimate
----------------------------------------------------
INTRCPT1, B0                        0.911
SEX, B1                        0.767
----------------------------------------------------
The value of the likelihood function at iteration 6 = -2.137029E+003
Final estimation of fixed effects:
----------------------------------------------------------------------------
Standard             Approx.
Fixed Effect         Coefficient   Error      T-ratio   d.f.     P-value
----------------------------------------------------------------------------
For       INTRCPT1, B0
INTRCPT2, G00           3.339816   0.160775    20.773        99    0.000
For      SEX slope, B1
INTRCPT2, G10           0.843146   0.059689    14.126        99    0.000
For     TEXP slope, B2
INTRCPT2, G20           0.108363   0.010215    10.609      1997    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           3.339816   0.165505    20.180        99    0.000
For      SEX slope, B1
INTRCPT2, G10           0.843146   0.059388    14.197        99    0.000
For     TEXP slope, B2
INTRCPT2, G20           0.108363   0.011382     9.521      1997    0.000
----------------------------------------------------------------------------

Final estimation of variance components:
-----------------------------------------------------------------------------
Random Effect           Standard      Variance     df    Chi-square  P-value
Deviation     Component
-----------------------------------------------------------------------------
INTRCPT1,       U0        0.64152       0.41155    99    1125.84022    0.000
SEX slope, U1        0.52277       0.27329    99     426.12953    0.000
level-1,       R         0.62648       0.39248
-----------------------------------------------------------------------------

Statistics for current covariance components model
--------------------------------------------------
Deviance                       = 4274.057054
Number of estimated parameters = 4
Part 5: Interaction of sex and texp is included.
 Sigma_squared =      0.39242
Tau
INTRCPT1,B0      0.41197       0.02346
SEX,B1      0.02346       0.22634

Tau (as correlations)
INTRCPT1,B0  1.000  0.077
SEX,B1  0.077  1.000
----------------------------------------------------
Random level-1 coefficient   Reliability estimate
----------------------------------------------------
INTRCPT1, B0                        0.911
SEX, B1                        0.731
----------------------------------------------------
The value of the likelihood function at iteration 6 = -2.134216E+003
Final estimation of fixed effects:
----------------------------------------------------------------------------
Standard             Approx.
Fixed Effect         Coefficient   Error      T-ratio   d.f.     P-value
----------------------------------------------------------------------------
For       INTRCPT1, B0
INTRCPT2, G00           3.313525   0.161010    20.580        99    0.000
For      SEX slope, B1
INTRCPT2, G10           1.329591   0.133020     9.995        98    0.000
MTEXP, G11          -0.034035   0.008455    -4.025        98    0.000
For     TEXP slope, B2
INTRCPT2, G20           0.110235   0.010232    10.774      1996    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           3.313525   0.167065    19.834        99    0.000
For      SEX slope, B1
INTRCPT2, G10           1.329591   0.108340    12.272        98    0.000
MTEXP, G11          -0.034035   0.007293    -4.667        98    0.000
For     TEXP slope, B2
INTRCPT2, G20           0.110235   0.011466     9.614      1996    0.000
----------------------------------------------------------------------------

Final estimation of variance components:
-----------------------------------------------------------------------------
Random Effect           Standard      Variance     df    Chi-square  P-value
Deviation     Component
-----------------------------------------------------------------------------
INTRCPT1,       U0        0.64185       0.41197    99    1126.46051    0.000
SEX slope, U1        0.47575       0.22634    98     367.93782    0.000
level-1,       R         0.62643       0.39242
-----------------------------------------------------------------------------

Statistics for current covariance components model
--------------------------------------------------
Deviance                       = 4268.431491
Number of estimated parameters = 4
Table 4.4 can be produced manually based on the equations provided in this section. We omit the calculation here.

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