Table 2.1, page 24. Ten selected schools for NELS-88: within-school means.
use https://stats.idre.ucla.edu/stat/stata/examples/mlm_imm/imm10, clear
table schnum, cont(freq mean math mean homework) format(%6.2f)
----------------------------------------------------------
group(sch |
id) | Freq. mean(math) mean(homework)
----------+-----------------------------------------------
1 | 23 45.74 1.39
2 | 20 42.15 2.35
3 | 24 53.25 1.83
4 | 22 43.55 1.64
5 | 22 49.86 0.86
6 | 20 46.40 1.15
7 | 67 62.82 3.30
8 | 21 49.67 2.10
9 | 21 46.33 1.33
10 | 20 47.85 1.60
----------------------------------------------------------
Table 2.2, page 24. Ten selected schools from NELS-88: within school dispersions and correlations. The variances produced by Stata are not the same as in the book even when adjusted by (n-1)/n. It is unclear why these differences exist.
statsby , by(schnum): corr math homework, cov
(running correlate on estimation sample)
command: correlate math homework, cov
N: r(N)
cov_12: r(cov_12)
Var_2: r(Var_2)
Var_1: r(Var_1)
by: schnum
Statsby groups
----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5
.........
clist
schnum N cov_12 Var_2 Var_1
1. 1 23 -4.438735 1.249012 56.74704
2. 2 20 -5.002632 1.713158 69.18684
3. 3 24 10.08696 1.275362 132.8044
4. 4 22 12.54113 2.242424 100.1645
5. 5 22 -2.829004 .5995671 71.26624
6. 6 20 -1.642105 .6605263 18.67369
7. 7 67 3.251244 2.970149 32.20986
8. 8 21 8.383333 1.290476 106.8333
9. 9 21 4.883333 .8333333 91.23333
10. 10 20 12.93684 2.042105 127.7132
use https://stats.idre.ucla.edu/stat/stata/examples/mlm_imm/imm10, clear
statsby , by(schnum): corr math homework
(running correlate on estimation sample)
command: correlate math homework
N: r(N)
rho: r(rho)
by: schnum
Statsby groups
----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5
.........
clist
schnum N rho
1. 1 23 -.5272352
2. 2 20 -.4595027
3. 3 24 .7750634
4. 4 22 .8367981
5. 5 22 -.4327856
6. 6 20 -.4675638
7. 7 67 .3324038
8. 8 21 .7139838
9. 9 21 .5600544
10. 10 20 .8010717
Table 2.3, page 27. Total regression for 10 schools. Equations for null model and with homework.
use https://stats.idre.ucla.edu/stat/stata/examples/mlm_imm/imm10, clear
regress math
Source | SS df MS Number of obs = 260
-------------+------------------------------ F( 0, 259) = 0.00
Model | 0.00 0 . Prob > F = .
Residual | 32116.60 259 124.002317 R-squared = 0.0000
-------------+------------------------------ Adj R-squared = 0.0000
Total | 32116.60 259 124.002317 Root MSE = 11.136
------------------------------------------------------------------------------
math | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_cons | 51.3 .6906026 74.28 0.000 49.94009 52.65991
------------------------------------------------------------------------------
regress math homework
Source | SS df MS Number of obs = 260
-------------+------------------------------ F( 1, 258) = 84.64
Model | 7933.80702 1 7933.80702 Prob > F = 0.0000
Residual | 24182.793 258 93.7317557 R-squared = 0.2470
-------------+------------------------------ Adj R-squared = 0.2441
Total | 32116.60 259 124.002317 Root MSE = 9.6815
------------------------------------------------------------------------------
math | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
homework | 3.571856 .3882366 9.20 0.000 2.80734 4.336372
_cons | 44.07386 .988641 44.58 0.000 42.12703 46.02069
------------------------------------------------------------------------------
Table 2.4. page 28. Aggregate regression for 10 schools.
egen n=count(schnum), by(schnum)
sort schnum
by schnum: generate i = _n
egen mmath = mean(math), by(schnum)
egen mhmwk = mean(homework), by(schnum)
regress mmath if i==1 [aw=n]
(sum of wgt is 2.6000e+02)
Source | SS df MS Number of obs = 10
-------------+------------------------------ F( 0, 9) = 0.00
Model | 0.00 0 . Prob > F = .
Residual | 539.635975 9 59.9595528 R-squared = 0.0000
-------------+------------------------------ Adj R-squared = 0.0000
Total | 539.635975 9 59.9595528 Root MSE = 7.7434
------------------------------------------------------------------------------
mmath | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_cons | 51.3 2.448664 20.95 0.000 45.76074 56.83926
------------------------------------------------------------------------------
regress mmath mhmwk if i==1 [aw=n]
(sum of wgt is 2.6000e+02)
Source | SS df MS Number of obs = 10
-------------+------------------------------ F( 1, 8) = 14.33
Model | 346.267285 1 346.267285 Prob > F = 0.0054
Residual | 193.36869 8 24.1710863 R-squared = 0.6417
-------------+------------------------------ Adj R-squared = 0.5969
Total | 539.635975 9 59.9595528 Root MSE = 4.9164
------------------------------------------------------------------------------
mmath | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
mhmwk | 7.014745 1.853336 3.78 0.005 2.740944 11.28855
_cons | 37.10863 4.058993 9.14 0.000 27.74858 46.46869
------------------------------------------------------------------------------
Table 2.5, page 29. Contextual model for 10 schools.
regress math homework mhmwk
Source | SS df MS Number of obs = 260
-------------+------------------------------ F( 2, 257) = 67.00
Model | 11006.6159 2 5503.30794 Prob > F = 0.0000
Residual | 21109.9841 257 82.1400161 R-squared = 0.3427
-------------+------------------------------ Adj R-squared = 0.3376
Total | 32116.60 259 124.002317 Root MSE = 9.0631
------------------------------------------------------------------------------
math | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
homework | 2.136635 .4326083 4.94 0.000 1.284726 2.988543
mhmwk | 4.87811 .797556 6.12 0.000 3.307533 6.448687
_cons | 37.10863 1.467442 25.29 0.000 34.21889 39.99837
------------------------------------------------------------------------------
Table 2.6, page 30. Cronbach model for 10 schools. The intercept given in the book seems to by in error. The printed intercept can be obtained with the model, regress math chmwk mhmwk.
generate chmwk = homework - mhmwk /* centered on group mean */
egen gmhmwk = mean(homework)
generate cghmwk = mhmwk - gmhmwk /* centered on grand mean */
regress math chmwk cghmwk
Source | SS df MS Number of obs = 260
-------------+------------------------------ F( 2, 257) = 67.00
Model | 11006.6159 2 5503.30795 Prob > F = 0.0000
Residual | 21109.9841 257 82.140016 R-squared = 0.3427
-------------+------------------------------ Adj R-squared = 0.3376
Total | 32116.60 259 124.002317 Root MSE = 9.0631
------------------------------------------------------------------------------
math | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
chmwk | 2.136635 .4326083 4.94 0.000 1.284726 2.988543
cghmwk | 7.014744 .670034 10.47 0.000 5.695288 8.3342
_cons | 51.3 .5620704 91.27 0.000 50.19315 52.40685
------------------------------------------------------------------------------
Table 2.7, page 31. ANCOVA for 10 schools. The first set coefficients are for the null model while the second set are with the homework variable.
tabulate schnum, gen(sch)
group(schid |
) | Freq. Percent Cum.
------------+-----------------------------------
1 | 23 8.85 8.85
2 | 20 7.69 16.54
3 | 24 9.23 25.77
4 | 22 8.46 34.23
5 | 22 8.46 42.69
6 | 20 7.69 50.38
7 | 67 25.77 76.15
8 | 21 8.08 84.23
9 | 21 8.08 92.31
10 | 20 7.69 100.00
------------+-----------------------------------
Total | 260 100.00
regress math sch1-sch10, nocons tsscons
Source | SS df MS Number of obs = 260
-------------+------------------------------ F( 9, 250) = 21.55
Model | 14030.5357 9 1558.94841 Prob > F = 0.0000
Residual | 18086.0643 250 72.3442573 R-squared = 0.4369
-------------+------------------------------ Adj R-squared = 0.4166
Total | 32116.60 259 124.002317 Root MSE = 8.5055
------------------------------------------------------------------------------
math | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
sch1 | 45.73913 1.773528 25.79 0.000 42.24617 49.23209
sch2 | 42.15 1.901897 22.16 0.000 38.40422 45.89578
sch3 | 53.25 1.736187 30.67 0.000 49.83058 56.66942
sch4 | 43.54545 1.813388 24.01 0.000 39.97399 47.11692
sch5 | 49.86364 1.813388 27.50 0.000 46.29217 53.4351
sch6 | 46.4 1.901897 24.40 0.000 42.65422 50.14578
sch7 | 62.8209 1.039117 60.46 0.000 60.77436 64.86744
sch8 | 49.66667 1.856062 26.76 0.000 46.01116 53.32218
sch9 | 46.33333 1.856062 24.96 0.000 42.67782 49.98884
sch10 | 47.85 1.901897 25.16 0.000 44.10422 51.59578
------------------------------------------------------------------------------
regress math sch1-sch10 homework, nocons tsscons
Source | SS df MS Number of obs = 260
-------------+------------------------------ F( 10, 249) = 24.83
Model | 16034.2029 10 1603.42029 Prob > F = 0.0000
Residual | 16082.3971 249 64.5879403 R-squared = 0.4992
-------------+------------------------------ Adj R-squared = 0.4791
Total | 32116.60 259 124.002317 Root MSE = 8.0367
------------------------------------------------------------------------------
math | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
sch1 | 42.76642 1.758701 24.32 0.000 39.30259 46.23025
sch2 | 37.12891 2.010493 18.47 0.000 33.16917 41.08865
sch3 | 49.33284 1.784876 27.64 0.000 45.81746 52.84821
sch4 | 40.04914 1.824791 21.95 0.000 36.45515 43.64314
sch5 | 48.01836 1.745158 27.52 0.000 44.58121 51.45551
sch6 | 43.94287 1.850409 23.75 0.000 40.29842 47.58732
sch7 | 55.77319 1.601596 34.82 0.000 52.61879 58.92759
sch8 | 45.18991 1.929157 23.42 0.000 41.39036 48.98945
sch9 | 43.48449 1.826809 23.80 0.000 39.88652 47.08246
sch10 | 44.43138 1.89898 23.40 0.000 40.69127 48.17149
homework | 2.136635 .3836129 5.57 0.000 1.381095 2.892174
------------------------------------------------------------------------------