Hi all, I am running a model looking at trends over time in gender in different groups of people. Goal is to plot predicted probabilities in each category of gender over time for each group.
I am trying to decide between two approaches (outcome is gender)
1) an interaction model => has a model for year, group, and year*group
2) a subgroup analysis => run the model separately for each group. model has one variable, for year.
I found that these two approaches produce: 1) exactly the same predicted probabilities, and 2) CIs around the predicted probabilities that are not exactly the same, but extremely close, so that the difference is negligible.
I lean toward the interaction model since this seems to be considered a better approach to subgroup analysis. The problem with interaction model: it says “not estimable” for two categories after margins. When I do the subgroup analysis on these two categories, I do get results for the margins. My question: would you just go with the subgroup analysis v. interaction model in this case? Alternatively, is there a way to get the interaction model to produce estimates for all groups? At this point I'm looking to just produce predicted probabilities for each group, not to compare the different groups.
Below I show code and output.
**RESULTS FROM INTERACTION MODEL
I am trying to decide between two approaches (outcome is gender)
1) an interaction model => has a model for year, group, and year*group
2) a subgroup analysis => run the model separately for each group. model has one variable, for year.
I found that these two approaches produce: 1) exactly the same predicted probabilities, and 2) CIs around the predicted probabilities that are not exactly the same, but extremely close, so that the difference is negligible.
I lean toward the interaction model since this seems to be considered a better approach to subgroup analysis. The problem with interaction model: it says “not estimable” for two categories after margins. When I do the subgroup analysis on these two categories, I do get results for the margins. My question: would you just go with the subgroup analysis v. interaction model in this case? Alternatively, is there a way to get the interaction model to produce estimates for all groups? At this point I'm looking to just produce predicted probabilities for each group, not to compare the different groups.
Below I show code and output.
**RESULTS FROM INTERACTION MODEL
Code:
. mlogit gender_n c.year##position_department_n, rrr vce(cluster person)
Iteration 0: log pseudolikelihood = -34931.124
Iteration 1: log pseudolikelihood = -34522.775
Iteration 2: log pseudolikelihood = -34505.94
Iteration 3: log pseudolikelihood = -34505.897
Iteration 4: log pseudolikelihood = -34505.897
Multinomial logistic regression Number of obs = 42,217
Wald chi2(30) = 473.31
Prob > chi2 = 0.0000
Log pseudolikelihood = -34505.897 Pseudo R2 = 0.0122
(Std. Err. adjusted for 16,011 clusters in person)
----------------------------------------------------------------------------------------------
| Robust
gender_n | RRR Std. Err. z P>|z| [95% Conf. Interval]
-----------------------------+----------------------------------------------------------------
F | (base outcome)
-----------------------------+----------------------------------------------------------------
M |
year | 1.087405 .0201943 4.51 0.000 1.048537 1.127714
|
position_department_n |
Principal, Marketing | 4.74e+65 2.93e+67 2.45 0.014 1.49e+13 1.5e+118
Principal, R&D | 3.58e+21 4.33e+23 0.41 0.681 5.50e-82 2.3e+124
Principal, Social Sci | 5.72e+39 2.49e+41 2.10 0.035 517.6844 6.32e+76
Senior, HR | 4.61e-42 4.90e-40 -0.90 0.370 1.6e-132 1.29e+49
Senior, Marketing | 5.08e+40 2.42e+42 1.96 0.050 1.147795 2.25e+81
Senior, R&D | 5.00e+23 2.36e+25 1.16 0.248 3.11e-17 8.07e+63
Senior, Social Sci | 5.10e+10 2.64e+12 0.48 0.634 4.56e-34 5.71e+54
|
position_department_n#c.year |
Principal, Marketing | .9275847 .028468 -2.45 0.014 .8734334 .9850933
Principal, R&D | .975824 .058644 -0.41 0.684 .867395 1.097807
Principal, Social Sci | .9555847 .0206889 -2.10 0.036 .9158835 .9970069
Senior, HR | 1.048612 .0554319 0.90 0.369 .9454057 1.163084
Senior, Marketing | .9546213 .0226777 -1.95 0.051 .9111926 1.00012
Senior, R&D | .9732994 .0228722 -1.15 0.249 .9294874 1.019176
Senior, Social Sci | .9877963 .0254299 -0.48 0.633 .9391913 1.038917
|
_cons | 1.88e-74 7.01e-73 -4.55 0.000 3.2e-106 1.11e-42
-----------------------------+----------------------------------------------------------------
U |
year | .7736713 .025425 -7.81 0.000 .7254101 .8251432
|
position_department_n |
Principal, Marketing | 5.3e-206 4.4e-204 -5.63 0.000 2.0e-277 1.4e-134
Principal, R&D | 2.4e-229 3.7e-227 -3.52 0.000 0 7.0e-102
Principal, Social Sci | 1.60e+65 1.27e+67 1.90 0.058 .007974 3.2e+132
Senior, HR | 6.1e-121 8.8e-119 -1.93 0.053 8.2e-243 45.42893
Senior, Marketing | 2.4e-167 1.8e-165 -5.08 0.000 1.2e-231 5.0e-103
Senior, R&D | 1.7e-125 1.3e-123 -3.68 0.000 5.2e-192 5.41e-59
Senior, Social Sci | 1.2e-131 9.2e-130 -3.83 0.000 1.4e-198 1.00e-64
|
position_department_n#c.year |
Principal, Marketing | 1.26561 .0528597 5.64 0.000 1.166134 1.373571
Principal, R&D | 1.299867 .0968639 3.52 0.000 1.12323 1.504281
Principal, Social Sci | .928099 .0365388 -1.90 0.058 .8591775 1.002549
Senior, HR | 1.147918 .081795 1.94 0.053 .9982941 1.319968
Senior, Marketing | 1.210673 .0455427 5.08 0.000 1.124622 1.303308
Senior, R&D | 1.153848 .0448898 3.68 0.000 1.069136 1.245271
Senior, Social Sci | 1.162135 .0454958 3.84 0.000 1.0763 1.254815
|
_cons | 9.7e+222 6.4e+224 7.78 0.000 6.4e+166 1.5e+279
----------------------------------------------------------------------------------------------
Note: _cons estimates baseline relative risk for each outcome.
.
**SOME OF THE MARGINS CAN'T BE ESTIMATED IN INTERACTION MODEL
. margins i.position_department_n, at(year=(2007(1)2013))
Adjusted predictions Number of obs = 42,217
Model VCE : Robust
1._predict : Pr(gender_n==F), predict(pr outcome(4))
2._predict : Pr(gender_n==M), predict(pr outcome(5))
3._predict : Pr(gender_n==U), predict(pr outcome(6))
1._at : year = 2007
2._at : year = 2008
3._at : year = 2009
4._at : year = 2010
5._at : year = 2011
6._at : year = 2012
7._at : year = 2013
----------------------------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-----------------------------------+----------------------------------------------------------------
_predict#_at#position_department_n |
1#1#Principal, HR | . (not estimable)
1#1#Principal, Marketing | .6583075 .0202208 32.56 0.000 .6186753 .6979396
1#1#Principal, R&D | . (not estimable)
1#1#Principal, Social Sci | .6250972 .0089476 69.86 0.000 .6075602 .6426342
1#1#Senior, HR | .6922345 .0329192 21.03 0.000 .627714 .756755
1#1#Senior, Marketing | .6404988 .0139097 46.05 0.000 .6132362 .6677613
1#1#Senior, R&D | .6891176 .011805 58.38 0.000 .6659802 .712255
1#1#Senior, Social Sci | .6970804 .0150392 46.35 0.000 .667604 .7265568
1#2#Principal, HR | . (not estimable)
1#2#Principal, Marketing | .6592583 .0181735 36.28 0.000 .6236388 .6948777
1#2#Principal, R&D | . (not estimable)
1#2#Principal, Social Sci | .6556696 .0072335 90.64 0.000 .6414923 .669847
1#2#Senior, HR | .6891251 .0261109 26.39 0.000 .6379487 .7403016
1#2#Senior, Marketing | .6407317 .0123407 51.92 0.000 .6165445 .664919
1#2#Senior, R&D | .6913654 .0102943 67.16 0.000 .6711889 .7115418
1#2#Senior, Social Sci | .7007748 .0135274 51.80 0.000 .6742616 .7272881
1#3#Principal, HR | . (not estimable)
1#3#Principal, Marketing | .6601594 .0171215 38.56 0.000 .6266018 .693717
1#3#Principal, R&D | . (not estimable)
1#3#Principal, Social Sci | .6778312 .0065145 104.05 0.000 .665063 .6905995
1#3#Senior, HR | .682689 .0213363 32.00 0.000 .6408707 .7245072
1#3#Senior, Marketing | .6404036 .0113035 56.66 0.000 .6182491 .662558
1#3#Senior, R&D | .6921605 .0093729 73.85 0.000 .6737899 .7105311
1#3#Senior, Social Sci | .7027991 .0127094 55.30 0.000 .6778891 .7277092
1#4#Principal, HR | . (not estimable)
1#4#Principal, Marketing | .6610112 .0172398 38.34 0.000 .6272217 .6948006
1#4#Principal, R&D | . (not estimable)
1#4#Principal, Social Sci | .6928427 .0064118 108.06 0.000 .6802758 .7054096
1#4#Senior, HR | .6729726 .0196286 34.29 0.000 .6345011 .711444
1#4#Senior, Marketing | .6395307 .0109476 58.42 0.000 .6180738 .6609877
1#4#Senior, R&D | .6915785 .0091341 75.71 0.000 .673676 .709481
1#4#Senior, Social Sci | .7031978 .0126017 55.80 0.000 .6784988 .7278967
1#5#Principal, HR | . (not estimable)
1#5#Principal, Marketing | .6618141 .018501 35.77 0.000 .6255528 .6980753
1#5#Principal, R&D | . (not estimable)
1#5#Principal, Social Sci | .7020658 .0067912 103.38 0.000 .6887552 .7153763
1#5#Senior, HR | .6600712 .0220509 29.93 0.000 .6168522 .7032901
1#5#Senior, Marketing | .6381306 .0113535 56.21 0.000 .6158782 .6603829
1#5#Senior, R&D | .6896983 .0096197 71.70 0.000 .670844 .7085526
1#5#Senior, Social Sci | .7020239 .0131906 53.22 0.000 .6761709 .7278769
1#6#Principal, HR | . (not estimable)
1#6#Principal, Marketing | .6625685 .0206949 32.02 0.000 .6220072 .7031298
1#6#Principal, R&D | . (not estimable)
1#6#Principal, Social Sci | .7067637 .0076539 92.34 0.000 .6917623 .7217651
1#6#Senior, HR | .6441298 .0282649 22.79 0.000 .5887315 .699528
1#6#Senior, Marketing | .6362212 .0124761 51.00 0.000 .6117685 .660674
1#6#Senior, R&D | .6866003 .0107752 63.72 0.000 .6654813 .7077193
1#6#Senior, Social Sci | .6993378 .0144285 48.47 0.000 .6710584 .7276173
1#7#Principal, HR | . (not estimable)
1#7#Principal, Marketing | .6632749 .0235625 28.15 0.000 .6170932 .7094566
1#7#Principal, R&D | . (not estimable)
1#7#Principal, Social Sci | .7080094 .008972 78.91 0.000 .6904245 .7255942
1#7#Senior, HR | .6253429 .0371503 16.83 0.000 .5525298 .6981561
1#7#Senior, Marketing | .6338215 .0141828 44.69 0.000 .6060237 .6616192
1#7#Senior, R&D | .682365 .0124851 54.65 0.000 .6578947 .7068353
1#7#Senior, Social Sci | .6952055 .0162499 42.78 0.000 .6633564 .7270547
2#1#Principal, HR | . (not estimable)
2#1#Principal, Marketing | .1924652 .0167435 11.49 0.000 .1596486 .2252818
2#1#Principal, R&D | . (not estimable)
2#1#Principal, Social Sci | .1840082 .0071937 25.58 0.000 .1699089 .1981075
2#1#Senior, HR | .1544592 .0245907 6.28 0.000 .1062624 .2026561
2#1#Senior, Marketing | .2209743 .0119726 18.46 0.000 .1975086 .2444401
2#1#Senior, R&D | .1817257 .0095304 19.07 0.000 .1630465 .2004049
2#1#Senior, Social Sci | .1444917 .0112957 12.79 0.000 .1223525 .1666309
2#2#Principal, HR | . (not estimable)
2#2#Principal, Marketing | .1944124 .0150486 12.92 0.000 .1649176 .2239072
2#2#Principal, R&D | . (not estimable)
2#2#Principal, Social Sci | .2005558 .0065126 30.79 0.000 .1877913 .2133204
2#2#Senior, HR | .1753334 .0213475 8.21 0.000 .1334932 .2171737
2#2#Senior, Marketing | .2294681 .0107672 21.31 0.000 .2083647 .2505714
2#2#Senior, R&D | .1929605 .0085814 22.49 0.000 .1761413 .2097797
2#2#Senior, Social Sci | .1560261 .0107474 14.52 0.000 .1349615 .1770907
2#3#Principal, HR | . (not estimable)
2#3#Principal, Marketing | .1963641 .0141295 13.90 0.000 .1686707 .2240575
2#3#Principal, R&D | . (not estimable)
2#3#Principal, Social Sci | .215443 .0060046 35.88 0.000 .2036742 .2272118
2#3#Senior, HR | .1980594 .0183081 10.82 0.000 .1621763 .2339426
2#3#Senior, Marketing | .2380796 .0099376 23.96 0.000 .2186022 .257557
2#3#Senior, R&D | .2044586 .0079183 25.82 0.000 .188939 .2199783
2#3#Senior, Social Sci | .1680772 .0104484 16.09 0.000 .1475987 .1885558
2#4#Principal, HR | . (not estimable)
2#4#Principal, Marketing | .1983202 .0141847 13.98 0.000 .1705187 .2261218
2#4#Principal, R&D | . (not estimable)
2#4#Principal, Social Sci | .2288264 .0058645 39.02 0.000 .2173321 .2403207
2#4#Senior, HR | .2226261 .0172002 12.94 0.000 .1889142 .2563379
2#4#Senior, Marketing | .2468041 .0096882 25.47 0.000 .2278155 .2657927
2#4#Senior, R&D | .2162111 .0077747 27.81 0.000 .2009729 .2314493
2#4#Senior, Social Sci | .18064 .0105847 17.07 0.000 .1598943 .2013857
2#5#Principal, HR | . (not estimable)
2#5#Principal, Marketing | .2002807 .0152473 13.14 0.000 .1703965 .230165
2#5#Principal, R&D | . (not estimable)
2#5#Principal, Social Sci | .2409405 .0062712 38.42 0.000 .2286491 .2532319
2#5#Senior, HR | .2489863 .0201027 12.39 0.000 .2095858 .2883868
2#5#Senior, Marketing | .2556366 .0101662 25.15 0.000 .2357112 .2755619
2#5#Senior, R&D | .2282094 .0083375 27.37 0.000 .2118682 .2445505
2#5#Senior, Social Sci | .1937078 .0113197 17.11 0.000 .1715216 .215894
2#6#Principal, HR | . (not estimable)
2#6#Principal, Marketing | .2022455 .01717 11.78 0.000 .1685929 .2358982
2#6#Principal, R&D | . (not estimable)
2#6#Principal, Social Sci | .2520384 .0072581 34.72 0.000 .2378128 .2662641
2#6#Senior, HR | .2770538 .027118 10.22 0.000 .2239034 .3302042
2#6#Senior, Marketing | .2645721 .0113736 23.26 0.000 .2422803 .2868639
2#6#Senior, R&D | .2404452 .0096269 24.98 0.000 .2215768 .2593136
2#6#Senior, Social Sci | .2072722 .0127283 16.28 0.000 .1823252 .2322191
2#7#Principal, HR | . (not estimable)
2#7#Principal, Marketing | .2042145 .019737 10.35 0.000 .1655307 .2428984
2#7#Principal, R&D | . (not estimable)
2#7#Principal, Social Sci | .2623567 .0087208 30.08 0.000 .2452643 .2794491
2#7#Senior, HR | .3067008 .0369607 8.30 0.000 .2342592 .3791425
2#7#Senior, Marketing | .2736058 .0131917 20.74 0.000 .2477506 .2994611
2#7#Senior, R&D | .2529104 .011524 21.95 0.000 .2303238 .2754969
2#7#Senior, Social Sci | .2213227 .0147861 14.97 0.000 .1923425 .250303
3#1#Principal, HR | . (not estimable)
3#1#Principal, Marketing | .1492273 .0149122 10.01 0.000 .1199999 .1784548
3#1#Principal, R&D | . (not estimable)
3#1#Principal, Social Sci | .1908946 .0070506 27.07 0.000 .1770757 .2047136
3#1#Senior, HR | .1533063 .0269603 5.69 0.000 .100465 .2061475
3#1#Senior, Marketing | .1385269 .0101728 13.62 0.000 .1185885 .1584653
3#1#Senior, R&D | .1291567 .0089419 14.44 0.000 .111631 .1466824
3#1#Senior, Social Sci | .1584279 .0119919 13.21 0.000 .1349242 .1819315
3#2#Principal, HR | . (not estimable)
3#2#Principal, Marketing | .1463293 .0135234 10.82 0.000 .119824 .1728347
3#2#Principal, R&D | . (not estimable)
3#2#Principal, Social Sci | .1437746 .0041703 34.48 0.000 .135601 .1519481
3#2#Senior, HR | .1355414 .019277 7.03 0.000 .0977592 .1733236
3#2#Senior, Marketing | .1298002 .0088667 14.64 0.000 .1124218 .1471786
3#2#Senior, R&D | .1156741 .0073956 15.64 0.000 .101179 .1301693
3#2#Senior, Social Sci | .143199 .0102279 14.00 0.000 .1231528 .1632453
3#3#Principal, HR | . (not estimable)
3#3#Principal, Marketing | .1434765 .0129078 11.12 0.000 .1181776 .1687755
3#3#Principal, R&D | . (not estimable)
3#3#Principal, Social Sci | .1067258 .0033748 31.62 0.000 .1001113 .1133402
3#3#Senior, HR | .1192516 .0144499 8.25 0.000 .0909303 .147573
3#3#Senior, Marketing | .1215168 .008054 15.09 0.000 .1057313 .1373023
3#3#Senior, R&D | .1033809 .0065696 15.74 0.000 .0905047 .1162571
3#3#Senior, Social Sci | .1291236 .0092939 13.89 0.000 .110908 .1473393
3#4#Principal, HR | . (not estimable)
3#4#Principal, Marketing | .1406686 .0130936 10.74 0.000 .1150055 .1663317
3#4#Principal, R&D | . (not estimable)
3#4#Principal, Social Sci | .0783309 .003537 22.15 0.000 .0713986 .0852633
3#4#Senior, HR | .1044014 .0127908 8.16 0.000 .0793318 .1294709
3#4#Senior, Marketing | .1136652 .0077097 14.74 0.000 .0985544 .1287759
3#4#Senior, R&D | .0922104 .0063246 14.58 0.000 .0798145 .1046063
3#4#Senior, Social Sci | .1161622 .0090283 12.87 0.000 .0984671 .1338574
3#5#Principal, HR | . (not estimable)
3#5#Principal, Marketing | .1379052 .0139769 9.87 0.000 .1105109 .1652995
3#5#Principal, R&D | . (not estimable)
3#5#Principal, Social Sci | .0569937 .0036408 15.65 0.000 .0498579 .0641296
3#5#Senior, HR | .0909425 .013445 6.76 0.000 .0645908 .1172942
3#5#Senior, Marketing | .1062329 .0077454 13.72 0.000 .0910522 .1214135
3#5#Senior, R&D | .0820923 .0064307 12.77 0.000 .0694883 .0946963
3#5#Senior, Social Sci | .1042683 .0091769 11.36 0.000 .0862819 .1222547
3#6#Principal, HR | . (not estimable)
3#6#Principal, Marketing | .135186 .0153761 8.79 0.000 .1050493 .1653226
3#6#Principal, R&D | . (not estimable)
3#6#Principal, Social Sci | .0411978 .003493 11.79 0.000 .0343518 .0480439
3#6#Senior, HR | .0788165 .0149149 5.28 0.000 .0495839 .1080491
3#6#Senior, Marketing | .0992067 .0080364 12.34 0.000 .0834556 .1149577
3#6#Senior, R&D | .0729545 .0066772 10.93 0.000 .0598674 .0860416
3#6#Senior, Social Sci | .09339 .0095025 9.83 0.000 .0747654 .1120146
3#7#Principal, HR | . (not estimable)
3#7#Principal, Marketing | .1325106 .0171124 7.74 0.000 .0989709 .1660503
3#7#Principal, R&D | . (not estimable)
3#7#Principal, Social Sci | .029634 .0031621 9.37 0.000 .0234363 .0358316
3#7#Senior, HR | .0679562 .0162829 4.17 0.000 .0360424 .0998701
3#7#Senior, Marketing | .0925727 .008465 10.94 0.000 .0759816 .1091638
3#7#Senior, R&D | .0647247 .0069292 9.34 0.000 .0511438 .0783056
3#7#Senior, Social Sci | .0834717 .0098446 8.48 0.000 .0641767 .1027668
----------------------------------------------------------------------------------------------------
Code:
. ***KEEP "PRINCIPAL, HR" (NOT ESTIMABLE IN INTERACTION MODEL), AND CAN GET ESTIMATES
.
. preserve
. keep if position_department_n==2
(36,686 observations deleted)
. mlogit gender_n year, rrr vce(cluster person)
Iteration 0: log pseudolikelihood = -4186.9752
Iteration 1: log pseudolikelihood = -4129.9265
Iteration 2: log pseudolikelihood = -4128.0176
Iteration 3: log pseudolikelihood = -4128.0128
Iteration 4: log pseudolikelihood = -4128.0128
Multinomial logistic regression Number of obs = 5,531
Wald chi2(2) = 89.33
Prob > chi2 = 0.0000
Log pseudolikelihood = -4128.0128 Pseudo R2 = 0.0141
(Std. Err. adjusted for 2,903 clusters in person)
------------------------------------------------------------------------------
| Robust
gender_n | RRR Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
F | (base outcome)
-------------+----------------------------------------------------------------
M |
year | 1.087405 .0201972 4.51 0.000 1.048531 1.12772
_cons | 1.88e-74 7.01e-73 -4.55 0.000 3.1e-106 1.13e-42
-------------+----------------------------------------------------------------
U |
year | .7736713 .0254284 -7.81 0.000 .7254038 .8251504
_cons | 9.7e+222 6.4e+224 7.78 0.000 6.3e+166 1.5e+279
------------------------------------------------------------------------------
Note: _cons estimates baseline relative risk for each outcome.
. margins, at(year = (2007(1)2013)) post
Adjusted predictions Number of obs = 5,531
Model VCE : Robust
1._predict : Pr(gender_n==F), predict(pr outcome(4))
2._predict : Pr(gender_n==M), predict(pr outcome(5))
3._predict : Pr(gender_n==U), predict(pr outcome(6))
1._at : year = 2007
2._at : year = 2008
3._at : year = 2009
4._at : year = 2010
5._at : year = 2011
6._at : year = 2012
7._at : year = 2013
------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_predict#_at |
1 1 | .7079095 .0128375 55.14 0.000 .6827484 .7330706
1 2 | .72283 .010783 67.03 0.000 .7016956 .7439643
1 3 | .7317935 .0099463 73.57 0.000 .7122992 .7512879
1 4 | .7355647 .0100209 73.40 0.000 .715924 .7552053
1 5 | .7349064 .0109203 67.30 0.000 .7135031 .7563098
1 6 | .7305254 .012644 57.78 0.000 .7057437 .7553072
1 7 | .7230448 .0151414 47.75 0.000 .6933681 .7527215
2 1 | .1449213 .0098004 14.79 0.000 .1257128 .1641297
2 2 | .1609096 .0091338 17.62 0.000 .1430076 .1788116
2 3 | .1771437 .0087361 20.28 0.000 .1600212 .1942662
2 4 | .1936196 .0089405 21.66 0.000 .1760965 .2111428
2 5 | .2103545 .0100154 21.00 0.000 .1907247 .2299844
2 6 | .227377 .0120018 18.95 0.000 .203854 .2509001
2 7 | .2447191 .0147649 16.57 0.000 .2157804 .2736577
3 1 | .1471693 .0101286 14.53 0.000 .1273175 .167021
3 2 | .1162604 .0071631 16.23 0.000 .102221 .1302999
3 3 | .0910628 .006052 15.05 0.000 .079201 .1029245
3 4 | .0708157 .005874 12.06 0.000 .0593029 .0823285
3 5 | .054739 .0058379 9.38 0.000 .043297 .0661811
3 6 | .0420976 .00565 7.45 0.000 .0310238 .0531714
3 7 | .0322362 .005283 6.10 0.000 .0218816 .0425907
------------------------------------------------------------------------------
. restore
