Hi all! I’m running multinomial logit models with gender as an outcome. Goal: look at gender over time for each category of position_department_n. Model has cluster standard errors to account for repeated observations within individuals.
When I include a year*position_department_n interaction, I get different predicted probabilities than if I choose a specific position_department_n and look at the trend over time. For example, first approach - 1#1#Senior, Social Sci - gives .6817881. The second approach when I only keep records of "Senior, Social Sci" and run a model with year as independent, I get _predict#_at |1 1 = .6639009.
Question: which of the two ways is the most accurate? The second one (no interaction) is easier to interpret, but not sure if that's a good enough justification to use it if the first approach is more accurate. any help is much appreciated!
More info on Data structure: There are no duplicate records across person, year, position_department_n, and gender_n. However, the same person can show up multiple times in the same year corresponding to different values of position_department_n, and same person can show up in several years. Data sample:
| person | year | position_department_n | gender_n |
| 1 | 2010 | Senior, Art | M |
| 1 | 2011 | Senior, Art | M |
| 1 | 2012 | Senior, Art | M |
| 1 | 2012 | Principal, Social Sci | M |
| 1 | 2013 | Principal, Social Sci | M |
| 1 | 2013 | Senior, Social Sci | M |
Results below:
First, I run the model with the interaction of year and position_department_n as the only explanatory variables (including the main effects led to some of the predicted probabilities not estimating):
Code:
. mlogit gender_n c.year#i.position_department_n, rrr vce(cluster person)
Iteration 0: log pseudolikelihood = -25756.382
Iteration 1: log pseudolikelihood = -25585.173
Iteration 2: log pseudolikelihood = -25583.289
Iteration 3: log pseudolikelihood = -25583.288
Multinomial logistic regression Number of obs = 31,306
Wald chi2(12) = 252.02
Prob > chi2 = 0.0000
Log pseudolikelihood = -25583.288 Pseudo R2 = 0.0067
(Std. Err. adjusted for 10,425 clusters in person)
----------------------------------------------------------------------------------------------
| Robust
gender_n | RRR Std. Err. z P>|z| [95% Conf. Interval]
-----------------------------+----------------------------------------------------------------
F | (base outcome)
-----------------------------+----------------------------------------------------------------
M |
position_department_n#c.year |
Principal, Art | 1.053355 .0092655 5.91 0.000 1.035351 1.071673
Principal, HR | 1.053391 .0092637 5.91 0.000 1.03539 1.071705
Principal, Social Sci | 1.053518 .0092623 5.93 0.000 1.03552 1.071829
Senior, Art | 1.053325 .0092646 5.91 0.000 1.035322 1.071641
Senior, HR | 1.053309 .0092623 5.91 0.000 1.03531 1.07162
Senior, Social Sci | 1.053433 .0092615 5.92 0.000 1.035436 1.071742
|
_cons | 1.19e-46 2.10e-45 -5.98 0.000 1.06e-61 1.33e-31
-----------------------------+----------------------------------------------------------------
U |
position_department_n#c.year |
Principal, Art | .8998399 .0109779 -8.65 0.000 .8785788 .9216156
Principal, HR | .8999677 .0109865 -8.63 0.000 .8786901 .9217605
Principal, Social Sci | .8998911 .0109781 -8.65 0.000 .8786297 .9216671
Senior, Art | .8996119 .0109747 -8.67 0.000 .878357 .9213811
Senior, HR | .8998544 .0109813 -8.65 0.000 .8785867 .9216369
Senior, Social Sci | .8997857 .0109742 -8.66 0.000 .8785317 .9215539
|
_cons | 2.12e+91 5.19e+92 8.58 0.000 2.90e+70 1.5e+112
----------------------------------------------------------------------------------------------
Note: _cons estimates baseline relative risk for each outcome.
. margins i.position_department_n, at(year=(2008(1)2013))
Adjusted predictions Number of obs = 31,306
Model VCE : Robust
1._predict : Pr(gender_n==F), predict(pr outcome(1))
2._predict : Pr(gender_n==M), predict(pr outcome(2))
3._predict : Pr(gender_n==U), predict(pr outcome(3))
1._at : year = 2008
2._at : year = 2009
3._at : year = 2010
4._at : year = 2011
5._at : year = 2012
6._at : year = 2013
----------------------------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-----------------------------------+----------------------------------------------------------------
_predict#_at#position_department_n |
1#1#Principal, Art | .6904148 .0146884 47.00 0.000 .6616262 .7192034
1#1#Principal, HR | .6534034 .0179981 36.30 0.000 .6181278 .688679
1#1#Principal, Social Sci | .6393116 .0117618 54.35 0.000 .6162589 .6623644
1#1#Senior, Art | .7371994 .0104295 70.68 0.000 .7167579 .7576409
1#1#Senior, HR | .6977463 .0130652 53.41 0.000 .6721391 .7233536
1#1#Senior, Social Sci | .6817881 .0087808 77.65 0.000 .664578 .6989982
1#2#Principal, Art | .6932711 .0142585 48.62 0.000 .6653249 .7212173
1#2#Principal, HR | .6583121 .0176441 37.31 0.000 .6237302 .692894
1#2#Principal, Social Sci | .6406808 .0112269 57.07 0.000 .6186766 .6626851
1#2#Senior, Art | .7366476 .0101531 72.55 0.000 .7167479 .7565474
1#2#Senior, HR | .7015478 .0126924 55.27 0.000 .6766712 .7264244
1#2#Senior, Social Sci | .6825181 .0081336 83.91 0.000 .6665765 .6984596
1#3#Principal, Art | .6948569 .0141003 49.28 0.000 .6672208 .7224929
1#3#Principal, HR | .6618178 .0175169 37.78 0.000 .6274853 .6961503
1#3#Principal, Social Sci | .6407483 .0109669 58.43 0.000 .6192537 .662243
1#3#Senior, Art | .7350899 .0101333 72.54 0.000 .715229 .7549508
1#3#Senior, HR | .7040617 .0125678 56.02 0.000 .6794293 .7286941
1#3#Senior, Social Sci | .6820508 .007796 87.49 0.000 .666771 .6973305
1#4#Principal, Art | .6952305 .0142038 48.95 0.000 .6673914 .7230695
1#4#Principal, HR | .6639706 .0176048 37.72 0.000 .6294659 .6984753
1#4#Principal, Social Sci | .6395812 .010991 58.19 0.000 .6180393 .661123
1#4#Senior, Art | .7325831 .0103738 70.62 0.000 .7122508 .7529154
1#4#Senior, HR | .705343 .012678 55.64 0.000 .6804944 .7301915
1#4#Senior, Social Sci | .6804506 .0077986 87.25 0.000 .6651656 .6957357
1#5#Principal, Art | .6944533 .0145583 47.70 0.000 .6659195 .7229871
1#5#Principal, HR | .6648276 .017899 37.14 0.000 .6297463 .699909
1#5#Principal, Social Sci | .6372502 .0113034 56.38 0.000 .615096 .6594044
1#5#Senior, Art | .729183 .0108715 67.07 0.000 .7078752 .7504908
1#5#Senior, HR | .70545 .0130121 54.21 0.000 .6799468 .7309533
1#5#Senior, Social Sci | .6777837 .0081535 83.13 0.000 .6618031 .6937643
1#6#Principal, Art | .6925886 .0151514 45.71 0.000 .6628924 .7222847
1#6#Principal, HR | .6644512 .018393 36.13 0.000 .6284016 .7005009
1#6#Principal, Social Sci | .6338283 .011899 53.27 0.000 .6105066 .6571499
1#6#Senior, Art | .7249436 .0116154 62.41 0.000 .7021779 .7477094
1#6#Senior, HR | .7044437 .0135605 51.95 0.000 .6778655 .7310219
1#6#Senior, Social Sci | .6741162 .0088449 76.22 0.000 .6567806 .6914518
2#1#Principal, Art | .175149 .0110554 15.84 0.000 .1534807 .1968173
2#1#Principal, HR | .1773813 .0134333 13.20 0.000 .1510524 .2037101
2#1#Principal, Social Sci | .2211269 .0099466 22.23 0.000 .201632 .2406218
2#1#Senior, Art | .1765052 .0088592 19.92 0.000 .1591415 .1938688
2#1#Senior, HR | .1619424 .0100195 16.16 0.000 .1423046 .1815802
2#1#Senior, Social Sci | .2005883 .0075333 26.63 0.000 .1858233 .2153533
2#2#Principal, Art | .1852574 .0113472 16.33 0.000 .1630174 .2074974
2#2#Principal, HR | .1882555 .0138436 13.60 0.000 .1611226 .2153884
2#2#Principal, Social Sci | .2334601 .0097708 23.89 0.000 .2143097 .2526105
2#2#Senior, Art | .1857781 .0089387 20.78 0.000 .1682587 .2032976
2#2#Senior, HR | .1715046 .0102093 16.80 0.000 .1514947 .1915145
2#2#Senior, Social Sci | .2115326 .0071727 29.49 0.000 .1974743 .2255908
2#3#Principal, Art | .1955882 .0117739 16.61 0.000 .1725117 .2186646
2#3#Principal, HR | .1993627 .0143567 13.89 0.000 .171224 .2275013
2#3#Principal, Social Sci | .2459803 .0097742 25.17 0.000 .2268231 .2651374
2#3#Senior, Art | .1952709 .0091886 21.25 0.000 .1772616 .2132802
2#3#Senior, HR | .1812946 .0105209 17.23 0.000 .1606741 .2019152
2#3#Senior, Social Sci | .2226828 .0070125 31.76 0.000 .2089385 .2364271
2#4#Principal, Art | .2061346 .012355 16.68 0.000 .1819193 .2303499
2#4#Principal, HR | .2106899 .0149893 14.06 0.000 .1813114 .2400684
2#4#Principal, Social Sci | .2586726 .0100062 25.85 0.000 .2390607 .2782845
2#4#Senior, Art | .2049823 .009637 21.27 0.000 .1860941 .2238705
2#4#Senior, HR | .1913067 .0109782 17.43 0.000 .1697899 .2128235
2#4#Senior, Social Sci | .2340311 .0071308 32.82 0.000 .2200549 .2480073
2#5#Principal, Art | .2168903 .0131032 16.55 0.000 .1912084 .2425721
2#5#Principal, HR | .2222253 .0157547 14.11 0.000 .1913467 .2531038
2#5#Principal, Social Sci | .271523 .0104999 25.86 0.000 .2509436 .2921024
2#5#Senior, Art | .2149108 .0102991 20.87 0.000 .1947249 .2350967
2#5#Senior, HR | .2015356 .0115993 17.37 0.000 .1788014 .2242698
2#5#Senior, Social Sci | .2455698 .0075781 32.41 0.000 .2307169 .2604226
2#6#Principal, Art | .227849 .0140246 16.25 0.000 .2003614 .2553367
2#6#Principal, HR | .2339575 .0166618 14.04 0.000 .201301 .2666141
2#6#Principal, Social Sci | .2845183 .0112657 25.26 0.000 .262438 .3065986
2#6#Senior, Art | .2250549 .0111768 20.14 0.000 .2031488 .2469609
2#6#Senior, HR | .2119763 .012395 17.10 0.000 .1876825 .2362701
2#6#Senior, Social Sci | .2572915 .0083605 30.77 0.000 .2409053 .2736778
3#1#Principal, Art | .1344362 .0120228 11.18 0.000 .1108719 .1580005
3#1#Principal, HR | .1692153 .0153947 10.99 0.000 .1390423 .1993883
3#1#Principal, Social Sci | .1395614 .0090152 15.48 0.000 .1218919 .157231
3#1#Senior, Art | .0862954 .0068023 12.69 0.000 .0729632 .0996276
3#1#Senior, HR | .1403113 .0105034 13.36 0.000 .119725 .1608975
3#1#Senior, Social Sci | .1176236 .0061717 19.06 0.000 .1055273 .1297199
3#2#Principal, Art | .1214715 .010956 11.09 0.000 .0999982 .1429449
3#2#Principal, HR | .1534324 .0143656 10.68 0.000 .1252763 .1815885
3#2#Principal, Social Sci | .1258591 .0081374 15.47 0.000 .10991 .1418081
3#2#Senior, Art | .0775743 .0061057 12.71 0.000 .0656073 .0895412
3#2#Senior, HR | .1269476 .0096766 13.12 0.000 .1079819 .1459133
3#2#Senior, Social Sci | .1059494 .005386 19.67 0.000 .095393 .1165058
3#3#Principal, Art | .1095549 .0100884 10.86 0.000 .089782 .1293279
3#3#Principal, HR | .1388195 .0135051 10.28 0.000 .11235 .1652891
3#3#Principal, Social Sci | .1132714 .0075119 15.08 0.000 .0985484 .1279944
3#3#Senior, Art | .0696392 .0055765 12.49 0.000 .0587094 .080569
3#3#Senior, HR | .1146437 .0090519 12.67 0.000 .0969023 .1323851
3#3#Senior, Social Sci | .0952664 .0048896 19.48 0.000 .085683 .1048499
3#4#Principal, Art | .0986349 .0093833 10.51 0.000 .080244 .1170259
3#4#Principal, HR | .1253395 .012776 9.81 0.000 .100299 .1503799
3#4#Principal, Social Sci | .1017463 .0070819 14.37 0.000 .087866 .1156265
3#4#Senior, Art | .0624346 .0051781 12.06 0.000 .0522856 .0725835
3#4#Senior, HR | .1033504 .0085803 12.05 0.000 .0865332 .1201675
3#4#Senior, Social Sci | .0855183 .0046211 18.51 0.000 .076461 .0945755
3#5#Principal, Art | .0886564 .0088039 10.07 0.000 .071401 .1059118
3#5#Principal, HR | .1129471 .0121433 9.30 0.000 .0891467 .1367476
3#5#Principal, Social Sci | .0912269 .0067881 13.44 0.000 .0779225 .1045312
3#5#Senior, Art | .0559062 .0048751 11.47 0.000 .0463513 .0654611
3#5#Senior, HR | .0930144 .008215 11.32 0.000 .0769133 .1091155
3#5#Senior, Social Sci | .0766465 .0045056 17.01 0.000 .0678158 .0854773
3#6#Principal, Art | .0795624 .0083167 9.57 0.000 .0632619 .0958629
3#6#Principal, HR | .1015912 .011577 8.78 0.000 .0789007 .1242817
3#6#Principal, Social Sci | .0816534 .006577 12.41 0.000 .0687627 .0945441
3#6#Senior, Art | .0500015 .0046363 10.78 0.000 .0409146 .0590884
3#6#Senior, HR | .08358 .0079158 10.56 0.000 .0680653 .0990947
3#6#Senior, Social Sci | .0685923 .0044734 15.33 0.000 .0598246 .07736
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.
Then, I choose one specific posittion_department_n = “Senior, Social Sci” and run a model with just year.
Code:
.
. preserve
. keep if position_department_n==6
(20,148 observations deleted)
. mlogit gender_n year, rrr vce(cluster person)
Iteration 0: log pseudolikelihood = -9145.8643
Iteration 1: log pseudolikelihood = -9104.1549
Iteration 2: log pseudolikelihood = -9103.6146
Iteration 3: log pseudolikelihood = -9103.6145
Multinomial logistic regression Number of obs = 11,158
Wald chi2(2) = 83.93
Prob > chi2 = 0.0000
Log pseudolikelihood = -9103.6145 Pseudo R2 = 0.0046
(Std. Err. adjusted for 5,403 clusters in person)
------------------------------------------------------------------------------
| Robust
gender_n | RRR Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
F | (base outcome)
-------------+----------------------------------------------------------------
M |
year | 1.034325 .0131964 2.65 0.008 1.008781 1.060515
_cons | 1.14e-30 2.92e-29 -2.69 0.007 1.67e-52 7.79e-09
-------------+----------------------------------------------------------------
U |
year | .8388152 .017835 -8.27 0.000 .8045775 .8745098
_cons | 3.8e+152 1.6e+154 8.22 0.000 1.6e+116 8.7e+188
------------------------------------------------------------------------------
Note: _cons estimates baseline relative risk for each outcome.
. margins, at(year = (2008(1)2013)) post
Adjusted predictions Number of obs = 11,158
Model VCE : Robust
1._predict : Pr(gender_n==F), predict(pr outcome(1))
2._predict : Pr(gender_n==M), predict(pr outcome(2))
3._predict : Pr(gender_n==U), predict(pr outcome(3))
1._at : year = 2008
2._at : year = 2009
3._at : year = 2010
4._at : year = 2011
5._at : year = 2012
6._at : year = 2013
------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_predict#_at |
1 1 | .6639009 .0097464 68.12 0.000 .6447982 .6830035
1 2 | .6735234 .0084356 79.84 0.000 .6569898 .6900569
1 3 | .6808553 .0078396 86.85 0.000 .66549 .6962206
1 4 | .6861241 .0079737 86.05 0.000 .6704959 .7017522
1 5 | .6895562 .0087716 78.61 0.000 .6723643 .7067482
1 6 | .6913693 .0101041 68.42 0.000 .6715656 .7111731
2 1 | .2040169 .0083203 24.52 0.000 .1877094 .2203245
2 2 | .2140783 .007479 28.62 0.000 .1994196 .2287369
2 3 | .2238369 .0070453 31.77 0.000 .2100284 .2376454
2 4 | .2333116 .0072142 32.34 0.000 .2191722 .2474511
2 5 | .2425272 .0080547 30.11 0.000 .2267402 .2583142
2 6 | .2515114 .0094775 26.54 0.000 .2329359 .2700869
3 1 | .1320822 .0070437 18.75 0.000 .1182767 .1458877
3 2 | .1123984 .0055449 20.27 0.000 .1015306 .1232662
3 3 | .0953078 .0049427 19.28 0.000 .0856204 .1049953
3 4 | .0805643 .0048944 16.46 0.000 .0709715 .0901571
3 5 | .0679166 .005036 13.49 0.000 .0580463 .077787
3 6 | .0571193 .0051586 11.07 0.000 .0470087 .0672299
------------------------------------------------------------------------------
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