Interaction terms in collapsed data.

[Sumedha Gupta]

Dear All,

I have individual level data on poisonings in the 50 US states and I want to study the impact of state regulations on drug dispensing on incidence of poisonings. My raw data of individual poisoning incidences includes a dummy for whether the state adopted drug dispensing regulations (treatMA), a dummy for whether the poisoning episode included multiple substances (poly) and an interaction dummy post that takes a value of 1 if the episode occurred in a state that adopted regulation (treatMA=1) and it is the period after the new regulation. My raw data looks as follows:

* Example generated by -dataex-. To install: ssc install dataex
clear
input double caseid str3 state float(qtr poly) byte treatMA float post
   53202011 "CT"  1 1 1 .
  123362017 "NY" 25 1 1 1
  573202012 "CT"  5 1 1 .
  803362014 "NY" 13 1 1 1
  893362014 "NY" 13 1 1 1
 1503362017 "NY" 25 1 1 1
 2353362011 "NY"  1 1 1 .
 2433362011 "NY"  1 1 1 .
 3813202012 "CT"  5 1 1 .
 4273202012 "CT"  5 1 1 .
 4523362011 "NY"  1 1 1 .
 4913362014 "NY" 13 1 1 1
 4973202012 "CT"  5 1 1 .
 5043622011 "NY"  1 1 1 .
 5113202012 "CT"  5 1 1 .
 5143202012 "CT"  5 1 1 .
 5143622011 "NY"  1 1 1 .
 5743362013 "NY"  9 1 1 .
 6233622011 "NY"  1 1 1 .
 6713622011 "NY"  1 1 1 .
 6753202012 "CT"  5 . 1 .
 6753622011 "NY"  1 1 1 .
 6793622011 "NY"  1 1 1 .
 6863622011 "NY"  1 1 1 .
 6923202012 "CT"  5 1 1 .
 6973362011 "NY"  1 1 1 .
 6993362017 "NY" 25 1 1 1
 7103202012 "CT"  5 1 1 .
 7513202011 "CT"  1 1 1 .
 7543202012 "CT"  5 1 1 .
 7573362013 "NY"  9 1 1 .
 7613202011 "CT"  1 1 1 .
 7623362013 "NY"  9 1 1 .
 7643362011 "NY"  1 1 1 .
 8233202012 "CT"  5 1 1 .
 8273362014 "NY" 13 1 1 1
 8363362017 "NY" 25 1 1 1
 8683362017 "NY" 25 1 1 1
 8973362014 "NY" 13 1 1 1
 8973622011 "NY"  1 1 1 .
 9013202012 "CT"  5 . 1 .
 9223362014 "NY" 13 1 1 1
 9613362014 "NY" 13 1 1 1
 9673362013 "NY"  9 1 1 .
 9683362013 "NY"  9 1 1 .
 9753362017 "NY" 25 1 1 1
 9853362017 "NY" 25 1 1 1
 9873202012 "CT"  5 1 1 .
 9903362017 "NY" 25 1 1 1
10003622011 "NY"  1 1 1 .
10143362017 "NY" 25 1 1 1
10303362011 "NY"  1 . 1 .
10773622011 "NY"  1 1 1 .
12103362011 "NY"  1 1 1 .
12103622011 "NY"  1 1 1 .
12473622011 "NY"  1 1 1 .
12543362017 "NY" 25 1 1 1
12893202012 "CT"  5 . 1 .
13143362011 "NY"  1 1 1 .
13393362011 "NY"  1 1 1 .
13683202011 "CT"  1 1 1 .
13763362017 "NY" 25 1 1 1
14163202011 "CT"  1 1 1 .
14343622011 "NY"  1 . 1 .
14753362017 "NY" 25 . 1 1
15183202012 "CT"  5 1 1 .
15263202011 "CT"  1 1 1 .
15883362013 "NY"  9 1 1 .
15913622011 "NY"  1 1 1 .
16143202011 "CT"  1 1 1 .
16413362013 "NY"  9 1 1 .
16743622011 "NY"  1 1 1 .
16923622011 "NY"  1 1 1 .
17003202011 "CT"  1 1 1 .
17343362013 "NY"  9 1 1 .
17483362017 "NY" 25 1 1 1
17663202011 "CT"  1 1 1 .
18133202011 "CT"  1 1 1 .
18213362011 "NY"  1 1 1 .
18263202011 "CT"  1 . 1 .
18343622011 "NY"  1 . 1 .
18423202012 "CT"  5 1 1 .
18793202012 "CT"  5 . 1 .
19103622011 "NY"  1 1 1 .
19153362014 "NY" 13 1 1 1
19653362014 "NY" 13 1 1 1
19793622011 "NY"  1 1 1 .
20043202012 "CT"  5 1 1 .
20243202011 "CT"  1 1 1 .
21003362017 "NY" 25 1 1 1
21623202012 "CT"  5 1 1 .
21703622011 "NY"  1 1 1 .
21763202012 "CT"  5 1 1 .
22013362013 "NY"  9 1 1 .
22063362013 "NY"  9 1 1 .
22083362017 "NY" 25 1 1 1
22093622011 "NY"  1 1 1 .
22113362013 "NY"  9 . 1 .
22223362013 "NY"  9 1 1 .
22823362011 "NY"  1 1 1 .
end

To evaluate the impact of the state regulations on the 'rates of poisonings' I collapse the data at the state-quarter level :

collapse (count) caseid (mean) treatMA post poly, by(state qtr)

and then calculate the rate of poisoning as the number of episodes per 100,000 persons in the state. This looks as follows:

* Example generated by -dataex-. To install: ssc install dataex
clear
input float rate_poisoning str5 state float qtr long poly byte treatMA float post
 .6743052 "AK" 23  10 1 0
1.6183325 "AK" 21  18 1 0
.40675375 "AK" 20   9 1 0
 .8135075 "AK" 19  12 1 0
.27135384 "AK"  9   7 1 0
 .8140616 "AK" 11  10 1 0
 1.506026 "AK"  5  14 1 0
 .9694781 "AK"  1  13 1 0
 .6790646 "AK" 13   7 1 0
1.1079749 "AK"  3  13 1 0
.54764587 "AK"  7   6 1 0
 .8214688 "AK"  6  10 1 0
1.3567692 "AK" 10  12 1 0
1.2137494 "AK" 24  12 1 0
 .8135075 "AK" 17  12 1 0
 .6845573 "AK"  8  12 1 0
1.2464718 "AK"  2  12 1 0
1.4869165 "AK" 26  15 1 0
1.2223163 "AK" 16  13 1 0
1.0865033 "AK" 14  11 1 0
1.3517423 "AK" 25  16 1 0
2.0337687 "AK" 18  16 1 0
 .8148775 "AK" 15  12 1 0
1.0788883 "AK" 22  15 1 0
 1.938956 "AK"  4  19 1 0
1.3567692 "AK" 12  15 1 0
 1.169202 "AL" 25  80 0 0
1.2919805 "AL"  3  91 0 0
1.0714668 "AL" 17  76 0 0
1.2835217 "AL" 11  93 0 0
1.3336573 "AL"  1  84 0 0
1.5694435 "AL" 14  97 0 0
 1.377256 "AL" 22  89 0 0
 1.312819 "AL"  2  91 0 0
1.0072471 "AL" 24  73 0 0
1.1100273 "AL" 23  69 0 0
1.0278031 "AL" 21  62 0 0
1.3249255 "AL" 10  94 0 0
  1.34979 "AL"  6  84 0 0
1.3456275 "AL"  9  86 0 0
1.5074917 "AL" 13  97 0 0
  1.55745 "AL"  7  98 0 0
 1.370556 "AL"  5  85 0 0
 1.236308 "AL" 19  81 0 0
1.3422872 "AL" 16  94 0 0
1.0835966 "AL"  4  72 0 0
 1.256913 "AL" 20  82 0 0
 .9684412 "AL" 18  61 0 0
 1.594051 "AL" 12 113 0 0
1.1897143 "AL" 26  72 0 0
 1.548793 "AL" 15 105 0 0
 1.515918 "AL"  8 101 0 0
1.3653027 "AR" 26  57 1 1
1.1704081 "AR" 22  53 1 0
  .986258 "AR"  2  35 1 0
 .9182402 "AR"  3  35 1 0
 .8447233 "AR" 11  35 1 0
 .5781513 "AR"  4  22 1 0
 .8468522 "AR"  6  31 1 0
 1.337609 "AR" 23  59 1 0
 .8423958 "AR" 16  36 1 0
 .6993014 "AR" 25  37 1 1
1.0072498 "AR" 18  45 1 0
1.0700874 "AR" 24  43 1 0
 .8760917 "AR" 13  38 1 0
 .8807263 "AR"  5  32 1 0
 .8447233 "AR" 10  33 1 0
  .779104 "AR"  8  32 1 0
 .8109344 "AR"  9  33 1 0
 .8468522 "AR"  7  33 1 0
 .5728292 "AR" 14  23 1 0
1.6115998 "AR" 19  64 1 0
 .8729499 "AR" 17  41 1 0
 .9460901 "AR" 12  33 1 0
1.2038482 "AR" 21  56 1 0
 .7076125 "AR" 15  33 1 0
 .7481958 "AR"  1  30 1 0
1.3429998 "AR" 20  54 1 0
1.5592886 "AZ" 14 151 1 0
1.3170226 "AZ" 19 142 1 0
1.4470392 "AZ" 25 142 1 0
1.4946705 "AZ"  7 141 1 0
1.5693723 "AZ" 23 148 1 0
1.5071592 "AZ"  9 140 1 0
 1.591103 "AZ"  1 150 1 0
1.2810854 "AZ" 12 116 1 0
 1.513865 "AZ"  4 138 1 0
1.8302088 "AZ"  6 176 1 0
 1.468587 "AZ" 22 141 1 0
1.4256353 "AZ" 16 127 1 0
  1.61869 "AZ" 15 169 1 0
1.4318013 "AZ" 10 130 1 0
 1.295812 "AZ" 21 119 1 0
 1.331656 "AZ" 20 129 1 0
 1.582517 "AZ" 11 134 1 0
  1.40316 "AZ"  5 144 1 0
1.6837885 "AZ"  3 159 1 0
1.4489152 "AZ"  8 130 1 0
1.3901905 "AZ" 17 132 1 0
 1.336533 "AZ" 13 122 1 0
end

So now I have a panel for the 50 US states for 26 quarters each. To estimate the impact of the new regulation on the rate of poisonings I regress:

reg

rate_poisoning treatMA post i.qtr i.state [aweight=population], vce(cluster state)

I find:

(Std. Err. adjusted for 47 clusters in state)
----------------------------------------------------------------------------------------
| Robust
narc_nocod2 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-----------------------+----------------------------------------------------------------
post | .0987154 .035155 2.81 0.007 .027952 .1694787
treatMA | 2.840195 4.95225 0.57 0.569 -7.128167 12.80856

-----------------------+----------------------------------------------------------------



Next, I want to see if the increase in the rate of poisonings is driven by the incidence of poly-drug poisonings. The poly variable is simple the count of the poly-drug poisoning episodes in the state and not a *rate* per 100,000 persons like the outcome variable. For this I estimate:

reg

rate_poisoning treatMA post##poly i.qtr i.state [aweight=population], vce(cluster state)

and get:

(Std. Err. adjusted for 47 clusters in state)
----------------------------------------------------------------------------------------
| Robust
narc_nocod2 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-----------------------+----------------------------------------------------------------
post | .0040671 .0660497 0.06 0.951 -.1288841 .1370183
poly | .0055046 .0011748 4.69 0.000 .0031399 .0078693
poly_post | .0004862 .0005581 0.87 0.388 -.0006371 .0016096
treatMA | 2.335998 2.621396 0.89 0.377 -2.9406 7.612595

-----------------------+----------------------------------------------------------------

However, I am not sure if the interaction term really captures that? I will appreciate any direction I may get to specify a model that helps me capture that the increase in the poisonings rate is driven by an increase in the poly drug poisonings following state regulation.

Sorry for the long post but I wanted to share the data and output.

Thank you in advance,
Sincerely,
Sumedha.

[Phil Bromiley]

You didn't get a quick response. You'll increase your chances of a useful answer by following the FAQ on asking questions - provide Stata code in code delimiters, readable Stata output, and sample data using dataex.

Did the change hit all states or just some? If some, then you could use a difference-in-differences design. I'm surprised to see reg output without a constant (when you have not put in noconstant as an option). I'm not sure why you don't normalize poly by state population - everything else is normalized.

You need to use margins after the regression to understand the results. I'd also see what happens if you include poly in the estimate without the interaction. I'm finding the difference between the two sets of estimates troubling so I'd want to look closer.

There is a problem with poly drug afterwards as an explanatory variable. By construction the same poly drug and y dv are correlated (since poly drug is one of the categories of poisoning. So you might consider a mediated model rather than moderated where post influences poly and poly and post influence the dv or some such.

[Sumedha Gupta]

Dear Prof. Bromiley,

Thank you for your very helpful response. I am sorry my post was not clear and am going to give it another shot. Since I included the sample data using dataex, let me provide the stata code in code delimiters and readable stat output.

I collapsed the raw individual level data on poisoning episodes to create a state-quarter panel as follows:

collapse (count) caseid (mean) treatMA post poly, by(state qtr)

Thereafter, I created normalized rates of poisonings and poly-drug poisonings (following your previous message) per 100,000 persons in the state as follows:

rate_poisoning=(caseid/popestimate)*100000
poly_rate=(poly/popestimate)*100000

Since different states implemented the treatment at different times I estimate a simple difference-in-difference model as follows:

reg rate_poisoning treatMA post i.qtr i.state [aweight=population], vce(cluster state)

Here the coefficient on *post* can be interpreted as the differene-in-difference estimate. I get the following output:


(analytic weights assumed)
(sum of wgt is 7.6912e+09)
note: 51.stateFIPS omitted because of collinearity
note: 53.stateFIPS omitted because of collinearity
note: 54.stateFIPS omitted because of collinearity
note: 55.stateFIPS omitted because of collinearity
note: 55.stateFIPS#c.qtr omitted because of collinearity
note: 55.stateFIPS#c.qtrsq omitted because of collinearity

Linear regression Number of obs = 1,128
F(29, 46) = .
Prob > F = .
R-squared = 0.8880
Root MSE = .073

(Std. Err. adjusted for 47 clusters in state)

Robust
lnnarc_nocod2 Coef. Std. Err. t P>t [95% Conf. Interval]

post .0539737 .0154946 3.48 0.001 .0227847 .0851627
treatMA 1.064165 2.182869 0.49 0.628 -3.329722 5.458052
qavg_pct_lf_unemp -.0026507 .0103623 -0.26 0.799 -.023509 .0182075
pct_lhs .1987338 1.77678 0.11 0.911 -3.377738 3.775206
pct_hs -.0710482 1.42461 -0.05 0.960 -2.938639 2.796543
perc_black -.0379206 .1605073 -0.24 0.814 -.361005 .2851638
perc_nonwhite .0089682 .1246781 0.07 0.943 -.2419958 .2599322
pctmale 45.1515 43.99797 1.03 0.310 -43.41182 133.7148
pctover65 24.92339 11.08235 2.25 0.029 2.615776 47.23099
state_share_rural_2010 -5.391026 110.5444 -0.05 0.961 -227.9055 217.1234
md_100000 -.0126277 .0373142 -0.34 0.737 -.0877372 .0624819
pa_100000 -.0116365 .1093813 -0.11 0.916 -.2318095 .2085366
rn_100000 .00443 .0116301 0.38 0.705 -.0189801 .0278401

qtr
2 -.0176234 .0148933 -1.18 0.243 -.047602 .0123553
3 -.0101236 .0170314 -0.59 0.555 -.044406 .0241587
4 -.0487586 .0215127 -2.27 0.028 -.0920615 -.0054556
5 -.1656895 .0625692 -2.65 0.011 -.2916349 -.0397442
6 -.1976432 .0649383 -3.04 0.004 -.3283572 -.0669292
7 -.1991956 .0638959 -3.12 0.003 -.3278114 -.0705799
8 -.2314979 .0671996 -3.44 0.001 -.3667637 -.0962321
9 -.33933 .1198866 -2.83 0.007 -.5806492 -.0980107
10 -.3340309 .1195809 -2.79 0.008 -.5747347 -.0933271
11 -.3552928 .1237298 -2.87 0.006 -.6043479 -.1062377
12 -.4001864 .1223429 -3.27 0.002 -.6464499 -.153923
13 -.5183838 .1772166 -2.93 0.005 -.8751023 -.1616652
14 -.5106039 .1790296 -2.85 0.006 -.8709719 -.1502359
15 -.487224 .1794408 -2.72 0.009 -.8484196 -.1260285
16 -.5239069 .1754596 -2.99 0.005 -.8770888 -.1707249
17 -.6493742 .231227 -2.81 0.007 -1.11481 -.1839383
18 -.6179051 .2345983 -2.63 0.011 -1.090127 -.1456832
19 -.6107674 .2362067 -2.59 0.013 -1.086227 -.135308
20 -.6458752 .2360453 -2.74 0.009 -1.12101 -.1707407
21 -.725385 .2923069 -2.48 0.017 -1.313768 -.1370017
22 -.7007621 .2929017 -2.39 0.021 -1.290343 -.1111815
23 -.7061979 .2954119 -2.39 0.021 -1.300831 -.1115647
24 -.7123607 .3001499 -2.37 0.022 -1.316531 -.1081904

stateFIPS
2 .6695943 13.55937 0.05 0.961 -26.62401 27.9632
4 -2.586268 19.72235 -0.13 0.896 -42.28531 37.11277
5 -1.595819 3.715981 -0.43 0.670 -9.0757 5.884062
6 -3.361057 25.80293 -0.13 0.897 -55.29966 48.57754
8 .2261894 3.732997 0.06 0.952 -7.287945 7.740324
9 -.2102147 12.87839 -0.02 0.987 -26.13307 25.71264
10 -1.864615 19.76104 -0.09 0.925 -41.64153 37.9123
12 -1.378922 25.66031 -0.05 0.957 -53.03045 50.27261
13 -.0996623 11.83305 -0.01 0.993 -23.91835 23.71903
15 -1.655602 11.59022 -0.14 0.887 -24.9855 21.6743
16 .0138756 5.08917 0.00 0.998 -10.23009 10.25784
17 -1.781339 18.45858 -0.10 0.924 -38.93653 35.37385
18 -1.507275 14.63249 -0.10 0.918 -30.96094 27.94639
19 .3610417 7.621292 0.05 0.962 -14.97982 15.70191
20 -.6460091 1.722396 -0.38 0.709 -4.113013 2.820995
21 -.9963165 3.86488 -0.26 0.798 -8.775916 6.783283
22 -.8390934 20.73189 -0.04 0.968 -42.57023 40.89204
23 1.761387 34.42728 0.05 0.959 -67.53713 71.0599
24 1.355601 11.39045 0.12 0.906 -21.57218 24.28338
25 -.7571422 14.03236 -0.05 0.957 -29.00281 27.48853
26 1.231085 3.300062 0.37 0.711 -5.411596 7.873766
27 -1.318289 6.720508 -0.20 0.845 -14.84597 12.20939
28 -.0376315 7.639979 -0.00 0.996 -15.41611 15.34085
29 -.2373231 4.202727 -0.06 0.955 -8.696974 8.222328
30 1.178204 24.22647 0.05 0.961 -47.58716 49.94357
31 -1.301104 2.54043 -0.51 0.611 -6.414725 3.812517
32 -2.557716 30.9385 -0.08 0.934 -64.83368 59.71824
33 -.2130638 16.7625 -0.01 0.990 -33.95423 33.5281
34 -.9015866 24.58211 -0.04 0.971 -50.3828 48.57963
35 -1.695537 12.1087 -0.14 0.889 -26.06909 22.67802
36 -.0247109 18.24863 -0.00 0.999 -36.75731 36.70789
37 .3974667 3.388033 0.12 0.907 -6.422289 7.217222
39 -1.063536 15.96516 -0.07 0.947 -33.19975 31.07267
40 -.5808873 3.941486 -0.15 0.883 -8.514687 7.352912
41 .5836962 1.391772 0.42 0.677 -2.217795 3.385187
42 -.4799974 18.10344 -0.03 0.979 -36.92033 35.96034
44 -2.025182 23.84781 -0.08 0.933 -50.02834 45.97798
45 -1.311868 4.671179 -0.28 0.780 -10.71446 8.090728
46 -2.833711 11.27282 -0.25 0.803 -25.52471 19.85729
47 -1.154388 8.98342 -0.13 0.898 -19.23707 16.9283
48 -2.345647 23.10637 -0.10 0.920 -48.85636 44.16506
49 -.7899106 10.10336 -0.08 0.938 -21.12692 19.5471
51 0 (omitted)
53 0 (omitted)
54 0 (omitted)
55 0 (omitted)

stateFIPS#c.qtr
1 .041542 .0038231 10.87 0.000 .0338466 .0492375
2 -.0172247 .0216013 -0.80 0.429 -.0607058 .0262564
4 .0024807 .0048476 0.51 0.611 -.007277 .0122385
5 .0133284 .002943 4.53 0.000 .0074045 .0192524
6 .0313367 .0054744 5.72 0.000 .0203172 .0423561
8 .0066564 .0118604 0.56 0.577 -.0172173 .0305301
9 .0554549 .004207 13.18 0.000 .0469866 .0639231
10 .0042682 .0090489 0.47 0.639 -.0139463 .0224827
12 -.0200802 .0042251 -4.75 0.000 -.0285849 -.0115756
13 -.0046926 .0052798 -0.89 0.379 -.0153203 .0059351
15 .022357 .019929 1.12 0.268 -.0177579 .0624719
16 .0577198 .0042853 13.47 0.000 .0490938 .0663457
17 .0351813 .0022174 15.87 0.000 .030718 .0396446
18 .0177329 .0028728 6.17 0.000 .0119503 .0235156
19 .0262233 .0046888 5.59 0.000 .0167851 .0356614
20 .0356955 .0060296 5.92 0.000 .0235584 .0478325
21 -.0348935 .0045681 -7.64 0.000 -.0440886 -.0256984
22 .0431711 .0050762 8.50 0.000 .0329533 .0533889
23 .0461521 .0090271 5.11 0.000 .0279815 .0643227
24 -.0216174 .0094574 -2.29 0.027 -.0406541 -.0025807
25 .0061742 .0101711 0.61 0.547 -.0142992 .0266476
26 .0218814 .0041749 5.24 0.000 .0134778 .0302851
27 .0372943 .0048276 7.73 0.000 .027577 .0470117
28 .0315015 .0027992 11.25 0.000 .025867 .037136
29 .0167904 .0030479 5.51 0.000 .0106554 .0229254
30 .0311367 .0061454 5.07 0.000 .0187667 .0435067
31 .0285436 .0069092 4.13 0.000 .0146361 .0424512
32 .0014984 .0092716 0.16 0.872 -.0171644 .0201613
33 -.0029964 .0086603 -0.35 0.731 -.0204286 .0144358
34 .0178639 .0046383 3.85 0.000 .0085275 .0272002
35 -.020299 .0074394 -2.73 0.009 -.0352737 -.0053244
36 -.0062944 .0090552 -0.70 0.490 -.0245216 .0119328
37 .0273549 .0062218 4.40 0.000 .0148311 .0398787
39 .0096971 .0046039 2.11 0.041 .0004299 .0189643
40 -.0653291 .0054796 -11.92 0.000 -.076359 -.0542993
41 -.016274 .0064291 -2.53 0.015 -.029215 -.003333
42 .041066 .0056585 7.26 0.000 .0296761 .052456
44 -.0174506 .0031519 -5.54 0.000 -.0237949 -.0111062
45 .0159864 .0074061 2.16 0.036 .0010787 .0308942
46 .0780571 .0307614 2.54 0.015 .0161376 .1399766
47 .0075209 .005702 1.32 0.194 -.0039565 .0189983
48 .0252987 .0041979 6.03 0.000 .0168489 .0337486
49 .0200457 .0081594 2.46 0.018 .0036217 .0364696
51 .0195385 .0076415 2.56 0.014 .0041569 .0349202
53 .0081446 .0079752 1.02 0.312 -.0079088 .0241979
54 -.0105567 .005173 -2.04 0.047 -.0209694 -.0001441
55 0 (omitted)

stateFIPS#c.qtrsq
1 -.0013708 .0001411 -9.71 0.000 -.0016548 -.0010867
2 .0005929 .0006133 0.97 0.339 -.0006415 .0018274
4 -.0001644 .0001162 -1.41 0.164 -.0003984 .0000695
5 .0004498 .0001018 4.42 0.000 .0002448 .0006547
6 -.0011234 .0001144 -9.82 0.000 -.0013536 -.0008931
8 -.0003792 .000172 -2.20 0.033 -.0007255 -.0000329
9 -.0016619 .0001868 -8.90 0.000 -.0020378 -.0012859
10 -.0001541 .0001638 -0.94 0.352 -.0004839 .0001757
12 .0005416 .0001701 3.18 0.003 .0001992 .000884
13 .0003066 .0001753 1.75 0.087 -.0000463 .0006595
15 -.0006821 .0003803 -1.79 0.079 -.0014476 .0000835
16 -.0012187 .0001439 -8.47 0.000 -.0015083 -.0009291
17 -.0006965 .00007 -9.96 0.000 -.0008374 -.0005557
18 -.0003839 .0000917 -4.19 0.000 -.0005685 -.0001994
19 -.000236 .0000479 -4.92 0.000 -.0003325 -.0001395
20 -.0008806 .0001633 -5.39 0.000 -.0012092 -.000552
21 .0008894 .0001623 5.48 0.000 .0005628 .0012161
22 -.0009484 .000145 -6.54 0.000 -.0012402 -.0006565
23 -.0019209 .0002118 -9.07 0.000 -.0023471 -.0014946
24 .0005873 .0002302 2.55 0.014 .000124 .0010506
25 -.0004127 .0001676 -2.46 0.018 -.00075 -.0000754
26 -.0010259 .0000782 -13.13 0.000 -.0011832 -.0008686
27 -.000904 .0000951 -9.51 0.000 -.0010953 -.0007127
28 -.0006021 .0002196 -2.74 0.009 -.0010442 -.0001601
29 -.0004086 .000091 -4.49 0.000 -.0005916 -.0002255
30 -.0013977 .0001037 -13.48 0.000 -.0016064 -.0011891
31 -.0005668 .0000975 -5.81 0.000 -.000763 -.0003706
32 .0000794 .0002159 0.37 0.715 -.0003551 .0005139
33 -.0000903 .000164 -0.55 0.584 -.0004204 .0002398
34 -.0006948 .0001497 -4.64 0.000 -.000996 -.0003935
35 .000476 .0002024 2.35 0.023 .0000686 .0008833
36 .0000973 .0002258 0.43 0.668 -.0003571 .0005518
37 -.0008274 .000148 -5.59 0.000 -.0011254 -.0005295
39 -.0004424 .0001544 -2.87 0.006 -.0007531 -.0001317
40 .0012975 .0002112 6.14 0.000 .0008723 .0017227
41 .0005239 .000251 2.09 0.042 .0000187 .0010291
42 -.0010879 .0001344 -8.09 0.000 -.0013584 -.0008174
44 .0007084 .0001344 5.27 0.000 .0004379 .0009789
45 -.0002933 .0001661 -1.77 0.084 -.0006276 .0000411
46 -.0022364 .000447 -5.00 0.000 -.0031362 -.0013365
47 .0001771 .0001659 1.07 0.291 -.0001569 .0005111
48 -.000848 .000115 -7.38 0.000 -.0010795 -.0006166
49 -.0004068 .0001717 -2.37 0.022 -.0007525 -.0000611
51 -.0005592 .0002235 -2.50 0.016 -.001009 -.0001094
53 -.0001941 .0001779 -1.09 0.281 -.0005521 .0001639
54 -.0007431 .0001415 -5.25 0.000 -.0010279 -.0004583
55 0 (omitted)

_cons -24.0235 38.30153 -0.63 0.534 -101.1205 53.07347



I had previously omitted the many state and quarter dummies to save space.

Next, I want to see if the rise in poly-drug poisonings is driving this increase in total poisoning calls. I agree with you that including the poly_rate as an independent variable does not make a lot of sense since poly poisonings are a part of the total poisonings and thus are highly correlated. We can see that if I run the following

reg 
rate_poisoning poly_rate treatMA post i.qtr i.state [aweight=population], vce(cluster state)

I get the following:

(analytic weights assumed)
(sum of wgt is 7.6912e+09)
note: 51.stateFIPS omitted because of collinearity
note: 53.stateFIPS omitted because of collinearity
note: 54.stateFIPS omitted because of collinearity
note: 55.stateFIPS omitted because of collinearity
note: 55.stateFIPS#c.qtr omitted because of collinearity
note: 55.stateFIPS#c.qtrsq omitted because of collinearity

Linear regression Number of obs = 1,128
F(30, 46) = .
Prob > F = .
R-squared = 0.9927
Root MSE = .01866

(Std. Err. adjusted for 47 clusters in state)

Robust
lnnarc_nocod2 Coef. Std. Err. t P>t [95% Conf. Interval]

post .0108377 .0050614 2.14 0.038 .0006496 .0210257
poly_rate .4685614 .0194583 24.08 0.000 .4293938 .5077289
treatMA -.5225981 .4154362 -1.26 0.215 -1.358828 .3136316
qavg_pct_lf_unemp .0016073 .0022838 0.70 0.485 -.0029899 .0062044
pct_lhs -.4943263 .458107 -1.08 0.286 -1.416448 .4277953
pct_hs -.404921 .3492784 -1.16 0.252 -1.107982 .2981399
perc_black .002767 .0526817 0.05 0.958 -.1032758 .1088099
perc_nonwhite -.0034352 .0448892 -0.08 0.939 -.0937926 .0869221
pctmale 4.943127 11.41753 0.43 0.667 -18.03918 27.92543
pctover65 2.956875 2.666321 1.11 0.273 -2.410151 8.3239
state_share_rural_2010 30.15746 27.54142 1.09 0.279 -25.28054 85.59547
md_100000 .0098038 .0085815 1.14 0.259 -.0074698 .0270775
pa_100000 -.0062798 .0173351 -0.36 0.719 -.0411735 .0286139
rn_100000 -.0020075 .0020956 -0.96 0.343 -.0062258 .0022108

qtr
2 -.0033249 .0038611 -0.86 0.394 -.0110969 .0044471
3 -.0026072 .0045351 -0.57 0.568 -.0117358 .0065214
4 -.0106235 .0036307 -2.93 0.005 -.0179318 -.0033152
5 -.0229169 .0148567 -1.54 0.130 -.0528219 .0069882
6 -.0285644 .0152701 -1.87 0.068 -.0593015 .0021728
7 -.0308226 .0162067 -1.90 0.063 -.063445 .0017997
8 -.0337278 .0155266 -2.17 0.035 -.0649813 -.0024744
9 -.0503634 .029519 -1.71 0.095 -.109782 .0090552
10 -.0502561 .0288509 -1.74 0.088 -.10833 .0078178
11 -.0488494 .0283782 -1.72 0.092 -.1059717 .0082729
12 -.0612609 .0290315 -2.11 0.040 -.1196983 -.0028235
13 -.0674435 .0419199 -1.61 0.114 -.151824 .016937
14 -.0695328 .0415997 -1.67 0.101 -.1532688 .0142031
15 -.0685982 .0414244 -1.66 0.105 -.1519813 .0147848
16 -.0720492 .0414645 -1.74 0.089 -.1555129 .0114145
17 -.084547 .0546729 -1.55 0.129 -.1945979 .0255039
18 -.0829848 .0551365 -1.51 0.139 -.1939689 .0279992
19 -.0874449 .0548063 -1.60 0.117 -.1977643 .0228744
20 -.0901794 .0549194 -1.64 0.107 -.2007264 .0203676
21 -.0901643 .0682888 -1.32 0.193 -.2276226 .047294
22 -.0915331 .0683747 -1.34 0.187 -.2291643 .0460981
23 -.0949995 .0689542 -1.38 0.175 -.2337971 .043798
24 -.0928595 .0700137 -1.33 0.191 -.2337898 .0480709

stateFIPS
2 -2.950328 3.370198 -0.88 0.386 -9.734186 3.83353
4 5.534708 4.944365 1.12 0.269 -4.417783 15.4872
5 .7617276 .5041544 1.51 0.138 -.2530826 1.776538
6 7.334804 6.372834 1.15 0.256 -5.493046 20.16265
8 .4578693 .9006561 0.51 0.614 -1.355057 2.270796
9 3.376131 3.244513 1.04 0.304 -3.154735 9.906997
10 5.079146 4.734179 1.07 0.289 -4.450262 14.60855
12 6.92968 6.554302 1.06 0.296 -6.263445 20.12281
13 3.262483 2.959024 1.10 0.276 -2.693723 9.21869
15 3.994757 2.307317 1.73 0.090 -.6496319 8.639146
16 -1.205873 1.09508 -1.10 0.277 -3.410155 .9984098
17 4.953005 4.458699 1.11 0.272 -4.02189 13.9279
18 4.030988 3.405819 1.18 0.243 -2.82457 10.88655
19 -2.074147 1.865884 -1.11 0.272 -5.829977 1.681682
20 -.4099003 .3747377 -1.09 0.280 -1.164208 .3444076
21 .9707456 .83421 1.16 0.251 -.708432 2.649923
22 5.460444 5.092904 1.07 0.289 -4.791039 15.71193
23 -9.31174 8.47446 -1.10 0.278 -26.36994 7.746463
24 2.704542 2.80574 0.96 0.340 -2.94312 8.352204
25 3.517392 3.352968 1.05 0.300 -3.231783 10.26657
26 .6477266 .8646753 0.75 0.458 -1.092774 2.388228
27 -1.754534 1.760573 -1.00 0.324 -5.298384 1.789316
28 -2.273059 2.00136 -1.14 0.262 -6.301588 1.75547
29 .7637968 .7363091 1.04 0.305 -.7183166 2.24591
30 -6.55053 5.875417 -1.11 0.271 -18.37713 5.276072
31 -.1607232 .5096346 -0.32 0.754 -1.186564 .8651181
32 8.747558 7.661579 1.14 0.259 -6.6744 24.16952
33 -4.627992 4.196356 -1.10 0.276 -13.07482 3.818836
34 6.781143 5.980356 1.13 0.263 -5.25669 18.81898
35 3.627228 3.080962 1.18 0.245 -2.574427 9.828882
36 4.965411 4.636643 1.07 0.290 -4.367666 14.29849
37 -.827971 .6052588 -1.37 0.178 -2.046294 .3903518
39 4.238833 3.74558 1.13 0.264 -3.300629 11.7783
40 1.091361 .7824731 1.39 0.170 -.4836753 2.666398
41 -.3757181 .2529063 -1.49 0.144 -.8847921 .1333559
42 4.90352 4.559268 1.08 0.288 -4.273811 14.08085
44 6.27984 5.670432 1.11 0.274 -5.134149 17.69383
45 1.096629 1.095154 1.00 0.322 -1.107801 3.301059
46 -2.573767 2.990173 -0.86 0.394 -8.592674 3.445139
47 2.440722 2.064966 1.18 0.243 -1.715839 6.597284
48 6.438287 5.80478 1.11 0.273 -5.246128 18.1227
49 2.852273 2.551951 1.12 0.270 -2.284538 7.989085
51 0 (omitted)
53 0 (omitted)
54 0 (omitted)
55 0 (omitted)

stateFIPS#c.qtr
1 .0003449 .0017546 0.20 0.845 -.0031869 .0038767
2 -.0015349 .005041 -0.30 0.762 -.011682 .0086122
4 .0050773 .0011904 4.27 0.000 .0026812 .0074734
5 -.0002586 .0005882 -0.44 0.662 -.0014426 .0009254
6 .0091429 .0019508 4.69 0.000 .0052161 .0130697
8 .0058017 .0018963 3.06 0.004 .0019847 .0096186
9 .0095947 .002591 3.70 0.001 .0043793 .0148102
10 .0015013 .0019331 0.78 0.441 -.0023899 .0053925
12 .0020396 .0012904 1.58 0.121 -.0005579 .0046371
13 .0014497 .0010518 1.38 0.175 -.0006674 .0035668
15 .0132702 .0065838 2.02 0.050 .0000178 .0265226
16 .0085403 .0027755 3.08 0.004 .0029535 .0141271
17 .0078292 .0014277 5.48 0.000 .0049555 .0107029
18 .0073641 .000649 11.35 0.000 .0060577 .0086706
19 .0055414 .0014802 3.74 0.001 .0025619 .0085208
20 .0086809 .0022523 3.85 0.000 .0041471 .0132146
21 .0079879 .0018539 4.31 0.000 .0042563 .0117196
22 .0112551 .0021384 5.26 0.000 .0069508 .0155594
23 .0068841 .003505 1.96 0.056 -.000171 .0139393
24 .0115013 .0016467 6.98 0.000 .0081866 .0148159
25 .004177 .0027439 1.52 0.135 -.0013462 .0097001
26 .0050686 .0015619 3.25 0.002 .0019247 .0082126
27 .0055793 .0017182 3.25 0.002 .0021209 .0090378
28 .0081355 .0012486 6.52 0.000 .0056222 .0106487
29 .0041731 .0011929 3.50 0.001 .001772 .0065742
30 .0117066 .0022305 5.25 0.000 .0072168 .0161964
31 .0022547 .001935 1.17 0.250 -.0016402 .0061495
32 .0049138 .0015523 3.17 0.003 .0017891 .0080385
33 .0015914 .0024288 0.66 0.516 -.0032974 .0064803
34 .0078698 .0016027 4.91 0.000 .0046437 .0110959
35 .0083009 .0022423 3.70 0.001 .0037873 .0128144
36 .0038909 .0016764 2.32 0.025 .0005165 .0072654
37 .0051793 .0011705 4.42 0.000 .0028231 .0075355
39 .0020356 .0016234 1.25 0.216 -.0012321 .0053034
40 .031725 .0039581 8.02 0.000 .0237577 .0396923
41 .008729 .0016412 5.32 0.000 .0054254 .0120325
42 .0114293 .0024694 4.63 0.000 .0064587 .0163998
44 .0031358 .0009592 3.27 0.002 .0012051 .0050666
45 .0042922 .0014675 2.92 0.005 .0013383 .007246
46 -.00179 .0063399 -0.28 0.779 -.0145516 .0109715
47 .0026301 .001379 1.91 0.063 -.0001457 .0054058
48 .0071639 .0015049 4.76 0.000 .0041347 .010193
49 .0103294 .0017172 6.02 0.000 .0068729 .0137859
51 .0039385 .0024392 1.61 0.113 -.0009714 .0088484
53 .0072432 .0022151 3.27 0.002 .0027844 .0117021
54 .0219415 .0017377 12.63 0.000 .0184437 .0254393
55 0 (omitted)

stateFIPS#c.qtrsq
1 .0000167 .0000803 0.21 0.836 -.0001449 .0001783
2 .0000832 .0001375 0.61 0.548 -.0001935 .0003599
4 -.0000876 .000027 -3.25 0.002 -.0001419 -.0000333
5 .0001672 .000026 6.44 0.000 .000115 .0002195
6 -.0002522 .0000587 -4.30 0.000 -.0003704 -.0001341
8 -.0001196 .0000275 -4.35 0.000 -.0001749 -.0000642
9 -.0003171 .0000937 -3.38 0.001 -.0005058 -.0001285
10 -.0000121 .0000484 -0.25 0.803 -.0001096 .0000854
12 -.0000119 .0000431 -0.28 0.783 -.0000986 .0000747
13 -3.03e-06 .0000451 -0.07 0.947 -.0000938 .0000877
15 -.0003952 .0001099 -3.60 0.001 -.0006163 -.000174
16 -.0002435 .0000538 -4.52 0.000 -.0003519 -.0001351
17 -.0001692 .0000328 -5.15 0.000 -.0002353 -.0001031
18 -.0002249 .000028 -8.02 0.000 -.0002814 -.0001685
19 -.0001469 .000012 -12.29 0.000 -.0001709 -.0001228
20 -.0002327 .0000622 -3.74 0.001 -.0003578 -.0001076
21 -.0002421 .0000515 -4.70 0.000 -.0003457 -.0001385
22 -.0002375 .0000581 -4.09 0.000 -.0003545 -.0001205
23 -.0003105 .0001062 -2.92 0.005 -.0005242 -.0000968
24 -.0001733 .0000471 -3.68 0.001 -.0002681 -.0000784
25 -.0001309 .0000563 -2.32 0.025 -.0002444 -.0000175
26 -.0000416 .000054 -0.77 0.444 -.0001502 .000067
27 -.0000906 .0000423 -2.14 0.038 -.0001758 -5.43e-06
28 -.0001847 .0000657 -2.81 0.007 -.0003169 -.0000525
29 -.0001215 .0000305 -3.98 0.000 -.000183 -.00006
30 -.0004252 .000045 -9.46 0.000 -.0005157 -.0003347
31 -.0000585 .0000383 -1.53 0.134 -.0001356 .0000187
32 -.0000162 .0000533 -0.30 0.762 -.0001236 .0000911
33 -.0000372 .0000437 -0.85 0.399 -.0001251 .0000507
34 -.0002213 .000055 -4.03 0.000 -.0003319 -.0001106
35 -.0003058 .0000643 -4.75 0.000 -.0004352 -.0001763
36 -.0001127 .0000498 -2.26 0.028 -.0002129 -.0000124
37 -.0001095 .000047 -2.33 0.024 -.000204 -.0000149
39 -.00008 .0000521 -1.54 0.131 -.0001847 .0000248
40 -.0009365 .0000833 -11.24 0.000 -.0011041 -.0007688
41 -.0001713 .0000718 -2.39 0.021 -.0003157 -.0000268
42 -.000336 .0000642 -5.23 0.000 -.0004652 -.0002067
44 -.0000759 .0000515 -1.47 0.147 -.0001796 .0000278
45 -.0000589 .0000531 -1.11 0.273 -.0001658 .0000479
46 -.000018 .0001077 -0.17 0.868 -.0002348 .0001988
47 -.0000349 .0000498 -0.70 0.486 -.0001351 .0000652
48 -.0002004 .0000489 -4.10 0.000 -.0002987 -.000102
49 -.00026 .0000503 -5.17 0.000 -.0003613 -.0001587
51 -.0000875 .0000711 -1.23 0.225 -.0002306 .0000556
53 -.0000553 .0000348 -1.59 0.119 -.0001253 .0000147
54 -.0005323 .0000418 -12.74 0.000 -.0006165 -.0004482
55 0 (omitted)

_cons 5.367915 10.49004 0.51 0.611 -15.74744 26.48327


poly_rate pretty much explains everything. If I now include the interaction that is statistically insignificant but the coefficient on poly_rate remains massive.


I do want to run a 'mediated' model. But I am not sure how to do that. Is there a particular set up/ command I can use to capture that?

I will be grateful for your help.
Sincerely,
Sumedha.