Dear Clyde Schechter,
as I appreciate your insights regarding interaction terms, I was hoping you might help me interpret my results.
I am working on graphing the interaction results of my fixed-effect regression. (panel data: UltimateParentID Year).
I have a sample of organizations from the U.S. and Europe. I analyze the effect of DSGR_L1 on ENV.
The results indicate that the effect of DSGR_L1 is contingent upon whether the organization is based in the U.S. (positive effect, US=1) or Europe (negative effect, US=0).
I have two other variables that interact with my IV DSGR_L1. One of these variables is esg_diff_l1. Running the model with both interaction terms shows that both are significant.
So far so good, my problem, however, arises when I use the margins command to plot my interactions. Specifically, I wanted to show the moderation effect of esg_diff_l1 for both regions (US and Europe). So I started with:
Maginsplot shows that the moderation effect of esg_diff_l1 is negative for organizations from the U.S. and Europe. From a subsample analysis, I know that the effect of esg_diff_l1 is negative for the U.S. and positive for Europe. My initial thought was that my command did not tell Stata correctly to differentiate between the U.S. and Europe when creating the graph as both interaction terms are separately included in my model. Thus, I conducted a three-way interaction.
This plot indeed shows the correct relationship of esg_diff_l1 being a negative moderator for the organizations from the U.S. and a positive moderator for organizations from Europe. However, I am still a little bit confused. The, the three-way interaction term c.DSGR_L1##i.US##c.esg_diff_l1 is not statistically significant even though the term DSGR_L1##c.esg_diff_l1 is significant if I test it in the US-only sample. Can you help me with interpreting these results? In my discipline, it is common to introduce the moderation effects in isolation and then test them in combination.
Thanks in advance for your help
Patrick
as I appreciate your insights regarding interaction terms, I was hoping you might help me interpret my results.
I am working on graphing the interaction results of my fixed-effect regression. (panel data: UltimateParentID Year).
I have a sample of organizations from the U.S. and Europe. I analyze the effect of DSGR_L1 on ENV.
Code:
xtreg ENV c.DSGR_L1##i.US Totalassets_L1 ROA_L1 SustCommitt_L1 TMTESG_L1 GDP_L1 FDI_L1 i.Year, fe vce(robust)
I have two other variables that interact with my IV DSGR_L1. One of these variables is esg_diff_l1. Running the model with both interaction terms shows that both are significant.
Code:
xtreg ENV c.DSGR_L1##i.US c.DSGR_L1##c.esg_diff_l1 Totalassets_L1 ROA_L1 SustCommitt_L1 TMTESG_L1 GDP_L1 FDI_L1 i.Year, fe vce(robust).
Code:
xtreg ENV c.DSGR_L1##i.US c.DSGR_L1##c.esg_diff_l1 Totalassets_L1 ROA_L1 SustCommitt_L1 TMTESG_L1 GDP_L1 FDI_L1 i.Year, fe vce(robust) margins US, dydx(DSGR_L1) at(esg_diff_l1 = (0 50 100 150 200 250 300)) noestimcheck marginsplot
Code:
xtreg ENV c.DSGR_L1##i.US##c.esg_diff_l1 Totalassets_L1 ROA_L1 SustCommitt_L1 TMTESG_L1 GDP_L1 FDI_L1 i.Year, fe vce(robust) margins US, dydx(DSGR_L1) at(esg_diff_l1 = (0 50 100 150 200 250 300)) noestimcheck marginsplot
Code:
xtreg ENV c.DSGR_L1##i.US Totalassets_L1 ROA_L1 SustCommitt_L1 TMTESG_L1 GDP_L1 FDI_L1 i.Year, fe vce(robust) xtreg ENV c.DSGR_L1##c.esg_diff_l1 Totalassets_L1 ROA_L1 SustCommitt_L1 TMTESG_L1 GDP_L1 FDI_L1 i.Year, fe vce(robust) xtreg ENV c.DSGR_L1##i.US c.DSGR_L1##c.esg_diff_l1 Totalassets_L1 ROA_L1 SustCommitt_L1 TMTESG_L1 GDP_L1 FDI_L1 i.Year, fe vce(robust)
Patrick
Code:
* Example generated by -dataex-. To install: ssc install dataex clear input double UltimateParentID int Year double ENV float DSGR_L1 int esg_diff_l1 byte US float(Totalassets_L1 ROA_L1 SustCommitt_L1 TMTESG_L1) double(GDP_L1 FDI_L1) 4295641240 2017 5.44087665647298 0 305 1 510564992 4.485109 . . 18695110842000 2.537497659196815 4295858988 2014 34.5515083440308 18 154 0 653032000 9.450018 . . 430190979705.962 .1048621859852468 4295858988 2015 35.3520671834625 13 159 0 954963968 12.13187 0 0 442584815286.03375 .386858115054066 4295858988 2016 30.9385167110322 7 236 0 1223380992 13.649537 0 0 381971148530.5428 -2.08805653898309 4295858988 2017 29.2615245214633 7 305 0 1422988032 7.776542 0 0 395837353031.499 -7.310916958037089 4295859306 2011 17.1794871794871 0 143 0 7.547e+08 6.573964 0 0 481420882905.0009 26.06698199624618 4295859306 2012 16.4672841094245 0 146 0 814566976 9.716128 0 0 523330354138.1333 31.26598334890303 4295859306 2013 21.3055865229778 0 149 0 921878976 10.791467 0 0 496152879924.7267 2.380369601496919 4295859306 2014 25.7891737891737 0 154 0 1047822016 5.718838 0 0 521791015247.0603 -5.680612374306783 4295859306 2015 45.8000949667616 0 159 0 1075384064 2.0372021 0 0 535390200131.0177 -2.840147495087677 4295859306 2016 60.0688538188538 0 236 0 1140327040 -1.7584423 1 1 462335574841.48413 -4.22079695282357 4295859306 2017 60.5692918192918 0 305 0 1159230976 2.2100768 1 0 476062757356.92725 12.08629547636072 4295860976 2016 14.033264033264 0 236 1 416044992 8.771708 . . 18206020741000 2.809147629104088 4295860976 2017 12.7060439560439 1 305 1 425636992 5.228341 0 0 18695110842000 2.537497659196815 4295865864 2011 38.0459459459459 0 143 0 2.5617e+09 -1.259957 1 0 321995279401.5016 -3.654669083017719 4295865864 2012 35.4941094941094 0 146 0 2.5082e+09 1.1045582 1 0 344003137611.2712 3.941503187586579 4295865864 2013 29.7948717948717 0 149 0 2.8922e+09 2.714614 1 0 327148943812.1366 -4.997670325554282 4295865864 2014 32.4207504207504 0 154 0 2.7568e+09 -5.625774 1 0 343584391647.92706 .1980121805520809 4295865864 2015 31.5469975752389 0 159 0 2.8921e+09 -8.061747 1 0 352993631617.708 1.863305283018756 4295865864 2016 29.9643033858768 0 236 0 3.449e+09 -19.154406 1 0 302673070846.85724 .6114751833331019 4295865864 2017 31.8978723404255 0 305 0 2.8318e+09 -6.298561 1 0 313115929314.3386 2.492374260307158 4295866378 2011 70.4494767541602 0 143 0 1.2406e+09 4.064206 0 0 249424310816.66714 4.899686358623893 4295866378 2012 68.7433129280081 0 146 0 1.2799e+09 5.070423 1 0 275604356167.31573 -2.179936953365001 4295866378 2013 68.2020149399234 0 149 0 1.1796e+09 2.39073 1 0 258290060227.73444 1.909129174632278 4295866378 2014 71.9788673877528 0 154 0 1.0946e+09 5.470056 1 0 271362405890.589 -1.813913578914756 4295866378 2015 73.1561302681992 0 159 0 1.0315e+09 3.292413 1 0 274862826772.15588 6.377217393475116 4295866378 2016 71.8427660400657 0 236 0 1.0863e+09 8.546605 1 0 234534382384.7655 7.455255505912498 4295866378 2017 69.3128493603397 0 305 0 1.0745e+09 9.922251 1 0 240771351298.83328 2.128191378780703 4295866480 2011 68.4313725490196 68 143 0 3.9123e+10 3.587983 1 1 249424310816.66714 4.899686358623893 4295866480 2012 89.576124567474 56 146 0 3.6205e+10 -3.950722 1 1 275604356167.31573 -2.179936953365001 4295866480 2013 83.9965397923875 72 149 0 2.9984e+10 -4.481107 1 1 258290060227.73444 1.909129174632278 4295866480 2014 82.1940953884133 57 154 0 2.5191e+10 .4639783 1 1 271362405890.589 -1.813913578914756 4295866480 2015 83.5994397759103 41 159 0 2.1063e+10 11.752497 1 0 274862826772.15588 6.377217393475116 4295866480 2016 92.8566176470588 15 236 0 2.0926e+10 5.687204 1 0 234534382384.7655 7.455255505912498 4295866480 2017 93.1421256897035 5 305 0 4.4901e+10 -2.7708995 1 0 240771351298.83328 2.128191378780703 4295866790 2016 76.4606102262552 0 236 0 3.8213e+09 2.247896 . . 2439188643162.4985 1.755723741416579 4295866790 2017 72.4421928318466 0 305 0 3.8849e+09 3.7632036 1 0 2472964344587.1655 1.326491698127181 4295866983 2011 0 0 143 0 4717032960 6.058258 1 0 2645187882116.672 1.470195726973971 4295866983 2012 16.1906625445153 0 146 0 4751194112 7.493335 1 0 2865157541994.169 1.542875408373239 4295866983 2013 18.4599619382228 0 149 0 4.9704e+09 7.017368 1 0 2683671716967.188 1.227596621061495 4295866983 2014 23.5836627140975 0 154 0 5.605e+09 6.993589 1 0 2811876903329.0273 1.123423424160419 4295866983 2015 24.8447204968944 0 159 0 7.0059e+09 5.014709 1 0 2855964488590.186 .2032545627180351 4295866983 2016 36.3739183040059 0 236 0 7.6589e+09 5.048824 1 0 2439188643162.4985 1.755723741416579 4295866983 2017 39.0338675189111 0 305 0 8.8821e+09 4.3866754 1 0 2472964344587.1655 1.326491698127181 4295867015 2011 47.0530489315872 1 143 0 4.4791e+09 2.643231 1 0 2645187882116.672 1.470195726973971 4295867015 2012 47.3304924806802 1 146 0 7.3778e+09 3.08681 1 0 2865157541994.169 1.542875408373239 4295867015 2013 45.185271502035 3 149 0 7.4473e+09 3.058327 1 0 2683671716967.188 1.227596621061495 4295867015 2014 44.4700102967594 0 154 0 7.2022e+09 3.52367 0 0 2811876903329.0273 1.123423424160419 4295867015 2015 44.0469348659003 0 159 0 9.0388e+09 3.50471 0 1 2855964488590.186 .2032545627180351 4295867015 2016 42.1656520937096 0 236 0 1.06808e+10 4.405769 0 1 2439188643162.4985 1.755723741416579 4295867015 2017 71.9128003046615 1 305 0 1.34003e+10 5.235641 0 1 2472964344587.1655 1.326491698127181 4295867357 2011 74.2808943786813 0 143 0 3071834112 8.217268 0 0 2645187882116.672 1.470195726973971 4295867357 2012 72.8828410796942 1 146 0 3516784128 8.818268 1 0 2865157541994.169 1.542875408373239 4295867357 2013 77.0099893982598 2 149 0 3612425984 9.505373 1 0 2683671716967.188 1.227596621061495 4295867357 2014 72.9262709769089 0 154 0 4187892992 9.10655 1 0 2811876903329.0273 1.123423424160419 4295867357 2015 77.0162835249042 0 159 0 4962383872 6.392156 1 0 2855964488590.186 .2032545627180351 4295867357 2016 78.4504030074149 1 236 0 6311430144 7.201662 1 0 2439188643162.4985 1.755723741416579 4295867357 2017 76.0641370718923 2 305 0 6943066112 6.823451 1 0 2472964344587.1655 1.326491698127181 4295867377 2011 33.397190293742 0 143 0 1184118016 -3.768238 1 0 2645187882116.672 1.470195726973971 4295867377 2012 63.3349084314576 0 146 0 1057902016 -4.649379 1 0 2865157541994.169 1.542875408373239 4295867377 2013 64.2050370451609 0 149 0 1098616064 3.461228 1 0 2683671716967.188 1.227596621061495 4295867377 2014 63.0012041575122 0 154 0 1257437952 5.503439 1 0 2811876903329.0273 1.123423424160419 4295867377 2015 64.1810344827586 0 159 0 1339314944 -5.046687 1 0 2855964488590.186 .2032545627180351 4295867377 2016 40.8958986656828 0 236 0 1752472064 5.618045 1 0 2439188643162.4985 1.755723741416579 4295867377 2017 41.5608903605592 0 305 0 2020829056 4.950996 1 0 2472964344587.1655 1.326491698127181 4295868093 2017 36.8995789387621 0 305 0 1328967040 8.62386 . . 2472964344587.1655 1.326491698127181 4295868112 2011 14.1975308641975 0 143 0 1.9704e+09 7.744469 1 0 2645187882116.672 1.470195726973971 4295868112 2012 19.3672839506172 1 146 0 2.0556e+09 7.794337 1 0 2865157541994.169 1.542875408373239 4295868112 2013 18.287037037037 1 149 0 2.2429e+09 7.193207 1 0 2683671716967.188 1.227596621061495 4295868112 2014 23.5339506172839 1 154 0 2.4859e+09 6.822027 1 0 2811876903329.0273 1.123423424160419 4295868112 2015 21.2962962962962 1 159 0 2.5793e+09 6.475559 1 0 2855964488590.186 .2032545627180351 4295868112 2016 18.8271604938271 0 236 0 3.0422e+09 4.7247176 1 0 2439188643162.4985 1.755723741416579 4295868112 2017 64.8119908859713 0 305 0 2.8433e+09 4.421035 1 0 2472964344587.1655 1.326491698127181 4295868416 2011 81.9483150252156 3 143 0 9.4275e+10 4.111564 1 0 2645187882116.672 1.470195726973971 4295868416 2012 83.4472713575705 1 146 0 9.6083e+10 4.0218954 1 0 2865157541994.169 1.542875408373239 4295868416 2013 85.4223393353828 5 149 0 8.998e+10 1.3124586 1 0 2683671716967.188 1.227596621061495 4295868416 2014 85.6642958392693 1 154 0 8.5833e+10 2.4776325 1 0 2811876903329.0273 1.123423424160419 4295868416 2015 85.0033675072962 3 159 0 8.8404e+10 1.561092 1 0 2855964488590.186 .2032545627180351 4295868416 2016 82.9752886714537 2 236 0 9.143e+10 2.791463 1 1 2439188643162.4985 1.755723741416579 4295868416 2017 87.0392298122048 0 305 0 9.4668e+10 1.0854496 1 1 2472964344587.1655 1.326491698127181 4295869055 2017 37.0058896817306 0 305 0 1.0568e+09 .8295195 . . 3469853463945.5337 1.865906916904581 4295869278 2011 2.33079336620349 0 143 0 1271328000 9.843366 0 0 3399667820000.0063 2.530762023160379 4295869278 2012 1.58102766798419 0 146 0 1187010944 13.206722 0 0 3749314991050.591 2.601419304202527 4295869278 2013 1.58102766798419 0 149 0 1107708032 9.437844 0 0 3527143188785.157 1.855413407665223 4295869278 2014 1.75376957985653 0 154 0 1270294016 17.408396 . . 3733804649549.0303 1.799764603835211 4295869278 2015 2.32919254658385 0 159 0 3673424896 18.100706 0 0 3889093051023.5156 .5022271926341265 4295869278 2016 14.1481890633631 0 236 0 3885430016 9.699327 0 0 3357585719351.5605 1.860729181617582 4295869278 2017 35.8103858347575 0 305 0 4073733888 4.416519 0 0 3469853463945.5337 1.865906916904581 4295869822 2011 0 0 143 0 1599609984 10.79304 0 0 3399667820000.0063 2.530762023160379 4295869822 2012 0 0 146 0 1680695040 10.804422 0 0 3749314991050.591 2.601419304202527 4295869822 2013 0 0 149 0 1771858944 9.539431 0 0 3527143188785.157 1.855413407665223 4295869822 2014 0 0 154 0 1996852992 7.111766 0 0 3733804649549.0303 1.799764603835211 4295869822 2015 0 1 159 0 1848935936 5.749197 0 0 3889093051023.5156 .5022271926341265 4295869822 2016 4.67625899280575 0 236 0 1814769024 7.620974 0 0 3357585719351.5605 1.860729181617582 4295869822 2017 10.9271523178807 0 305 0 1957217024 7.441862 0 0 3469853463945.5337 1.865906916904581 4295870063 2011 61.1204430332945 9 143 0 4.993e+09 6.667379 0 0 3399667820000.0063 2.530762023160379 4295870063 2012 51.2465277777777 10 146 0 5.873e+09 13.694092 0 0 3749314991050.591 2.601419304202527 4295870063 2013 58.1161748220823 16 149 0 5.898e+09 7.340073 1 0 3527143188785.157 1.855413407665223 4295870063 2014 62.8256345241261 21 154 0 5.905e+09 4.795391 1 0 3733804649549.0303 1.799764603835211 4295870063 2015 72.3091498671667 18 159 0 6.438e+09 7.907316 1 0 3889093051023.5156 .5022271926341265 end format %ty Year
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