for my thesis i am currently investigating the effects of emissions on health on a regional basis. the dependent variable is bicategorical which takes the value 0 (if health is good) and 1 (if health is bad) with the exception of emissions and capita_gdp every variable is categorical: here is an exemplary regression:
probit health i.year i.region##emissions age educ smoker gender urban capita_gdp, robust nofvlabel allbaselevels Probit regression Number of obs = 67,041 Wald chi2(64) = 5850.28 Prob > chi2 = 0.0000 Log pseudolikelihood = -43026.965 Pseudo R2 = 0.0660 ------------------------------------------------------------------------------------- | Robust health | Coef. Std. Err. z P>|z| [95% Conf. Interval] --------------------+---------------------------------------------------------------- year | 1 | 0 (base) 2 | -.0236149 .0290446 -0.81 0.416 -.0805412 .0333115 3 | -.0552885 .0343119 -1.61 0.107 -.1225386 .0119615 4 | -.7498958 .0521191 -14.39 0.000 -.8520474 -.6477442 | region | 1 | 0 (base) 2 | .3424928 .1944582 1.76 0.078 -.0386383 .723624 3 | .6631291 .343445 1.93 0.054 -.0100107 1.336269 4 | 1.005453 .1809361 5.56 0.000 .6508251 1.360081 5 | .5202438 .2705144 1.92 0.054 -.0099547 1.050442 6 | .853456 .2053275 4.16 0.000 .4510215 1.25589 7 | -1.32784 1.329886 -1.00 0.318 -3.934369 1.278688 8 | .2074103 .5587633 0.37 0.710 -.8877457 1.302566 9 | .8778635 1.005655 0.87 0.383 -1.093184 2.848911 10 | .614019 .2058646 2.98 0.003 .2105317 1.017506 11 | 1.103564 .2395228 4.61 0.000 .6341078 1.57302 12 | -.9928198 1.189953 -0.83 0.404 -3.325084 1.339444 13 | .2024027 .3014841 0.67 0.502 -.3884953 .7933008 14 | .8510637 .1966648 4.33 0.000 .4656078 1.23652 15 | -.4685238 1.062594 -0.44 0.659 -2.551171 1.614123 16 | .1222191 .4271317 0.29 0.775 -.7149435 .9593818 17 | 1.777416 .9296525 1.91 0.056 -.0446694 3.599502 18 | .7016812 .3960197 1.77 0.076 -.0745032 1.477866 19 | .2164103 .2324297 0.93 0.352 -.2391436 .6719642 20 | -.8683004 2.079837 -0.42 0.676 -4.944707 3.208106 21 | .6094313 .1969787 3.09 0.002 .2233601 .9955025 22 | .4586692 .2175369 2.11 0.035 .0323048 .8850336 23 | .1376296 .316405 0.43 0.664 -.4825129 .7577721 24 | .8800929 .2139805 4.11 0.000 .4606989 1.299487 25 | .5008748 .181908 2.75 0.006 .1443417 .8574079 26 | .7885192 .2055236 3.84 0.000 .3857004 1.191338 27 | .8370192 .2066431 4.05 0.000 .4320061 1.242032 28 | .0342872 .3383975 0.10 0.919 -.6289597 .697534 | emissions | .2331187 .0475761 4.90 0.000 .1398713 .3263662 | region#c.emissions| 1 | 0 (base) 2 | -.1763598 .0473856 -3.72 0.000 -.2692338 -.0834858 3 | .0902526 .3483855 0.26 0.796 -.5925705 .7730757 4 | -.2545669 .0436166 -5.84 0.000 -.3400539 -.1690798 5 | -.1903919 .0525988 -3.62 0.000 -.2934837 -.0873002 6 | -.2595892 .0565328 -4.59 0.000 -.3703914 -.148787 7 | .3660934 .3615611 1.01 0.311 -.3425534 1.07474 8 | -.1810636 .0873587 -2.07 0.038 -.3522836 -.0098436 9 | -.2360667 .2817683 -0.84 0.402 -.7883225 .316189 10 | -.2362498 .0452001 -5.23 0.000 -.3248403 -.1476593 11 | -.2986525 .0606014 -4.93 0.000 -.4174291 -.179876 12 | .4210453 .4355456 0.97 0.334 -.4326084 1.274699 13 | -.1393217 .063414 -2.20 0.028 -.2636109 -.0150324 14 | -.2428271 .0452505 -5.37 0.000 -.3315166 -.1541377 15 | -.1078827 .1281398 -0.84 0.400 -.359032 .1432667 16 | -.1121361 .0991541 -1.13 0.258 -.3064746 .0822024 17 | -.3670531 .1360779 -2.70 0.007 -.6337609 -.1003453 18 | -.241021 .1572069 -1.53 0.125 -.5491408 .0670988 19 | -.2128744 .0452858 -4.70 0.000 -.3016328 -.1241159 20 | .103139 .4313025 0.24 0.811 -.7421983 .9484763 21 | -.217597 .0532092 -4.09 0.000 -.3218851 -.1133089 22 | -.1796928 .0509009 -3.53 0.000 -.2794568 -.0799288 23 | -.1510797 .0529603 -2.85 0.004 -.2548799 -.0472795 24 | -.2589344 .0509662 -5.08 0.000 -.3588264 -.1590425 25 | -.231851 .0448358 -5.17 0.000 -.3197276 -.1439745 26 | -.2411263 .0442314 -5.45 0.000 -.3278182 -.1544344 27 | -.2452313 .0465597 -5.27 0.000 -.3364867 -.153976 28 | -.0563099 .1191566 -0.47 0.637 -.2898525 .1772328 | age | .1085835 .0049886 21.77 0.000 .098806 .1183609 educ | -.1802489 .0107034 -16.84 0.000 -.2012272 -.1592707 smoker | .080728 .0145963 5.53 0.000 .0521198 .1093362 gender | -.2019473 .0145416 -13.89 0.000 -.2304483 -.1734463 urban | -.1362217 .0112233 -12.14 0.000 -.1582189 -.1142245 capita_gdp | -8.36e-06 .0000194 -0.43 0.667 -.0000464 .0000297 _cons | -.4987429 .1638654 -3.04 0.002 -.8199132 -.1775726 ------------------------------------------------------------------------------------- My question is, how can I exactly interpret the coefficients of emissions and the interaction of region.c#emissions on the dependent variable ? To my understanding the coefficient of emissions for region 1 is the base level and the coefficient of emissions in region 2 is lower than region 1 by -.176 ?