Hi all, I’m having a bit of trouble understanding a few concepts regarding the inclusion of main effects alongside interactions terms.
My question is do I need to include main effects when I have included their interactions and if I don’t what does this mean? For instance below is the fixed effects model I am running – I have only included the variables that are time variant and I am using a panel dataset which follows the same women over two time periods:
My outcome variable is women’s conjugal power (a score) and my main predictor variable is whether a woman has a boy-child (son) and I am interacting this variable with four other variables: wealth quintiles, education, relative education and patrilocal households.
First I run the model where I omit my main effects (has son and wealth quintles, education, relative education and patrilocal households)
and then this is the model that includes my main effects and their interaction terms (Understandably so, many of the results are omitted due to collinearity)
In a third model that I run, as I am interested in plotting the interaction between having a boy-child and wealth quintiles I do not include any main effect and I change the notation for the interaction (i.sondum2#i.qwealth) yielding the following result:
I can’t quite grasp the difference between these models and if it affects their interpretation (of the interaction terms and the main effects). I’ve been reading up using several sources such as (https://stats.idre.ucla.edu/stata/fa...n-interaction/ ) But I can’t seem to understand the difference or apply it to my particular dataset.
Any help is appreciated.
My question is do I need to include main effects when I have included their interactions and if I don’t what does this mean? For instance below is the fixed effects model I am running – I have only included the variables that are time variant and I am using a panel dataset which follows the same women over two time periods:
My outcome variable is women’s conjugal power (a score) and my main predictor variable is whether a woman has a boy-child (son) and I am interacting this variable with four other variables: wealth quintiles, education, relative education and patrilocal households.
First I run the model where I omit my main effects (has son and wealth quintles, education, relative education and patrilocal households)
Code:
xtreg M1 haschildren spercent2 totalchild dualearner i.round c.age#c.age2 gdp1 o1.sondum2#o0.releduc o1.sondum2#o1.educ o1.sondum2#o1.qwealth o1.sondum2#o0.patrilocal, fe
Code:
Fixed-effects (within) regression Number of obs = 4,560 Group variable: Findid Number of groups = 2,280 R-sq: Obs per group: within = 0.0236 min = 2 between = 0.0002 avg = 2.0 overall = 0.0009 max = 2 F(27,2253) = 2.02 corr(u_i, Xb) = -0.2875 Prob > F = 0.0014 -------------------------------------------------------------------------------------- M1 | Coef. Std. Err. t P>|t| [95% Conf. Interval] ---------------------+---------------------------------------------------------------- haschildren | -.2520974 .176294 -1.43 0.153 -.597813 .0936182 spercent2 | .2941761 .2280691 1.29 0.197 -.1530714 .7414237 totalchild | -.0409311 .0569732 -0.72 0.473 -.1526566 .0707943 dualearner | .0145703 .0913376 0.16 0.873 -.1645443 .1936849 | round | 2012 | .0758831 .124811 0.61 0.543 -.1688734 .3206396 | c.age#c.age2 | 4.09e-06 4.34e-06 0.94 0.347 -4.43e-06 .0000126 | gdp1 | -.005971 .00338 -1.77 0.077 -.0125992 .0006572 | sondum2#releduc | Has sons#W>H | -.07597 .1402888 -0.54 0.588 -.3510787 .1991388 Has sons#H>W | .2070449 .1483036 1.40 0.163 -.0837811 .4978708 No son#H=W | 0 (omitted) No son#W>H | .0307854 .2061227 0.15 0.881 -.3734247 .4349956 No son#H>W | .4634932 .2193291 2.11 0.035 .0333851 .8936013 | sondum2#educ | Has sons#Primary | .4615321 .178392 2.59 0.010 .1117023 .811362 Has sons#Secondary | .5136993 .3702903 1.39 0.165 -.2124465 1.239845 Has sons#University | -.1859308 .3569265 -0.52 0.602 -.8858699 .5140083 No son#Illiterate | 0 (omitted) No son#Primary | .1558035 .2367281 0.66 0.511 -.3084245 .6200314 No son#Secondary | -.491498 .5254403 -0.94 0.350 -1.521896 .5388996 No son#University | -.4076214 .4075595 -1.00 0.317 -1.206853 .3916099 | sondum2#qwealth | Has sons#Rich | -.0424609 .1018518 -0.42 0.677 -.2421941 .1572722 Has sons#Middle | -.0459057 .1152923 -0.40 0.691 -.2719959 .1801844 Has sons#Poor | .0461349 .1341339 0.34 0.731 -.2169041 .3091739 Has sons#Poorest | .0354346 .164277 0.22 0.829 -.2867154 .3575846 No son#Richest | 0 (omitted) No son#Rich | .2831306 .1871543 1.51 0.130 -.0838822 .6501434 No son#Middle | -.0802566 .1937097 -0.41 0.679 -.4601248 .2996116 No son#Poor | -.0866428 .2226979 -0.39 0.697 -.5233573 .3500717 No son#Poorest | -.1119703 .2927556 -0.38 0.702 -.686069 .4621285 | sondum2#patrilocal | Has sons#1 | -.0587571 .1586316 -0.37 0.711 -.3698365 .2523223 No son#0 | 0 (omitted) No son#1 | .2773891 .2653202 1.05 0.296 -.2429086 .7976867 | _cons | -.2326615 .3308439 -0.70 0.482 -.8814521 .4161291 ---------------------+---------------------------------------------------------------- sigma_u | 1.1186275 sigma_e | 1.3282613 rho | .41495063 (fraction of variance due to u_i) -------------------------------------------------------------------------------------- F test that all u_i=0: F(2279, 2253) = 1.22 Prob > F = 0.0000 .
Code:
xtreg M1 haschildren spercent2 hasson primary secondary university WgreaterH HgreaterW patrilocal i.qwealth totalchild dualearner i.round c.age#c.age2 gdp1 o1.sondum2#o0.releduc o1.sondum2#o1.educ o1.sondum2#o1.qwealth o1.sondum2#o0.patrilocal, fe
Code:
Fixed-effects (within) regression Number of obs = 4,560 Group variable: Findid Number of groups = 2,280 R-sq: Obs per group: within = 0.0237 min = 2 between = 0.0002 avg = 2.0 overall = 0.0010 max = 2 F(28,2252) = 1.95 corr(u_i, Xb) = -0.2858 Prob > F = 0.0021 -------------------------------------------------------------------------------------- M1 | Coef. Std. Err. t P>|t| [95% Conf. Interval] ---------------------+---------------------------------------------------------------- haschildren | -.2492079 .1765717 -1.41 0.158 -.5954682 .0970524 spercent2 | .2726707 .2382755 1.14 0.253 -.1945919 .7399332 hasson | .1299825 .4160749 0.31 0.755 -.6859478 .9459128 primary | .2167467 .3067879 0.71 0.480 -.3848698 .8183632 secondary | -.4228871 .56959 -0.74 0.458 -1.539863 .6940891 university | -.3360392 .4676262 -0.72 0.472 -1.253063 .5809842 WgreaterH | .0370848 .2071477 0.18 0.858 -.3691356 .4433051 HgreaterW | .4763202 .2231824 2.13 0.033 .0386555 .9139848 patrilocal | .2783719 .265392 1.05 0.294 -.2420666 .7988105 | qwealth | Rich | -.0467512 .1027937 -0.45 0.649 -.2483314 .1548291 Middle | -.0516164 .1167552 -0.44 0.658 -.2805755 .1773427 Poor | .0390054 .136088 0.29 0.774 -.2278657 .3058764 Poorest | .0275883 .1662184 0.17 0.868 -.298369 .3535456 | totalchild | -.0440935 .0578767 -0.76 0.446 -.1575909 .0694038 dualearner | .0154103 .0913955 0.17 0.866 -.1638178 .1946384 | round | 2012 | .0748453 .1248802 0.60 0.549 -.1700469 .3197376 | c.age#c.age2 | 4.12e-06 4.35e-06 0.95 0.343 -4.40e-06 .0000126 | gdp1 | -.0059751 .0033807 -1.77 0.077 -.0126046 .0006545 | sondum2#releduc | Has sons#W>H | -.1124946 .1955466 -0.58 0.565 -.495965 .2709757 Has sons#H>W | -.2733663 .2257303 -1.21 0.226 -.7160274 .1692948 No son#H=W | 0 (omitted) No son#W>H | 0 (omitted) No son#H>W | 0 (omitted) | sondum2#educ | Has sons#Primary | .2273548 .3295539 0.69 0.490 -.4189062 .8736159 Has sons#Secondary | .9161934 .6322402 1.45 0.147 -.3236409 2.156028 Has sons#University | .1289173 .3905026 0.33 0.741 -.6368654 .8946999 No son#Illiterate | 0 (omitted) No son#Primary | 0 (omitted) No son#Secondary | 0 (omitted) No son#University | 0 (omitted) | sondum2#qwealth | No son#Richest | 0 (omitted) No son#Rich | .3484459 .2170782 1.61 0.109 -.0772483 .7741401 No son#Middle | -.0045688 .2282547 -0.02 0.984 -.4521802 .4430427 No son#Poor | -.0997328 .2582418 -0.39 0.699 -.6061495 .406684 No son#Poorest | -.1056691 .333686 -0.32 0.752 -.7600333 .548695 | sondum2#patrilocal | Has sons#1 | -.3380668 .2816849 -1.20 0.230 -.8904559 .2143223 No son#0 | 0 (omitted) No son#1 | 0 (omitted) | _cons | -.3201305 .4334688 -0.74 0.460 -1.170171 .5299097 ---------------------+---------------------------------------------------------------- sigma_u | 1.1179643 sigma_e | 1.3285274 rho | .4145655 (fraction of variance due to u_i) -------------------------------------------------------------------------------------- F test that all u_i=0: F(2279, 2252) = 1.22 Prob > F = 0.0000 . . .
Code:
Fixed-effects (within) regression Number of obs = 4,560 Group variable: Findid Number of groups = 2,280 R-sq: Obs per group: within = 0.0237 min = 2 between = 0.0002 avg = 2.0 overall = 0.0010 max = 2 F(28,2252) = 1.95 corr(u_i, Xb) = -0.2858 Prob > F = 0.0021 -------------------------------------------------------------------------------------- M1 | Coef. Std. Err. t P>|t| [95% Conf. Interval] ---------------------+---------------------------------------------------------------- haschildren | -.2492079 .1765717 -1.41 0.158 -.5954682 .0970524 spercent2 | .2726707 .2382755 1.14 0.253 -.1945919 .7399332 totalchild | -.0440935 .0578767 -0.76 0.446 -.1575909 .0694038 dualearner | .0154103 .0913955 0.17 0.866 -.1638178 .1946384 | round | 2012 | .0748453 .1248802 0.60 0.549 -.1700469 .3197376 | c.age#c.age2 | 4.12e-06 4.35e-06 0.95 0.343 -4.40e-06 .0000126 | gdp1 | -.0059751 .0033807 -1.77 0.077 -.0126046 .0006545 | sondum2#releduc | Has sons#W>H | -.0754099 .1403283 -0.54 0.591 -.3505962 .1997765 Has sons#H>W | .2029539 .1489102 1.36 0.173 -.0890618 .4949695 No son#H=W | 0 (omitted) No son#W>H | .0370848 .2071477 0.18 0.858 -.3691356 .4433051 No son#H>W | .4763202 .2231824 2.13 0.033 .0386555 .9139848 | sondum2#educ | Has sons#Primary | .4441015 .1869481 2.38 0.018 .077493 .8107101 Has sons#Secondary | .4933063 .3760733 1.31 0.190 -.2441803 1.230793 Has sons#University | -.2071219 .3633853 -0.57 0.569 -.919727 .5054831 No son#Illiterate | 0 (omitted) No son#Primary | .2167467 .3067879 0.71 0.480 -.3848698 .8183632 No son#Secondary | -.4228871 .56959 -0.74 0.458 -1.539863 .6940891 No son#University | -.3360392 .4676262 -0.72 0.472 -1.253063 .5809842 | sondum2#qwealth | Has sons#Rich | -.0467512 .1027937 -0.45 0.649 -.2483314 .1548291 Has sons#Middle | -.0516164 .1167552 -0.44 0.658 -.2805755 .1773427 Has sons#Poor | .0390054 .136088 0.29 0.774 -.2278657 .3058764 Has sons#Poorest | .0275883 .1662184 0.17 0.868 -.298369 .3535456 No son#Richest | -.1299825 .4160749 -0.31 0.755 -.9459128 .6859478 No son#Rich | .1717123 .4027911 0.43 0.670 -.6181683 .9615928 No son#Middle | -.1861676 .3904797 -0.48 0.634 -.9519054 .5795701 No son#Poor | -.1907099 .400728 -0.48 0.634 -.9765446 .5951248 No son#Poorest | -.2080633 .4246817 -0.49 0.624 -1.040872 .6247451 | sondum2#patrilocal | Has sons#1 | -.0596949 .1586918 -0.38 0.707 -.3708924 .2515026 No son#0 | 0 (omitted) No son#1 | .2783719 .265392 1.05 0.294 -.2420666 .7988105 | _cons | -.190148 .3578002 -0.53 0.595 -.8918005 .5115045 ---------------------+---------------------------------------------------------------- sigma_u | 1.1179643 sigma_e | 1.3285274 rho | .4145655 (fraction of variance due to u_i) -------------------------------------------------------------------------------------- F test that all u_i=0: F(2279, 2252) = 1.22 Prob > F = 0.0000 .
I can’t quite grasp the difference between these models and if it affects their interpretation (of the interaction terms and the main effects). I’ve been reading up using several sources such as (https://stats.idre.ucla.edu/stata/fa...n-interaction/ ) But I can’t seem to understand the difference or apply it to my particular dataset.
Any help is appreciated.
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