I'm stuck with some unexpected findings that seem to contradict what I (thought I) knew about multicollinearity. Among others in this post, the discussion of multicollinearity suggests that estimates remain unbiased and the variance and standard errors of the estimates will increase. This I always presumed that including multi-collinear variables makes it less likely to have significant effects.
Now my question is, under which conditions does the opposite happen?
Specifically, I am dealing with regressions in which I am trying to look at the contingent effect of direct and indirect ties in a collaboration network on the impact of inventions. I reproduce the outcomes of three regressions: In the first one, I only include direct ties dt, in the second one only indirect ties it, and in the third one I include dt and it (note both have a correlation of 0.87).
As you can see the interaction effects are ONLY significant when both are included. Any suggestions on how to interpret this?
Note that running a simple OLS on the log of the response variable has the same peculiar results, with only significant interactions when both direct and indirect ties are included.
Now my question is, under which conditions does the opposite happen?
Specifically, I am dealing with regressions in which I am trying to look at the contingent effect of direct and indirect ties in a collaboration network on the impact of inventions. I reproduce the outcomes of three regressions: In the first one, I only include direct ties dt, in the second one only indirect ties it, and in the third one I include dt and it (note both have a correlation of 0.87).
Code:
xtpoisson fwd log_assets log_breadth log_depth firm_prod degree struct team_deg team_str_hole team_size team_div team_sim team_mk claims num > _cited_patents num_sbcls backcitation_struct lag it priv c.priv#c.priv pub c.pub#c.pub dt c.priv#c.dt c.priv#c.priv#c.dt c.pub#c.dt c.pub#c. > pub#c.dt i.app_year i.grant i.tech_cat, fe robust note: 10 groups (10 obs) dropped because of only one obs per group Iteration 0: log pseudolikelihood = -263803.46 Iteration 1: log pseudolikelihood = -244586.92 Iteration 2: log pseudolikelihood = -244120.53 Iteration 3: log pseudolikelihood = -244117.75 Iteration 4: log pseudolikelihood = -244117.75 Conditional fixed-effects Poisson regression Number of obs = 39,785 Group variable: firm Number of groups = 127 Obs per group: min = 2 avg = 313.3 max = 8,114 Wald chi2(44) = 55360.70 Log pseudolikelihood = -244117.75 Prob > chi2 = 0.0000 (Std. Err. adjusted for clustering on firm) ------------------------------------------------------------------------------------- | Robust fwd | Coef. Std. Err. z P>|z| [95% Conf. Interval] --------------------+---------------------------------------------------------------- log_assets | -.0421138 .0183623 -2.29 0.022 -.0781032 -.0061243 log_breadth | -.0621538 .0740653 -0.84 0.401 -.2073191 .0830115 log_depth | -.0143182 .0451562 -0.32 0.751 -.1028227 .0741862 firm_prod | -.0001577 .0000945 -1.67 0.095 -.0003428 .0000274 degree | .0003697 .0004692 0.79 0.431 -.00055 .0012894 struct | -.0872349 .0384485 -2.27 0.023 -.1625926 -.0118771 team_degree_cent | -.0000941 .0005957 -0.16 0.875 -.0012615 .0010734 team_str_hole | .0418548 .036082 1.16 0.246 -.0288646 .1125742 team_size | .037857 .0061041 6.20 0.000 .0258932 .0498208 team_div | .0015678 .0583958 0.03 0.979 -.1128859 .1160214 team_sim | -.0420113 .0478152 -0.88 0.380 -.1357274 .0517047 team_mk | .0080637 .0122664 0.66 0.511 -.015978 .0321053 claims | .0065597 .0005373 12.21 0.000 .0055065 .0076129 num_cited_patents | .0014349 .0003425 4.19 0.000 .0007637 .0021061 num_sbcls | .0210066 .0026866 7.82 0.000 .015741 .0262721 backcitation_struct | .0046322 .0054924 0.84 0.399 -.0061328 .0153971 lag | .001186 .1057822 0.01 0.991 -.2061433 .2085153 it | -.02097 .0265965 -0.79 0.430 -.0730983 .0311582 priv | .4264326 .1077134 3.96 0.000 .2153183 .637547 | c.priv#c.priv | -.4015753 .1140479 -3.52 0.000 -.6251051 -.1780454 | pub | .2271145 .070996 3.20 0.001 .0879649 .3662641 | c.pub#c.pub | -.1989517 .0592801 -3.36 0.001 -.3151385 -.0827649 | dt | .0026489 .0044727 0.59 0.554 -.0061175 .0114153 | c.priv#c.dt | .0065184 .0102537 0.64 0.525 -.0135786 .0266153 | c.priv#c.priv#c.dt | -.0025707 .009038 -0.28 0.776 -.0202848 .0151434 | c.pub#c.dt | .0055046 .0173412 0.32 0.751 -.0284835 .0394927 | c.pub#c.pub#c.dt | -.0078393 .0186939 -0.42 0.675 -.0444787 .0288001 | app_year | 2001 | -.0546176 .1084301 -0.50 0.614 -.2671367 .1579014 2002 | -.023543 .2147132 -0.11 0.913 -.4443732 .3972871 2003 | -.0025697 .3204385 -0.01 0.994 -.6306176 .6254782 2004 | -.1106726 .4307254 -0.26 0.797 -.9548789 .7335336 | grant | 2001 | -.3226067 .1814502 -1.78 0.075 -.6782426 .0330293 2002 | -.4679425 .2522891 -1.85 0.064 -.96242 .026535 2003 | -.5601343 .3512596 -1.59 0.111 -1.248591 .1283218 2004 | -1.296592 .4499721 -2.88 0.004 -2.178521 -.4146625 2005 | -.9112545 .5510036 -1.65 0.098 -1.991202 .1686928 2006 | -.953167 .6529846 -1.46 0.144 -2.232993 .3266594 2007 | -1.062879 .7565935 -1.40 0.160 -2.545775 .4200173 2008 | -1.142632 .8518252 -1.34 0.180 -2.812178 .526915 | tech_cat | 2 | .4231011 .0461803 9.16 0.000 .3325894 .5136128 3 | .2627944 .2686015 0.98 0.328 -.2636548 .7892437 4 | .3656174 .0411299 8.89 0.000 .2850043 .4462306 5 | .1058336 .0698564 1.52 0.130 -.0310824 .2427496 6 | .1518013 .0784977 1.93 0.053 -.0020514 .3056541 -------------------------------------------------------------------------------------
Code:
xtpoisson fwd log_assets log_breadth log_depth firm_prod degree struct team_deg team_str_hole team_size team_div team_sim team_mk claims num > _cited_patents num_sbcls backcitation_struct lag /// > priv c.priv#c.priv pub c.pub#c.pub it c.priv#c.it c.priv#c.priv#c.it c.pub#c.it c.pub#c.pub#c.it i.app_year i.grant i.tech_cat, fe robust note: 10 groups (10 obs) dropped because of only one obs per group Iteration 0: log pseudolikelihood = -263803.46 Iteration 1: log pseudolikelihood = -244617.71 Iteration 2: log pseudolikelihood = -244151.4 Iteration 3: log pseudolikelihood = -244148.57 Iteration 4: log pseudolikelihood = -244148.57 Conditional fixed-effects Poisson regression Number of obs = 39,785 Group variable: firm Number of groups = 127 Obs per group: min = 2 avg = 313.3 max = 8,114 Wald chi2(43) = 43653.67 Log pseudolikelihood = -244148.57 Prob > chi2 = 0.0000 (Std. Err. adjusted for clustering on firm) ------------------------------------------------------------------------------------- | Robust fwd | Coef. Std. Err. z P>|z| [95% Conf. Interval] --------------------+---------------------------------------------------------------- log_assets | -.0417972 .0184625 -2.26 0.024 -.0779831 -.0056114 log_breadth | -.0609179 .074052 -0.82 0.411 -.2060571 .0842213 log_depth | -.0139061 .0451387 -0.31 0.758 -.1023763 .0745641 firm_prod | -.0001575 .0000948 -1.66 0.097 -.0003434 .0000283 degree | .0003651 .0004677 0.78 0.435 -.0005516 .0012817 struct | -.0865138 .0385132 -2.25 0.025 -.1619983 -.0110293 team_degree_cent | -.0000917 .0006003 -0.15 0.879 -.0012682 .0010849 team_str_hole | .0408362 .0358463 1.14 0.255 -.0294212 .1110935 team_size | .0373599 .0063835 5.85 0.000 .0248486 .0498713 team_div | .0025884 .0604123 0.04 0.966 -.1158175 .1209943 team_sim | -.0415313 .0475202 -0.87 0.382 -.1346692 .0516065 team_mk | .0075196 .0118594 0.63 0.526 -.0157243 .0307636 claims | .0065466 .0005445 12.02 0.000 .0054794 .0076138 num_cited_patents | .0014235 .0003391 4.20 0.000 .0007589 .002088 num_sbcls | .0210129 .0026838 7.83 0.000 .0157527 .0262731 backcitation_struct | .0050463 .0056992 0.89 0.376 -.006124 .0162165 lag | .0015166 .1058611 0.01 0.989 -.2059674 .2090006 priv | .4084412 .1079815 3.78 0.000 .1968013 .6200812 | c.priv#c.priv | -.3834548 .1167273 -3.29 0.001 -.6122361 -.1546735 | pub | .2400234 .0716232 3.35 0.001 .0996444 .3804024 | c.pub#c.pub | -.2132266 .0570253 -3.74 0.000 -.3249941 -.101459 | it | -.0070345 .0077406 -0.91 0.363 -.0222058 .0081368 | c.priv#c.it | -.0211951 .0935572 -0.23 0.821 -.2045638 .1621736 | c.priv#c.priv#c.it | .0148457 .0691849 0.21 0.830 -.1207542 .1504456 | c.pub#c.it | .1324775 .0920244 1.44 0.150 -.0478869 .312842 | c.pub#c.pub#c.it | -.1396024 .072464 -1.93 0.054 -.2816292 .0024244 | app_year | 2001 | -.0545978 .1084881 -0.50 0.615 -.2672305 .1580349 2002 | -.0236868 .2148361 -0.11 0.912 -.4447579 .3973842 2003 | -.0021412 .3206502 -0.01 0.995 -.6306041 .6263217 2004 | -.1102924 .4309893 -0.26 0.798 -.9550158 .734431 | grant | 2001 | -.3217998 .1813656 -1.77 0.076 -.6772698 .0336703 2002 | -.4677767 .2523486 -1.85 0.064 -.9623709 .0268175 2003 | -.5597596 .3512835 -1.59 0.111 -1.248263 .1287434 2004 | -1.296205 .4500562 -2.88 0.004 -2.178299 -.4141108 2005 | -.9120754 .5512629 -1.65 0.098 -1.992531 .16838 2006 | -.9536463 .6532563 -1.46 0.144 -2.234005 .3267125 2007 | -1.063942 .756966 -1.41 0.160 -2.547568 .4196842 2008 | -1.143782 .8523521 -1.34 0.180 -2.814361 .5267978 | tech_cat | 2 | .4247155 .0460621 9.22 0.000 .3344355 .5149954 3 | .2651247 .2684868 0.99 0.323 -.2610997 .7913492 4 | .3663356 .041281 8.87 0.000 .2854264 .4472449 5 | .104499 .0699651 1.49 0.135 -.0326301 .2416281 6 | .1533703 .0775916 1.98 0.048 .0012936 .305447 -------------------------------------------------------------------------------------
Code:
xtpoisson fwd log_assets log_breadth log_depth firm_prod degree struct team_deg team_str_hole team_size team_div team_sim team_mk claims num > _cited_patents num_sbcls backcitation_struct lag /// > priv c.priv#c.priv pub c.pub#c.pub dt it c.priv#c.dt c.priv#c.priv#c.dt c.priv#c.it c.priv#c.priv#c.it c.pub#c.dt c.pub#c.pub#c.dt c.pub#c.i > t c.pub#c.pub#c.it /// > i.app_year i.grant i.tech_cat, fe robust note: 10 groups (10 obs) dropped because of only one obs per group Iteration 0: log pseudolikelihood = -263803.46 Iteration 1: log pseudolikelihood = -244485.64 Iteration 2: log pseudolikelihood = -244016.26 Iteration 3: log pseudolikelihood = -244013.44 Iteration 4: log pseudolikelihood = -244013.44 Conditional fixed-effects Poisson regression Number of obs = 39,785 Group variable: firm Number of groups = 127 Obs per group: min = 2 avg = 313.3 max = 8,114 Wald chi2(48) = 65473.80 Log pseudolikelihood = -244013.44 Prob > chi2 = 0.0000 (Std. Err. adjusted for clustering on firm) ------------------------------------------------------------------------------------- | Robust fwd | Coef. Std. Err. z P>|z| [95% Conf. Interval] --------------------+---------------------------------------------------------------- log_assets | -.0416536 .0185879 -2.24 0.025 -.0780853 -.0052219 log_breadth | -.063431 .0738539 -0.86 0.390 -.208182 .08132 log_depth | -.0137816 .0450594 -0.31 0.760 -.1020963 .0745332 firm_prod | -.0001579 .0000946 -1.67 0.095 -.0003433 .0000275 degree | .0003798 .0004742 0.80 0.423 -.0005497 .0013093 struct | -.0864763 .0388271 -2.23 0.026 -.1625761 -.0103765 team_degree_cent | -.0001107 .0005991 -0.18 0.853 -.0012849 .0010635 team_str_hole | .0414972 .0363237 1.14 0.253 -.0296959 .1126903 team_size | .0378755 .0061385 6.17 0.000 .0258443 .0499068 team_div | .0007188 .0581518 0.01 0.990 -.1132566 .1146941 team_sim | -.0402486 .0477124 -0.84 0.399 -.1337633 .0532661 team_mk | .0073269 .012242 0.60 0.550 -.016667 .0313208 claims | .0065359 .0005381 12.15 0.000 .0054813 .0075905 num_cited_patents | .0014213 .0003433 4.14 0.000 .0007484 .0020942 num_sbcls | .0209203 .002683 7.80 0.000 .0156617 .0261789 backcitation_struct | .0062702 .0058392 1.07 0.283 -.0051744 .0177148 lag | .0012678 .1057345 0.01 0.990 -.205968 .2085035 priv | .3277654 .1057273 3.10 0.002 .1205437 .5349871 | c.priv#c.priv | -.333851 .1163007 -2.87 0.004 -.5617962 -.1059058 | pub | .3216886 .0734082 4.38 0.000 .1778112 .465566 | c.pub#c.pub | -.2669564 .057914 -4.61 0.000 -.3804658 -.1534469 | dt | .0011642 .0054724 0.21 0.832 -.0095615 .01189 it | -.0148946 .0319061 -0.47 0.641 -.0774295 .0476403 | c.priv#c.dt | .0637551 .0240834 2.65 0.008 .0165524 .1109578 | c.priv#c.priv#c.dt | -.0336542 .0185492 -1.81 0.070 -.0700099 .0027016 | c.priv#c.it | -.352787 .1849786 -1.91 0.056 -.7153385 .0097644 | c.priv#c.priv#c.it | .1721147 .1350795 1.27 0.203 -.0926363 .4368657 | c.pub#c.dt | -.0737924 .0138189 -5.34 0.000 -.1008769 -.0467079 | c.pub#c.pub#c.dt | .0548186 .0163733 3.35 0.001 .0227275 .0869098 | c.pub#c.it | .5046088 .1258178 4.01 0.000 .2580105 .7512072 | c.pub#c.pub#c.it | -.3730006 .0887886 -4.20 0.000 -.5470232 -.198978 | app_year | 2001 | -.0545112 .1084542 -0.50 0.615 -.2670774 .1580551 2002 | -.0231496 .2147579 -0.11 0.914 -.4440673 .3977681 2003 | -.0026099 .3203355 -0.01 0.993 -.6304559 .6252361 2004 | -.1108742 .4305263 -0.26 0.797 -.9546902 .7329418 | grant | 2001 | -.3247795 .1811756 -1.79 0.073 -.6798773 .0303182 2002 | -.4692111 .251969 -1.86 0.063 -.9630614 .0246391 2003 | -.5624661 .3507764 -1.60 0.109 -1.249975 .125043 2004 | -1.298661 .4493931 -2.89 0.004 -2.179455 -.4178663 2005 | -.9139517 .5503947 -1.66 0.097 -1.992705 .164802 2006 | -.9544268 .6524444 -1.46 0.144 -2.233194 .3243408 2007 | -1.065164 .7559497 -1.41 0.159 -2.546799 .4164698 2008 | -1.144925 .8512318 -1.35 0.179 -2.813308 .523459 | tech_cat | 2 | .4252098 .046273 9.19 0.000 .3345164 .5159031 3 | .2677324 .2693331 0.99 0.320 -.2601507 .7956155 4 | .3684181 .0411073 8.96 0.000 .2878494 .4489868 5 | .1054494 .070141 1.50 0.133 -.0320244 .2429231 6 | .1546547 .0782129 1.98 0.048 .0013602 .3079493 -------------------------------------------------------------------------------------
Note that running a simple OLS on the log of the response variable has the same peculiar results, with only significant interactions when both direct and indirect ties are included.
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