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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