I want to better understand the differences in what is being predicted when using fixed and random effects after a regression
I run a regression that looks like this with DV a count variable that is severely skewed with and standard deviation significantly bigger than the mean, so negative binomial seems appropriate (and the norm in my field for these kinds of data). I have multiple firms with multiple observations per year over a 20 year period (unbalanced).
Now, the values for fe_dv are significantly smaller than those for re_dv, they differ by a factor of about 10 [9.08, 10.18] and they also differ within the firms (for the fixed effects). It is common practice to use fixed effects for this kind of data in my field but the predictions I can get from them much further away from the actual observations DV. That being said, the correlation between both fe_dv and re_dv is 100% [which is a bit weird given that they are not simple linear combinations of one another...
Because the prediction of the fixed effects model seems generally ten times smaller than the random effects model, I am struggling with the right interpretation of the following margins command:
margins determines the average marginal effect of a change in z1 on DV at distinct values of z2.
I am struggling to understand the difference between both versions of the margins command. I know the former is the predicted number of events, and the latter is the linear prediction but if that is correct, what does it mean if the values of both margins commands are nearly identical (they start differing only 3 or 4 numbers after the comma, see below)?
If I want to check the economic significance of the values of dy/dx, I have to compare them to a relevant reference value. Now what is the most sensible one to use? Is it the actual DV? Is it the predicted responses fe_dv, or something else?
And given that z1 is a continuous variable (between 0 and 7), could the following interpretation hold true?
Say, dydx at z2 = min equals 0.01 and dydx at z2 = mean equals 0.026
A change of 1 in the value of z1 from 0 to 1 leads to an increase in the number of incidences in the DV of 0.01 if z2 is at its minimum value and an increase of 0.026 if z2 is at its mean value.
I assume this is the interpretation after the
option. Is this correct and how does it differ after the second margins command I ran above? I thought it should differ substantially but according to the marginal effects I get, there is almost no difference whatsoever.
For sake of clarity, I show some output of the actual regression
Thanks for your time!
Simon
I run a regression that looks like this with DV a count variable that is severely skewed with and standard deviation significantly bigger than the mean, so negative binomial seems appropriate (and the norm in my field for these kinds of data). I have multiple firms with multiple observations per year over a 20 year period (unbalanced).
Code:
encode firm_id, gen(fid) iis fid xtnbreg DV c.z1##c.z2 $xvarlist , fe predict fe_dv, nu0 xtnbreg DV c.z1##c.z2 $xvarlist , re predict re_dv, nu0
Because the prediction of the fixed effects model seems generally ten times smaller than the random effects model, I am struggling with the right interpretation of the following margins command:
Code:
xtnbreg DV c.z1##c.z2 $xvarlist , fe
margins, dydx(z1) at(z2 = (0 5.6(8.6)23 )) predict(nu0)
margins, dydx(z1) at(z2 = (0 5.6(8.6)23))
I am struggling to understand the difference between both versions of the margins command. I know the former is the predicted number of events, and the latter is the linear prediction but if that is correct, what does it mean if the values of both margins commands are nearly identical (they start differing only 3 or 4 numbers after the comma, see below)?
If I want to check the economic significance of the values of dy/dx, I have to compare them to a relevant reference value. Now what is the most sensible one to use? Is it the actual DV? Is it the predicted responses fe_dv, or something else?
And given that z1 is a continuous variable (between 0 and 7), could the following interpretation hold true?
Say, dydx at z2 = min equals 0.01 and dydx at z2 = mean equals 0.026
A change of 1 in the value of z1 from 0 to 1 leads to an increase in the number of incidences in the DV of 0.01 if z2 is at its minimum value and an increase of 0.026 if z2 is at its mean value.
I assume this is the interpretation after the
Code:
predict(nu0)
For sake of clarity, I show some output of the actual regression
Code:
xtnbreg fwd10 c.log_dom##c.t_s_d##c.p_pria_usew p_pria_timew f_emp f_acap f_dar f_search f_inv_prod_5y p_inv log_other t_k_s team_t_1st col_difpairs team_m_patcount_5y p_classes dif_cpc p_cpc_1 p_pria p_claims priordum ts i.p_appy i.p_gry if compustat == 1, fe
note: 3 groups (3 obs) dropped because of only one obs per group
Conditional FE negative binomial regression Number of obs = 40,138
Group variable: fid Number of groups = 105
Obs per group:
min = 2
avg = 382.3
max = 8,484
Wald chi2(38) = 6522.35
Log likelihood = -128445.56 Prob > chi2 = 0.0000
-------------------------------------------------------------------------------------------------------------
fwd10 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
--------------------------------------------+----------------------------------------------------------------
log_dom_t | .0244366 .0048438 5.04 0.000 .0149429 .0339302
t_s_degree_cent | .0031362 .0014045 2.23 0.026 .0003834 .005889
|
c.log_dom_t#c.t_s_degree_cent | -.0012754 .0003445 -3.70 0.000 -.0019506 -.0006003
|
p_pria_usew | -.0012637 .0115459 -0.11 0.913 -.0238932 .0213658
|
c.log_dom_t#c.p_pria_usew | .0090225 .0036865 2.45 0.014 .0017972 .0162478
|
c.t_s_degree_cent#c.p_pria_usew | .0030458 .0013597 2.24 0.025 .0003808 .0057108
|
c.log_dom_t#c.t_s_degree_cent#c.p_pria_usew | -.000679 .0003071 -2.21 0.027 -.0012809 -.0000771
margins, dydx(log_dom_t) at(t_s_d = (0 5.66 14.4 23) p_pria_usew = (-1.5 -.9 0 .9 1.8 3.6)) predict(nu0)
Average marginal effects Number of obs = 40,138
Model VCE : OIM
Expression : Predicted number of events (assuming u_i=0), predict(nu0)
dy/dx w.r.t. : log_dom_t
------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
log_dom_t |
_at |
1 | .0107409 .0074239 1.45 0.148 -.0038096 .0252914
2 | .0162449 .0060048 2.71 0.007 .0044756 .0280141
3 | .0247225 .0049323 5.01 0.000 .0150554 .0343896
4 | .0334764 .0058737 5.70 0.000 .0219641 .0449887
5 | .0425183 .0082944 5.13 0.000 .0262616 .0587751
6 | .0615165 .0148566 4.14 0.000 .032398 .090635
7 | .0092054 .0064945 1.42 0.156 -.0035236 .0219344
8 | .012431 .0053276 2.33 0.020 .001989 .0228729
9 | .0174624 .0045355 3.85 0.000 .008573 .0263517
10 | .0227338 .0054916 4.14 0.000 .0119704 .0334972
11 | .028255 .0077184 3.66 0.000 .0131272 .0433829
12 | .0400876 .013751 2.92 0.004 .0131362 .0670391
13 | .0068984 .0081304 0.85 0.396 -.0090368 .0228337
14 | .0066254 .0066156 1.00 0.317 -.006341 .0195918
15 | .006182 .0055015 1.12 0.261 -.0046007 .0169648
16 | .005696 .006815 0.84 0.403 -.0076612 .0190531
17 | .0051646 .0099822 0.52 0.605 -.0144002 .0247293
18 | .0039548 .0187767 0.21 0.833 -.0328468 .0407564
19 | .0047026 .0117443 0.40 0.689 -.0183158 .027721
20 | .0010094 .0095372 0.11 0.916 -.0176831 .019702
21 | -.005011 .0077405 -0.65 0.517 -.0201822 .0101602
22 | -.0116496 .0098395 -1.18 0.236 -.0309347 .0076355
23 | -.0189558 .0152036 -1.25 0.212 -.0487543 .0108428
24 | -.0357875 .0308857 -1.16 0.247 -.0963223 .0247473
------------------------------------------------------------------------------
margins, dydx(log_dom_t) at(t_s_d = (0 5.66 14.4 23) p_pria_usew = (-1.5 -.9 0 .9 1.8 3.6))
Average marginal effects Number of obs = 40,138
Model VCE : OIM
Expression : Linear prediction, predict()
dy/dx w.r.t. : log_dom_t
------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
log_dom_t |
_at |
1 | .0109029 .0075135 1.45 0.147 -.0038233 .025629
2 | .0163163 .0059931 2.72 0.006 .00457 .0280627
3 | .0244366 .0048438 5.04 0.000 .0149429 .0339302
4 | .0325568 .0057465 5.67 0.000 .0212938 .0438197
5 | .040677 .0080373 5.06 0.000 .0249242 .0564298
6 | .0569174 .0139211 4.09 0.000 .0296326 .0842022
7 | .0094488 .0066705 1.42 0.157 -.0036251 .0225228
8 | .0125563 .0053762 2.34 0.020 .0020191 .0230935
9 | .0172176 .0044673 3.85 0.000 .0084619 .0259732
10 | .0218788 .0053233 4.11 0.000 .0114453 .0323122
11 | .02654 .0073517 3.61 0.000 .012131 .040949
12 | .0358624 .012548 2.86 0.004 .0112688 .060456
13 | .0072036 .0085747 0.84 0.401 -.0096025 .0240097
14 | .0067502 .0067921 0.99 0.320 -.006562 .0200624
15 | .0060702 .0054292 1.12 0.264 -.0045708 .0167111
16 | .0053901 .0064915 0.83 0.406 -.007333 .0181133
17 | .0047101 .0091719 0.51 0.608 -.0132665 .0226867
18 | .00335 .0160016 0.21 0.834 -.0280126 .0347126
19 | .0049943 .0125842 0.40 0.691 -.0196703 .0296589
20 | .0010371 .0098148 0.11 0.916 -.0181995 .0202738
21 | -.0048986 .0075191 -0.65 0.515 -.0196357 .0098385
22 | -.0108344 .0089803 -1.21 0.228 -.0284355 .0067667
23 | -.0167702 .0129869 -1.29 0.197 -.0422241 .0086838
24 | -.0286417 .0231603 -1.24 0.216 -.0740351 .0167517
------------------------------------------------------------------------------
Simon
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