Dear all,

I'm currently writing my pre-master thesis. For my thesis, I have panel data and ran a Negative binomial regression analysis with fixed effects.
I controlled for, fixed model or random-effects model by using the Hausman test which reported p<0.01 therefore, I used the fixed-effects model.

I also ran a negative binomial regression analysis with a random-effects model on my data to account for time-invariant industry effects. But this reported different results which do not make my results robust.
My question is How do I need to interpret these results? Does this mean that my dependent variable (environmental innovation) changes over time or my independent variable (CEO age)? If someone could elaborate on my results as I am not getting much wiser from the internet, I'm unsure if I understand correctly and how to proceed to know my results aren't robust.

See the boldly marked results for the changing results I mean:

Table 2
Results of negative binomial regression with fixed effects for the relationship between CEO age, R&D spending, and environmental innovation.
----------------------------------------------------------------------------------------------------
Dependent variable R&D Spending Environmental Innovation
---------------------------------------------------- -----------------------------------------
Model Model 2 Model 3 Model 4 Model 5

R&D intensity 2.073*** 2.055*** 10.90* 10.86* 6.172
(0.000) (0.000) (0.033) (0.034) (0.275)

Firm size 0.368*** 0.361*** 0.157 0.170 0.0329
(0.000) (0.000) (0.120) (0.105) (0.794)

Return on assets -0.327*** -0.329*** -1.037 -1.036 -0.572
(0.000) (0.000) (0.336) (0.336) (0.608)

CEO tenure -0.0000298*** -0.0000291*** -0.0000887* -0.0000880* -0.0000646
(0.000) (0.000) (0.035) (0.037) (0.146)

CEO salary 0.208*** 0.244*** -0.0936 -0.129 -0.0660
(0.000) (0.000) (0.770) (0.696) (0.842)

CEO bonus -0.0210** -0.0199** -0.0694 -0.0699 -0.0606
(0.001) (0.002) (0.446) (0.444) (0.496)

CEO age -0.00333** 0.00629 0.00489
(0.007) (0.655) (0.723)

R&D spending 0.000156*
(0.037)

Constant -2.120*** -2.113*** -0.335 -0.586 0.221
(0.000) (0.000) (0.854) (0.757) (0.910)
----------------------------------------------------------------------------------------------------
Observations 4805 4805 863 863 863
Log lik. -18517.5 -18513.9 -651.8 -651.7 -649.7
chi2 2449.5 2477.9 11.08 11.30 16.22
----------------------------------------------------------------------------------------------------
p-values in parentheses
* p<0.05, ** p<0.01, *** p<0.001




Results of negative binomial regression with random effects:
--------------------------------------------------------------------
(1) (2) (3)
number of ~ number of ~ number of ~
--------------------------------------------------------------------
number of green pa~
L.rdintensity -4.700 -4.272 -5.647*
(0.075) (0.103) (0.043)

firmsize 0.357*** 0.392*** 0.310***
(0.000) (0.000) (0.000)

roa -0.490 -0.506 -0.337
(0.484) (0.465) (0.650)

ceo_tenure -0.000106** -0.000111*** -0.0000956**
(0.002) (0.001) (0.005)

ceo_salary 0.174 0.101 0.143
(0.417) (0.607) (0.492)

L.ceo_bonus -0.0503 -0.0563 -0.0470
(0.528) (0.480) (0.542)

Executive's Age 0.0261* 0.0244*
(0.023) (0.030)

L.Research and Dev~e 0.000135*
(0.031)

Constant -4.229*** -5.534*** -5.125***
(0.001) (0.000) (0.000)
--------------------------------------------------------------------
/
ln_r 0.576*** 0.582*** 0.600***
(0.000) (0.000) (0.000)

ln_s -1.638*** -1.583*** -1.596***
(0.000) (0.000) (0.000)
--------------------------------------------------------------------
Observations 4925 4925 4925
Log lik. -1105.3 -1102.6 -1100.5
chi2 68.68 74.66 79.82
--------------------------------------------------------------------
p-values in parentheses
* p<0.05, ** p<0.01, *** p<0.001



Many thanks in advance!