I'm trying to predict the effect different regimetypes have on the likelihood of civil war onset. For this purpose I'm using xtlogit since my dependent variable (onset) is binary and the dataset is paneldata. Seeing that I want to compare different regression models I'll use the
Code:
margins, dydx(*)
. In one of the robustness models I substitute onset with another binary variable: governmental civil war onset (in danish regering). The problem is that the p-values change when I convert odds ratio to predicted probability using
Code:
margins, dydx(*)
. For category 3 (liberal democracy) the result is insignificant in the model using odds ratio (p-value = 0,068), however it becomes significant when using predicted probability (p-value = 0,009). How should I interpret this?

Code:
xtlogit regering i.v2x_regime_lag cgdppc_lag max_rdiscl_lag NHIxl_lag cinc_lag Total_Oil_Income_PC_lag    peace_year_lag    decay_function_lag    Americas    Eu
> rope MENA Asia if e2==1, or vce(cluster land)

Fitting comparison model:

Iteration 0:   log pseudolikelihood = -665.12183  
Iteration 1:   log pseudolikelihood =  -638.6753  
Iteration 2:   log pseudolikelihood = -631.36206  
Iteration 3:   log pseudolikelihood = -631.07399  
Iteration 4:   log pseudolikelihood = -631.07151  
Iteration 5:   log pseudolikelihood = -631.07151  

Fitting full model:

tau =  0.0     log pseudolikelihood = -631.07151
tau =  0.1     log pseudolikelihood = -631.45035

Iteration 0:   log pseudolikelihood = -631.45035  
Iteration 1:   log pseudolikelihood = -631.07129  
Iteration 2:   log pseudolikelihood = -631.03574  
Iteration 3:   log pseudolikelihood = -631.03068  
Iteration 4:   log pseudolikelihood = -631.03059  
Iteration 5:   log pseudolikelihood = -631.03059  

Calculating robust standard errors:

Random-effects logistic regression              Number of obs     =      6,724
Group variable: land                            Number of groups  =        152

Random effects u_i ~ Gaussian                   Obs per group:
min =         12
avg =       44.2
max =         59

Integration method: mvaghermite                 Integration pts.  =         12

Wald chi2(14)     =      41.50
Log pseudolikelihood  = -631.03059              Prob > chi2       =     0.0001

(Std. Err. adjusted for 152 clusters in land)

Robust
regering  Odds Ratio   Std. Err.      z    P>z     [95% Conf. Interval]

v2x_regime_lag 
1     1.703123   .3962947     2.29   0.022       1.0794    2.687259
2     .9463097   .3586698    -0.15   0.884      .450206    1.989094
3     .3185905   .1997512    -1.82   0.068     .0932273    1.088736

cgdppc_lag    .9999647   .0000271    -1.30   0.193     .9999116    1.000018
max_rdiscl_lag    1.904016   .8477297     1.45   0.148     .7955879    4.556728
NHIxl_lag     1.16897   .2459818     0.74   0.458      .773906    1.765706
cinc_lag    4.461662   18.04084     0.37   0.711      .001613    12341.03
Total_Oil_Income_PC_lag    1.000036   .0000525     0.68   0.496     .9999328    1.000139
peace_year_lag    .9962825   .0109373    -0.34   0.734     .9750748    1.017952
decay_function_lag    .7267845   .2485084    -0.93   0.351     .3718395    1.420547
Americas     1.16026   .2638379     0.65   0.513     .7430119    1.811818
Europe    .4185222   .1848075    -1.97   0.049     .1761376    .9944544
MENA    1.619499    .496078     1.57   0.116     .8884728    2.952005
Asia    .9230862   .2319049    -0.32   0.750     .5641529    1.510385
_cons    .0200784   .0079414    -9.88   0.000     .0092482     .043591

/lnsig2u   -3.245333   3.175614                     -9.469423    2.978756

sigma_u    .1973717   .3133882                       .008785    4.434337
rho    .0117025   .0367277                      .0000235    .8566707

Note: Estimates are transformed only in the first equation.
Note: _cons estimates baseline odds (conditional on zero random effects).
Code:
. margins, dydx(*)

Average marginal effects                        Number of obs     =      6,724
Model VCE    : Robust

Expression   : Pr(regering=1), predict(pr)
dy/dx w.r.t. : 1.v2x_regime_lag 2.v2x_regime_lag 3.v2x_regime_lag cgdppc_lag max_rdiscl_lag    NHIxl_lag    cinc_lag    Total_Oil_Income_PC_lag
peace_year_lag decay_function_lag Americas Europe MENA Asia


Delta-method
dy/dx   Std. Err.      z    P>z     [95% Conf. Interval]

v2x_regime_lag 
1     .0118224   .0052635     2.25   0.025      .001506    .0221387
2     -.000918   .0062151    -0.15   0.883    -.0130994    .0112634
3    -.0118171   .0045169    -2.62   0.009    -.0206701   -.0029641

cgdppc_lag   -6.92e-07   5.29e-07    -1.31   0.191    -1.73e-06    3.44e-07
max_rdiscl_lag    .0126371   .0088414     1.43   0.153    -.0046916    .0299659
NHIxl_lag    .0030637   .0041095     0.75   0.456    -.0049907    .0111182
cinc_lag     .029348   .0798936     0.37   0.713    -.1272406    .1859366
Total_Oil_Income_PC_lag    7.01e-07   1.02e-06     0.69   0.491    -1.29e-06    2.70e-06
peace_year_lag   -.0000731   .0002163    -0.34   0.735     -.000497    .0003508
decay_function_lag   -.0062625   .0067008    -0.93   0.350    -.0193958    .0068708
Americas     .002917   .0044431     0.66   0.511    -.0057913    .0116252
Europe   -.0170929    .008703    -1.96   0.050    -.0341505   -.0000353
MENA     .009461   .0062125     1.52   0.128    -.0027153    .0216373
Asia   -.0015706    .004936    -0.32   0.750     -.011245    .0081039

Note: dy/dx for factor levels is the discrete change from the base level.