I´m doing research on a political science topic and my models leave me behind with a big questionmark at this point. I have a dataset containing 79 observations on a number of variables and trying and testing out different models I have specified one control variable in several different ways, to which my variables of interest have reacted by either being significant at the 5% level or not at all. I can´t really find an answer to this, as there is no (theoretical) link between the two variables so in my understanding it´s not a classical confounder. I have copied the regression outputs below, but for your better understanding some more information: While my dataset is originally in a panel data form, I "collapsed" the panel data into a cross-sectional dataset only including the maximum values of my dependent variable for each country. The independent variable that´s giving me nightmares since days is one, that in the original panel data is reported as a running value of the individuals in the respective country that experienced a certain event a, and thus never decreases. My other explanatory variables are time-invariant factors. So the original dataset looks something like this:
Country Var1 Var2 Var3 region Var4 IndepVar Day
CountryA 0 4 6 1 2 34 1
CountryA 4 4 6 1 2 65 2
CountryA 9 4 6 1 2 65 3
CountryA 14 4 6 1 2 62 4
CountryA 17 4 6 1 2 82 5
CountryA 21 4 6 1 2 71 6
As described I changed this into a cross-sectional dataset, keeping only the first observation in which the Independent Variable reaches it´s maximum with respect to the country. So it looks something like this:
Country Var1 Var2 Var3 region Var4 IndepVar
CountryA 17 4 6 1 2 82
I further normalised Var1 on 100.000 citizens and did some additional transformations: A: the number of citizens first experiencing the event at the described time-point (on 100.000 citizens) B: the number of citizens first experiencing the event the week prior to the described time point. I estimated a linear regression with OLS, getting the following outputs:
For log of Var1 on 100.000 citizens
Residuals:
Min 1Q Median 3Q Max
-49.005 -4.818 1.881 7.794 18.363
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.677e+01 1.333e+01 3.508 0.000838 ***
Var2 7.619e-02 1.045e+00 0.073 0.942130
Var3 1.816e+00 9.228e-01 1.968 0.053462 .
log(Var1 on 100.000 cit) 1.851e+00 9.262e-01 1.999 0.049957 *
Var4 -3.334e-04 2.310e-04 -1.444 0.153815
Var5 4.591e+00 2.040e+00 2.250 0.027936 *
East.Europe_Centr.Asia -8.230e+00 6.089e+00 -1.352 0.181327
Sub.Sahara_Africa -3.485e+00 5.115e+00 -0.681 0.498115
MiddleEast_N.Africa -3.547e+00 5.970e+00 -0.594 0.554558
LA.America_Carribean -1.050e+01 7.416e+00 -1.416 0.161631
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 13.36 on 63 degrees of freedom
(6 observations deleted due to missingness)
Multiple R-squared: 0.2673, Adjusted R-squared: 0.1626
F-statistic: 2.554 on 9 and 63 DF, p-value: 0.01435
For A:
Residuals:
Min 1Q Median 3Q Max
-43.786 -4.342 1.413 7.200 22.515
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 6.377e+01 1.358e+01 4.694 1.46e-05 ***
Var2 -4.171e-02 9.977e-01 -0.042 0.966784
Var3 1.114e+00 8.872e-01 1.256 0.213858
log(A) 2.561e+00 6.857e-01 3.735 0.000402 ***
Var4 -3.921e-04 2.102e-04 -1.865 0.066735 .
Var5 4.293e+00 1.948e+00 2.203 0.031181 *
East.Europe_Centr.Asia -9.978e+00 5.271e+00 -1.893 0.062882 .
Sub.Sahara_Africa -4.915e+00 4.872e+00 -1.009 0.316783
MiddleEast_N.Africa -6.925e+00 5.713e+00 -1.212 0.229956
LA.America_Carribean -1.092e+01 7.073e+00 -1.544 0.127609
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 12.77 on 64 degrees of freedom
(5 observations deleted due to missingness)
Multiple R-squared: 0.3597, Adjusted R-squared: 0.2696
F-statistic: 3.994 on 9 and 64 DF, p-value: 0.0004369
For B:
Residuals:
Min 1Q Median 3Q Max
-48.398 -5.018 0.807 8.299 25.956
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.831e+01 1.341e+01 3.601 0.000619 ***
Var2 -1.905e-01 1.050e+00 -0.181 0.856602
Var3 1.904e+00 9.334e-01 2.040 0.045520 *
log(B) 1.945e+00 7.659e-01 2.539 0.013560 *
Var4 -4.109e-04 2.281e-04 -1.801 0.076414 .
Var5 5.530e+00 2.033e+00 2.720 0.008395 **
East.Europe_Centr.Asia -1.111e+01 5.866e+00 -1.893 0.062875 .
Sub.Sahara_Africa -4.147e+00 5.115e+00 -0.811 0.420498
MiddleEast_N.Africa -5.264e+00 6.140e+00 -0.857 0.394446
LA.America_Carribean -1.185e+01 7.556e+00 -1.569 0.121645
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 13.44 on 64 degrees of freedom
(5 observations deleted due to missingness)
Multiple R-squared: 0.2915, Adjusted R-squared: 0.1919
F-statistic: 2.926 on 9 and 64 DF, p-value: 0.005744
When omitting the variable at all, I get:
Residuals:
Min 1Q Median 3Q Max
-53.748 -4.453 1.743 7.763 18.564
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 45.9891033 13.9324535 3.301 0.00157 **
Var2 -0.0964768 1.0923946 -0.088 0.92990
Var3 1.5724778 0.9621439 1.634 0.10702
Var4 -0.0002251 0.0002250 -1.001 0.32072
Var5 5.2805804 2.1139426 2.498 0.01503 *
East.Europe_Centr.Asia -5.1318216 5.5944169 -0.917 0.36237
Sub.Sahara_Africa -3.5883081 5.3204603 -0.674 0.50243
MiddleEast_N.Africa 1.6412392 5.7302669 0.286 0.77547
LA.America_Carribean -7.8610240 7.6936320 -1.022 0.31068
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 13.99 on 65 degrees of freedom
(5 observations deleted due to missingness)
Multiple R-squared: 0.2201, Adjusted R-squared: 0.1241
F-statistic: 2.293 on 8 and 65 DF, p-value: 0.03136
you can see, how especially Var3 (together with Var2 this is one of the factors I´m actually interested in) changes it´s significance level depending on how Var1 is operationalized. I really don´t get what is going on there and I would appreciate if someone could give me hint on how to deal with this. I have already tested for (multi)collinearity, but the coeffcients are not above 1.5/2 so in my understanding not critical.
Thank you very much!
