Model 1

io.fit.poi.1 <- glm(iofound ~ iofound.t2 + iofound.total,
                          family="poisson",data=io.poi)
summary(io.fit.poi.1)

## 
## Call:
## glm(formula = iofound ~ iofound.t2 + iofound.total, family = "poisson", 
##     data = io.poi)
## 
## Deviance Residuals: 
##      Min        1Q    Median        3Q       Max  
## -22.4126   -1.3760   -1.0956   -0.5377   14.8151  
## 
## Coefficients:
##                 Estimate Std. Error z value Pr(>|z|)    
## (Intercept)   -5.439e-01  1.306e-02  -41.66   <2e-16 ***
## iofound.t2     4.145e-02  1.539e-04  269.27   <2e-16 ***
## iofound.total  2.223e-03  3.225e-05   68.93   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for poisson family taken to be 1)
## 
##     Null deviance: 105595  on 15470  degrees of freedom
## Residual deviance:  52605  on 15468  degrees of freedom
## AIC: 65137
## 
## Number of Fisher Scoring iterations: 6

Model 2

io.fit.poi.2 <- glm(iofound ~ iofound.t2 + iofound.total
                         + log(tpop) + cinc + polity2 + gdp.mix + trade + war,
                          family="poisson",data=io.poi)
summary(io.fit.poi.2)

## 
## Call:
## glm(formula = iofound ~ iofound.t2 + iofound.total + log(tpop) + 
##     cinc + polity2 + gdp.mix + trade + war, family = "poisson", 
##     data = io.poi)
## 
## Deviance Residuals: 
##      Min        1Q    Median        3Q       Max  
## -10.6870   -0.9760   -0.6335   -0.0290   11.3858  
## 
## Coefficients:
##                 Estimate Std. Error z value Pr(>|z|)    
## (Intercept)   -4.747e+00  6.667e-02 -71.193  < 2e-16 ***
## iofound.t2     3.794e-02  5.316e-04  71.363  < 2e-16 ***
## iofound.total  9.565e-04  4.602e-05  20.786  < 2e-16 ***
## log(tpop)      4.244e-01  7.133e-03  59.508  < 2e-16 ***
## cinc          -2.259e+01  7.519e-01 -30.048  < 2e-16 ***
## polity2        9.599e-02  1.845e-03  52.016  < 2e-16 ***
## gdp.mix        3.592e-05  8.149e-07  44.085  < 2e-16 ***
## trade          1.402e-04  4.005e-06  34.996  < 2e-16 ***
## war           -1.796e-01  3.612e-02  -4.974 6.56e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for poisson family taken to be 1)
## 
##     Null deviance: 62097  on 10926  degrees of freedom
## Residual deviance: 17739  on 10918  degrees of freedom
##   (4544 observations deleted due to missingness)
## AIC: 28492
## 
## Number of Fisher Scoring iterations: 6

Model 3

io.poi.panel <- plm.data(io.poi, index = c("ccode", "year"))
io.fit.poi.panel <- pglm(iofound ~ log(tpop) + cinc + polity2 + gdp.mix + trade + war 
                         + igosum  + abs(e_cen_w_3) 
                         + iofound.t2 + iofound.total,
                        data=io.poi.panel, family="poisson",
                        model = "random", effect=("individual"),
                        index = c("ccode","year"))

summary(io.fit.poi.panel)

## --------------------------------------------
## Maximum Likelihood estimation
## Newton-Raphson maximisation, 6 iterations
## Return code 2: successive function values within tolerance limit
## Log-Likelihood: -10504.06 
## 12  free parameters
## Estimates:
##                  Estimate Std. error t value  Pr(> t)    
## (Intercept)    -6.742e+00  3.442e-01 -19.590  < 2e-16 ***
## log(tpop)       5.403e-01  4.047e-02  13.349  < 2e-16 ***
## cinc           -6.606e+00  1.014e+00  -6.515 7.27e-11 ***
## polity2         1.363e-02  2.827e-03   4.823 1.41e-06 ***
## gdp.mix         8.157e-06  2.731e-06   2.987  0.00282 ** 
## trade           2.021e-05  6.330e-06   3.193  0.00141 ** 
## war            -9.802e-02  3.643e-02  -2.691  0.00713 ** 
## igosum          1.293e-02  9.323e-04  13.871  < 2e-16 ***
## abs(e_cen_w_3)  3.612e+00  2.203e-01  16.393  < 2e-16 ***
## iofound.t2      6.245e-03  1.004e-03   6.220 4.96e-10 ***
## iofound.total   1.808e-03  7.346e-05  24.616  < 2e-16 ***
## sigma           7.121e-01  8.171e-02   8.715  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## --------------------------------------------