Variables Separate Cmp on Cmp with Our method equations pooled data random effects xtcmp Binary outcome: ${\stackrel{˜}{y}}_{it}^{1}$ x1 $\underset{\left(0.0166\right)}{0.0238}$ $\underset{\left(0.0062\right)}{-0.0056}$ $\underset{\left(0.0224\right)}{0.0021}$ $\underset{\left(0.0082\right)}{0.0119}$ x2 $\underset{\left(0.0238\right)}{{0.2569}^{***}}$ $\underset{\left(0.0034\right)}{{0.0297}^{***}}$ $\underset{\left(0.0045\right)}{{0.0484}^{***}}$ $\underset{\left(0.0037\right)}{{0.0204}^{***}}$ x3 $\underset{\left(0.1228\right)}{{0.3171}^{**}}$ $\underset{\left(0.006\right)}{0.0053}$ $\underset{\left(0.0224\right)}{0.0351}$ $\underset{\left(0.0265\right)}{0.0254}$ x4 $\underset{\left(0.2182\right)}{-{0.5748}^{***}}$ $\underset{\left(0.0112\right)}{-0.0084}$ $\underset{\left(0.0399\right)}{-0.058}$ $\underset{\left(0.0471\right)}{-0.0463}$ Intercept $\underset{\left(0.375\right)}{-{6.4382}^{***}}$ $\underset{\left(0.0379\right)}{-{0.7083}^{***}}$ $\underset{\left(0.1339\right)}{{1.1074}^{***}}$ $\underset{\left(0.0535\right)}{-{2.7151}^{***}}$ Continuous outcome: ${\stackrel{˜}{y}}_{it}^{3}$ x7 $\underset{\left(0.0207\right)}{-{0.1528}^{***}}$ $\underset{\left(0.0168\right)}{-{0.0321}^{*}}$ $\underset{\left(0.015\right)}{-{0.1044}^{***}}$ $\underset{\left(0.0158\right)}{-{0.0422}^{***}}$ x9 $\underset{\left(0.004\right)}{{0.0384}^{***}}$ $\underset{\left(0.0047\right)}{{0.1035}^{***}}$ $\underset{\left(0.004\right)}{{0.0361}^{***}}$ $\underset{\left(0.0043\right)}{{0.096}^{***}}$ Intercept $\underset{\left(0.7339\right)}{{15.9964}^{***}}$ $\underset{\left(0.5086\right)}{{10.0568}^{***}}$ $\underset{\left(0.4477\right)}{{17.0243}^{***}}$ $\underset{\left(0.4779\right)}{{7.4308}^{***}}$ Covariance matrix: individual effects ${\sigma }_{1}$ $\underset{\left(0.2135\right)}{{3.8635}^{***}}$ - $\underset{\left(0.2144\right)}{{2.8431}^{***}}$ $\underset{\left(0.1263\right)}{{2.0702}^{***}}$ ${\sigma }_{2}$ 6.024 - $\underset{\left(0.1789\right)}{{5.706}^{***}}$ $\underset{\left(0.1421\right)}{{2.2481}^{***}}$ ${\rho }_{1}$ - - $\underset{\left(0.0247\right)}{{0.5135}^{***}}$ $\underset{\left(0.0417\right)}{{0.8196}^{***}}$ Covariance matrix: idiosyncratic errors $\sigma$ 2.6596 $\underset{\left(0.1172\right)}{{6.7719}^{***}}$ $\underset{\left(0.0481\right)}{{2.6725}^{***}}$ $\underset{\left(0.1182\right)}{{6.472}^{***}}$ $\rho$ - $\underset{\left(0.0349\right)}{{0.1525}^{***}}$ $\underset{\left(0.0528\right)}{0.0342}$ $\underset{\left(0.0418\right)}{{0.5087}^{***}}$