The $eta$-meson production in photon- and hadron-induced reactions, namely, $gamma p to p eta$, $pi^- p to n eta$, $pp to ppeta$, and $pn to pneta$, are investigated in a combined analysis in order to learn about the relevant production mechanisms and the possible role of nucleon resonances in these reactions. We consider the nucleonic, mesonic, and nucleon resonance currents constructed within an effective Lagrangian approach and compare the results with the available data for cross sections and spin asymmetries for these reactions. We found that the reaction $gamma p to p eta$ could be described well with the inclusion of the well-established $S_{11}(1535)$, $S_{11}(1650)$, $D_{13}(1520)$, and $D_{13}(1700)$ resonances, in addition to the mesonic current. Consideration of other well-established resonances in the same mass region, including the spin-5/2 resonances, $D_{15}(1675)$ and $F_{15}(1680)$, does not further improve the results qualitatively. For the reaction $pi^- p to n eta$, the $P_{13}(1720)$ resonance is found to be important for reproducing the structure observed in the differential cross section data. Our model also improves the description of the reaction $NN to NNeta$ to a large extent compared to the earlier results by Nakayama textit{et al.} [Phys. Rev. C textbf{68}, 045201 (2003)]. For this reaction, we address two cases where either the $S_{11}(1535)$ or the $D_{13}$ dominates. Further improvement in the description of these reactions and the difficulty to uniquely determine the nucleon resonance parameters in the present type of analysis are discussed.
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