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We revisit the question of the contributions of two-photon exchange with$\Delta(1232)$ excitation to the electron-proton scattering in a hadronicmodel. Three improvements over the previous calculations are made, namely,correct vertex function for $\gamma N\rightarrow\Delta$, realistic $\gammaN\Delta$ form factors, and coupling constants. The discrepancy between thevalues of $R\equiv \mu_p G_E/G_M$ extracted from Rosenbluth technique andpolarization transfer method can be reasonably accounted for if the data ofAndivahis {\it et al.} \cite{Andivahis94} are analyzed. However, substantialdiscrepancy remains if the data of Qattan {\it et al.} \cite{Qattan05} areused. For the ratio $R^\pm$ between $e^\pm p$ scatterings, our predictionsappear to be in satisfactory agreement with the preliminary data from VEPP-3.The agreement between our model predictions and the recent measurements onsingle spin asymmetry, transverse and longitudinal recoil proton polarizationsranges from good to poor.

$\Delta(1232)$ Resonance Contribution to Two-Photon Exchange in Electron-Proton Scattering Revisited