The　partially　linear　varying　coefficient　spatial　autoregressive　model　is　a　semi-parametric　spatial　autoregressive　model　in　which　the　coefficients　of　some　explanatory　variables　are　variable,　while　the　coefficients　of　the　remaining　explanatory　variables　are　constant.　For　the　nonparametric　part,　a　local　linear　smoothing　method　is　used　to　estimate　the　vector　of　coefficient　functions　in　the　model,　and,　to　investigate　its　variable　selection　problem, this　paper　proposes　a　penalized　robust　regression　estimation　based　on　exponential　squared　loss,　which　can　estimate　the　parameters　while　selecting　important　explanatory　variables.　A　unique　solution　algorithm　is　composed　using　the　block　coordinate　descent　(BCD)　algorithm　and　the concave-convex　process　(CCCP).　Robustness　of　the　proposed　variable　selection　method　is　demonstrated　by　numerical　simulations　and　illustrated　by　some　housing　data　from　Airbnb.　©　The　Author(s),　under　exclusive　licence　to　Springer　Science+Business　Media,　LLC,　part　of　Springer　Nature　2024.