Let $\theta\in\mathcal{Z}^{1,1}(X)$ be a closed $(1,1)$-form. A model function $\varphi\in\mathcal{D}(X)$ is said to be $\theta$-plurisubharmonic ($\theta$-psh for short) if the closed $(1,1)$-form $\theta+dd^{c}\varphi$ is semipositive.