Let $L$ be a line bundle on $X$. Let $\|\ \|$ be a model metric on $L^{\rm an}$ and $\theta\coloneqq c_{1}(L,\|\ \|)$. Let $\|\ \|^{\prime}$ be another metric on $L^{\rm an}$ and let $\varphi\coloneqq-\log(\|\ \|^{\prime}/\|\ \|)$. Then $\|\ \|^{\prime}$ is a model metric if and only if $\varphi$ is a model function. Moreover $\|\ \|^{\prime}$ is a semipositive model metric if and only if $\varphi$ is a $\theta$-psh model function.