  In this paper, we explore the physics of the accretion and jet in narrow-line
Seyfert 1 galaxies (NLS1). Specifically, we compile a sample composed of 16
nearby NLS1 with $L_{\rm bol}/L_{\rm Edd} \gtrsim 0.1$. We investigate the
mutual correlation between their radio luminosity $L_{\rm R}$, X-ray luminosity
$L_{\rm X}$, optical luminosity $L_{\rm 5100}$ and black hole mass $M_{\rm
BH}$. By adopting partial correlation analysis: (1) we find a positive
correlation between $L_{\rm X}$ and $M_{\rm BH}$, and (2) we find a weak
positive correlation between $L_{\rm R}$ and $L_{5100}$. However, we don't find
significant correlations between $L_{\rm R}$ and $L_{\rm X}$ or between $L_{\rm
X}$ and $L_{5100}$ after considering the effect of the black hole mass, which
leads to a finding of the independence of $L_{\rm X}/L_{\rm Edd}$ on
$L_{5100}/L_{\rm Edd}$. Interestingly, the findings that $L_{\rm X}$ is
correlated with $M_{\rm BH}$ and $L_{\rm X}/L_{\rm Edd}$ is not correlated with
$L_{5100}/L_{\rm Edd}$ support that the X-ray emission is saturated with
increasing $\dot{M}$ for $L_{\rm bol}/L_{\rm Edd} \gtrsim 0.1$ in NLS1s, which
may be understood in the framework of slim disc scenario. Finally, we suggest
that a larger NLS1 sample with high quality radio and X-ray data is needed to
further confirm this result in the future.
