Context : The geometry and physical properties of the accretion mode , and the radiative processes occurring in AGN-powered low ionization nuclear emission-line regions ( LINERs ) remain a riddle . Both a standard thin accretion disk and an inner-hot radiatively-inefficient accretion flow ( RIAF ) have been invoked . Models depending on only a jet have also been invoked to explain the broad-band spectral energy distribution ( SED ) of LINERs . Aims : We attempt to infer the accretion mechanism and radiative processes giving rise to the SEDs of a well-defined optically-selected sample of LINERs showing a definite detection of broad H \alpha emission ( LINER 1s ) . Methods : We construct SEDs for six LINER 1s with simultaneous UV and X-ray fluxes , and we looked for multiwavelength , radio to X-ray and UV to X-ray , correlations . Results : At a given X-ray luminosity , the average SED of the six LINER 1s in our sample : ( 1 ) resembles the SED of radio-loud quasars in the radio band , < \log~ { } R _ { X } > \approx - 2.7 , ( 2 ) exhibits a weak UV bump , < \alpha _ { ox } > \approx - 1.17 \pm 0.02 with a dispersion \sigma = 0.01 , and ( 3 ) displays a X-ray spectrum similar to radio-quiet quasars . The bolometric luminosities inferred from the SEDs of these LINER 1s are extremely faint , at least two orders of magnitude lower than AGN . The X-ray bolometric correction , \kappa _ { 2 - 10 ~ { } keV } , of our sample is lower than in the case of AGN , with a mean value of 16 . We find a strong anticorrelation between the radio loudness parameter , R _ { X } , and the Eddington ratio for our sample , confirming previous results . Moreover , we find a positive correlation between the radio luminosity and the X-ray luminosity which places AGN-powered LINERs , on a radio-power scale , right between low luminosity Seyferts and low luminosity radio galaxies . We complement our \alpha _ { ox } list with values derived on a well defined sample of UV-variable LINERs , and establish a strong positive correlation between \alpha _ { ox } ( considering negative values ) and the Eddington ratio , in contrast to the correlation found for luminous AGN . Lastly , we tested two different fundamental planes existing in the literature on our sample , in an attempt to put constraints on the debated origin of the X-ray emission , “ RIAF versus jet ” . The results came contradictory with one pointing toward a RIAF-dominated X-ray emission process and the other pointing toward a jet domination . Conclusions :