LAX86FA079

Drg arrival at an arpt near his home, the plt contacted apch control (ctl) & asked the ctlr for assistance in landing & said that the wx looked a little foggy. The ctlr informed the plt of the acft's position in relation to the arpt. As the acft was dscndg twd the arpt, the plt rprtd that he had entered fog at about 4000' MSL. The ctlr instructed the plt to climb & maintain VFR, then asked if the plt would like a localizer d apch to the arpt. Altho he was not certified forinstrument flt, the plt accepted the apch. The arpt wx at that time was rprtd (in part) as: 1500' scattered, vis 7 mi. Vectors were provided for the apch. As the acft was apchg the outer marker, the plt was instructed to change to tower freq. He acknowledged, but there was no further transmissions from the acft & radar contact was lost. Subsequently, the acft crashed aprx 5 mi east of the arpt, on a hdg of 050 deg, in the vicinity of where radar contact was lost. No preimpact mechanical problems were found. The 1746 PST san diego wx was, in part: 2000' broken, vis 5 mi with haze.