Confinement scalings of divertor and radiofrequency heated discharges are shown to differ significantly from the standard neutral beam heated limiter scaling. The random coefficient two stage regression algorithm is applied to a neutral beam heated limiter subset of the ITER L mode database as well as a combined dataset. We find a scaling similar to Goldston scaling for the NB limiter dataset and a scaling similar to ITER89P for the combined dataset. Various missing value algorithms are examined for the missing $B_t$ scalings. We assume that global confinement can be approximately described a power law scaling. After the second stage, the constraint of collisional Maxwell Vlasov similarity is tested and imposed. When the constraint of collisional Maxwell Vlasov similarity is imposed, the C.I.T. uncertainty is significantly reduced while the I.T.E.R. uncertainty is slightly reduced.