Confinement scalings of divertor discharges and radiofrequency heated discharges are shown to differ significantly from the standard scaling for neutral beam heated limiter discharges. 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. A scaling similar to the Goldston scaling is found for the neutral beam limiter dataset and a scaling similar to the ITER89P scaling is found for the combined dataset. Various missing-value algorithms are examined for the missing Bt scalings. It is assumed that global confinement can be approximately described by 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 uncertainty for CIT is significantly reduced, while the uncertainty for ITER is slightly reduced.