I conducted a LPA in Mplus and am choosing between a three-class solution with diagonal class-invariant structure and a two-class solution with a diagonal class-varying structure. The two-class solution is preferred by model fit statistics (BIC, Consistent AIC, approximate correct model probability, etc.), although the three-class solution is more theoretically compelling. I believe that I should select the two-class solution given better model fit; however, entropy is somewhat low (.69) which results in negative BCH weights when I attempt latent class regression.
In this circumstance, is it defensible to select the three-class model even though its relative fit indices are poorer, given that it has higher entropy (.89) and does not run into difficulty estimating BCH weights? Alternately, is there another method of LCR that you would recommend to sidestep the negative BCH weight problem?