The use of two-stage least squares (2SLS) for the estimation of feedback linkages is inappropriate for nonorthogonal data sets because 2SLS is extremely sensitive to multicollinearity. It is argued that what is needed is use of a different estimating criterion than the least squares criterion. Theoretically the variance normalization criterion has superior properties. When two-stage normalization regression (2SNR), which uses the variance normalization criterion, is used to estimate a psycholinguistic model of grade 4 literacy and numeracy, the multiple feedback parameters were shown to be more stable than those generated by the 2SLS technique. Thus, at the grade 4 level intuitive linguistic strategies were more influential in accounting for literacy and numeracy than formally learned strategies. The relationships between basic skills on the one hand and between literacy and numeracy on the other were mutually reinforcing, and the basic skills were found to be important variables mediating the relationship between cueing strategies and the acquisition of literacy and numeracy. Though the 2SNR technique in practice seemed to have important advantages over 2SLS, Monte Carlo simulations have to be conducted before it can be recommended as the standard nonrecursive estimating procedure. (Author/RL)