I am interested in statistical inference for the Deming regression model: $$ x_i=x^*_i + \epsilon_i$$ $$ y_i = (\alpha+\beta x^*_i) + \epsilon'_i$$ where the $x^*_i$'s are nonrandom fixed numbers, $\epsilon_i \sim {\cal N}(0,\sigma_x^2)$, $\epsilon'_i \sim {\cal N}(0,\sigma_y^2)$, and all variables $\epsilon_i, \epsilon'_i$ are mutually independent. I particularly focus on the case of the assumption $\sigma_x=\sigma_y$.
Graham Dunn's slides show how to treat the Deming regression with a two-stage least squares approach when the $x^*_i$'s are random (this model is sometimes termed as the ultrastructural model in the literature). I would like to know how to similarly treat the case when the $x^*_i$'s are nonrandom and whether it is possible to perform this approach with John Fox's "sem" R package.
