Did you read the original Olsson (1979) paper? I believe it still provides the best description of what polychoric correlations are (although I've probably skimmed only 10% of the existing literature, I have to admit; at some point, it just gets too repetitive of the limited number of ideas though). Polychoric correlations are ML estimates of the correlations of the underlying normal distribution, so you interpret them just as you would Pearson moment correlations with continuous data. Given the ML origins of polychoric correlations, I never understood the advice to use ADF or other least squares methods with them to obtain model parameter estimates, although I do understand that say diagonally weighted least squares (don't know if John Fox implemented them in sem though), while being less asymptotically efficient, don't need as much auxiliary information for estimation purposes.
There is no magic sample size number, like, you hit 2000 and -- BOOM! -- everything starts working. In my simulations (and I've done a few petaflops this way and that way for my papers), I've seen both cases when asymptotic results worked perfectly fine with $N=200$ and failed to work with $N=5000$. In the most peculiar cases, for the same method and distribution of the underlying data, some asymptotic aspects, such as confidence interval coverage say, would be OK for $N=300$, while others, like $\chi^2$ distribution of a test statistic, would not work until you have $N=1000$. So I am highly skeptical of any sample size advice, and would rather recommend to run a simulation addressing your particular sample size, model complexity and magnitude of the errors. The first paper to bash ADF (Hu, Bentler and Kano (1992)) used an insane degree of overidentification, something like 30 variables in the model, which translates to 400 degrees of freedom, and a sample size of 50. ADF wouldn't even begin to work in these circumstances, as it won't be able to invert the matrix of the fourth moments which will be rank-deficient. And to get 400 degrees of freedom for the test statistic with the sample size below 1000 is a high expectation, too.
So I understand the healthy skepticism that you are demonstrating, but there is simply nothing you can do in your situation about it. Just run polycor to get the correlation estimates, feed them to sem, and that would be it -- there is little you can do to produce a much better analysis.
If you were a Stata user, I would immediately recommend gllamm package, but I am not sure whether a direct analogue of it exists in R.
Much as I dislike stepwise regression, if you are going to do it, I think EM's behavior is appropriate.
1) Because a set of dummy variables all go together. In your model, you are saying that industry is a predictor, not a particular industry
2) If you dropped the nonsignificant dummy variables, the others would change because either you are then controlling for different things or eliminating some subjects from the sample.
Best Answer
No, it's not true. You enter them as dummy variables, just as you would if you wanted to control for them in regression.
Unless you want to treat the variables as ordinal - in which case you have the same problem you have in regression - either treat them as (unordered) categorical, or treat them as continuous.