We show that when the thresholds and the polychoric correlation are estimated in two stages, neither Pearson's X^2 nor the likelihood ratio G^2 goodness of fit test statistics are asymptotically chi-square. We propose a new test statistic, Mn, that is asymptotically chi-square in this situation....

We show how to test hypotheses for coefficient alpha in three different situations: (1) Hypothesis tests of whether coefficient alpha equals a prespecified value. (2) Hypothesis tests involving two statistically independent sample alphas as may arise when testing the equality of coefficient...

The classical method (Mosteller, 1951) for estimating Thurstone's Case V model for ranking data consists in a) transforming the observed ranking patterns to patterns of binary paired comparisons, b) obtaining the normal deviate corresponding to the men of each binary variable, and c) estimate...