Abstract In this article, we study the causal inference problem with a continuous treatment variable using propensity score-based methods. For a continuous treatment, the generalized propensity score is defined as the conditional density of the treatment-level given covariates (confounders). The...

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 common factor model assumes a linear relation between the observed variables and a set of underlying latent traits. It also assumes that the linear coefficients, intercepts and slopes (factor loadings), linking the observed variables to the latent traits are fixed coefficients (i.e., common...

High-dimensional contingency tables tend to be sparse and standard goodness-of-fit statistics such as X2 cannot be used without pooling categories. As an improvement on arbitrary pooling, for goodness-of-fit of large 2n contingency tables, we propose a class of quadratic form statistics based on...

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...

We introduce a family of goodness-of-fit statistics for testing composite null hypotheses in multidimensional contingency tables of arbitrary dimensions. These statistics are quadratic forms in marginal residuals up to order r. They are asymptotically chi-square under the null hypothesis when...

We introduce a multidimensional latent trait model for binary data with non-monotone item response functions. We assume that the conditional probability of endorsing an item is a normal probability density function, and that the latent traits are normally distributed. The model yields closed...

We consider the estimation of multivariate normal structural models that have been discretized according to a set of thresholds. A popular estimation procedure for this restricted multinomial model consists in the following three stage estimator: First, estimate by maximum likelihood the...