MTP2 and partial correlations in monotone higher-order factor models

Abstract

For binary variables, multivariate positivity of order 2 (MTP2) implies nonnegative partial correlations (NPC). This is so because for any triple of variables, MTP2 is equivalent with conditional association. Under weak distribution assumptions of the noise variables, monotone higherorder one-factor models imply MTP2 of the manifest variables. This remains true after discretization of the manifest variables. Therefore, MTP2 and NPC cannot be used to discriminate unidimensional monotone latent variable models from multidimensional monotone higher-order one-factor models.