Miscellanea. On the identification of a single-factor model with correlated residuals

Measurement bias and effect restoration in causal inference

“…In Fig.4 Stanghellini, 2004;Stanghellini and Wermuth, 2005;Vicard, 2000). Our approach extends the identification conditions to cases where the total effect can not be identified by any single strategy but by a combination of several strategies (e.g., the back door criterion and the CIV condition in this case).…”

Bayesian inference for graphical factor analysis models

“…Section 4 addresses the issue of identifiability. We present a sufficient condition for global identification of models with more than one factor, thereby generalising the results in Stanghellini (1997) and Vicard (2000). In section 5 we introduce the issue of model comparison, pointing out that, for our class of models, local computations are generally not possible in a frequentist setting.…”

“…Allowing a structure of associations gives information about the colTelalion left unexplained by the unobserved variables, which can be used both in the confirmatory and exploralory context. We first present a sufficient condition for global identifiability of this class of models with a generic number of factors, thereby extending the results in Stanghellini (1997) and Vicard (2000). We then consider the issue of model comparison and show that fast local computations are possible for this purpose, if lhe conditional independence graphs on the residuals are restricted to be decomposable and a Bayesian approach is adopted.…”

“…Analogous studies are in Stanghellini (1997) and Vicard (2000), where generalizations of a single-factor model are considered. Here we consider models with a generic number of factors.…”

Graphical Identifiability Criteria for Total Effects in Studies with an Unobserved Response Variable

“…Theorem 7 is related to the graphical identifiability criterion for a single factor model with correlated errors, which is studied by some researchers such as Stanghellini (1997), Stanghellini and Wermuth (2003) and Vicard (2000). The criterion is tested through the following procedure (for details, see Vicard (2000)):…”