@castro-schilo_augmenting_2016 suggested use of an additional, completely independent, data source for each trait; and @saris_comparing_2019 suggested leveraging information from multiple groups (countries) to aid estimation. Each of these solutions has its relative merits and disadvantages; specifically, each requires either the abandonment of method effects as target parameters, or additional information that may only sometimes be available. For these reasons, the final solution to estimation problems with MTMM is still under expert discussion.

In spite of the existence of suggested solutions–and regardless of their relative merits–relatively little is known about the *cause* of estimation problems in MTMM models: rank deficiencies in the model’s information matrix. In this paper, we will investigate that cause in analytical detail, and indicate exactly how it operates to generate nonconvergence and parameter instability (“inadmissible” estimates, bias in constrained estimation). To do this, we will use a particularly problematic version of the MTMM model as case study: the “reduced-group split-ballot multitrait-multimethod” model [@saris_new_2004]. This model is problematic because it involves a planned missing data design, and therefore estimation provides even more limited information about the parameters than is usually the case in MTMM.

The following section first defines the factor or structural equation (SEM) model framework that 