Nested set model

Abstract: Forecast evaluation often compares a parsimonious null model to a larger model that nests the null model. Under the null that the parsimonious model generates the data, the larger model introduces noise into its forecasts by estimating parameters whose population values are zero. We observe that the mean squared prediction error (MSPE) from the parsimonious model is therefore expected to be smaller than that of the larger model. We describe how to adjust MSPEs to account for this noise. We propose applying standard methods (West (1996)) to test whether the adjusted mean squared error difference is zero. We refer to nonstandard limiting distributions derived in Clark and McCracken (2001, 2005a) to argue that use of standard normal critical values will yield actual sizes close to, but a little less than, nominal size. Simulation evidence supports our recommended procedure.

Abstract: A taxonomy of covariance structure models for rep resenting multitrait-multimethod data is presented Us ing this taxonomy, it is possible to formulate alternate series of hierarchically ordered, or nested, models for such data By specifying hierarchically nested models, significance tests of differences between competing models are available Within the proposed framework, specific model comparisons may be formulated to test the significance of the convergent and the discriminant validity shown by a set of measures as well as the ex tent of method variance Application of the proposed framework to three multitrait-multimethod matrices al lowed resolution of contradictory conclusions drawn in previously published work, demonstrating the utility of the present approach