Fungible Parameter Estimates in Latent Curve Models
This chapter explores a phenomenon that occurs to some degree in the process of ﬁtting virtually any statistical model to empirical data. The phenomenon involves a kind of uncertainty that is inherent in parameter estimates, uncertainty arising from the sensitivity of the relationship between those parameter estimates and the ﬁt of the model to the data. If there is low sensitivity in this relationship, then small changes in model ﬁt would be associated with large changes in parameter estimates. Under such circumstances, very different parameter estimates will be associated with nearly identical model ﬁt, calling into question an investigator’s substantive interpretation of the optimal parameter estimates. On the other hand, high sensitivity would mean that small changes in ﬁt would be associated with small changes in parameter estimates, thus supporting more rigorous substantive interpretation of parameter estimates.