Design specification issues in time-series intervention models

It has been recognized that the two-phase version of the interrupted time-series design can be frequently modeled using a four-parameter design matrix. There are differences across writers, however, in the details of the recommended design matrices to be used in the estimation of the four parameters of the model. Various writers imply that different methods of specifying the four-parameter design matrix all lend to the same conclusions; they do not. The tests and estimates for level change are dramatically different under the various seemingly equivalent design specifications. Examples of egregious errors of interpretation are presented and recommendations regarding the correct specification of the design matrix are made. The recommendations hold whether the model is estimated using ordinary least squares (for the case of approximately independent errors) or some more complex time-series approach (for the case of autocorrelated errors).