The SSM Procedure

Types of Sequence Data

The state space model specification in the SSM procedure requires proper understanding of both the data organization and the form of the model. The SSMs that are appropriate for time series data might not be appropriate for irregularly spaced longitudinal data. The SSM procedure distinguishes three types of data organization based on the way the observations are sequenced by the index variable. If an index variable is not specified, it is assumed that the observations are sequenced according to the observation number.

Regular:

The observations are recorded at regularly spaced intervals; that is, $\tau _{1}, {\tau _2}, \ldots , \tau _{n}$ are regularly spaced. Moreover, at each observation instance $\tau _{i}$ a single observation is recorded; that is, $p_{t} = 1$ for all t. The standard time series data (both univariate and multivariate) fall in this category.

Regular with Replication:

The observations are recorded at regularly spaced intervals, but $p_{t} > 1 $ for at least one t. Here the word replication is used loosely—it does not mean that the multiple observations at $\tau _ t$ are replications in the precise statistical sense. The panel or cross-sectional data types fall into this category. In the panel data case with p cross-sections, $p_{t} = p$ for all t.

Irregular:

The observations are not recorded at regular intervals, and the number of observations $p_{t}$ at each index instance can be different. The longitudinal data fall into this category.

It is not always easy to decide whether the specified model is appropriate for the given data type. Whenever possible, the SSM procedure issues a note regarding the possible mismatch between the specified model and the data type being analyzed.