Rapid technological advances have resulted in continual changes in data acquisition and reporting processes. While such advances have benefited research in these areas, the changing technologies have, at the same time, created difficulty for statistical analysis by generating outdated data which are incompatible with data based on newer technology. Relationships between these incompatible variables are complicated; not only they are stochastic, but also often depend on other variables, rendering even a simple statistical analysis, such as estimation of a population mean, difficult in the presence of mixed data formats. Thus, technological advancement has brought forth, from the statistical perspective, a methodological problem of the analysis of newer data with outdated data. In this paper, we discuss general principles for addressing the statistical issues related to the analysis of incompatible data. The approach taken to the task at hand has three desirable properties, it is readily understood, since it builds upon a linear regression setting, it is flexible to allow for data incompatibility in either the response or covariate, and it is not computationally intensive. In addition, inferences may be made for a latent variable of interest. Our considerations to this problem are motivated by the analysis of delta wave counts, as a surrogate for sleep disorder, in the sleep laboratory of the Department of Psychiatry, University of Pittsburgh Medical Center, where two major changes had occurred in the acquisition of this data, resulting in three mixed formats. By developing appropriate methods for addressing this issue, we provide statistical advancement that is compatible with technological advancement.
