Fitting Multivariate Models to Unequally Spaced Data
Using state space representations, the author’s previous work on fitting continuous time autoregressions to unequally spaced univariate data is extended to several multivariate models of practical importance. Continuous time multivariate first order autoregressions and the limiting case of multivariate random walks are used to model multiple medical observations collected at unequally spaced time points. Mean levels can be included in these models as constants to be estimated or as random variables with prior variances. Maximum likelihood estimation of the unknown parameters allows the development of individual normal ranges so a physician can be alerted if a set of observations is out of line. Three examples based on medical data are presented. Extensions include optimal control when drug therapy is involved. Another application is transfer function estimation from unequally spaced data. A bicycle rider pedals against a load which varies as a stationary process. Various respiration gases are measured on a breath to breath basis which are unequally spaced in time. The transfer function of the body indicates the mechanisms of the body’s response to exercise.
KeywordsCovariance Matrix Random Walk Observational Error Random Input Space Time Point
Unable to display preview. Download preview PDF.
- Akaike, H., Information theory and an extension of the maximum likelihood principle, Second International Symposium on Information Theory (B. N. Petrov and F. Csaki, Eds.), Akademia Kaido, Budapest, 267–281.Google Scholar
- Harris, E. K., Some theory of references values. I. Stratified (categorized) normal ranges and a method for following an individual’s clinical laboratory values. Clinical Chemistry 21 (1975), 1457–1464.Google Scholar
- Harris, E. K., Some theory of references values. II. Comparison of some statistical models of intraindividual variation in blood constituents. Clinical Chemistry 22 (1976), 1343–1350.Google Scholar
- Harris, E. K., Further applications of time series analysis to short series of biochemical measurements. Reference Values in Laboratory Medicine (Gräsbeck, R. and T. Alström, Eds.), John Wiley & Sons Ltd.(1981), 167-176.Google Scholar
- Harris, E. K., T. Yasaka, M. R. Horton and G. Shakarji, Comparing multivariate and univariate subject-specific reference regions for blood constituents in healthy persons. Clinical Chemistry, 28 (1982), 422–426.Google Scholar
- Jones, R. H., Fitting a continuous time autoregression to discrete data. Applied Time Series Analysis II (Findley, D. F., Ed.), Academic Press (1981), 651-682.Google Scholar
- R. H. Jones and P. V. Tryon, Estimating time from atomic clocks. Journal of research of the National Bureau of Standards, 88 (1983), 17–14.Google Scholar
- Schnabel, R. B., J. E. Koontz and B. E. Weiss, A modular system of algorithms for unconstrained minimization, National Bureau of Standards, Boulder, Colorado (1983), University of Colorado Department of Computer Science Technical Report CU-CS-240-82, November, 1982.Google Scholar
- P. V. Tryon and R. H. Jones, Estimation of parameters in models for cesium beam atomic clocks. Journal of Research of the National Bureau of Standards, 88 (1983), 3–16.Google Scholar