Mathematical Modeling of Serial Data

1. Mathematical Modeling of Serial Data

2. Modeling Serial Data • Differs from simple equation fitting in that the parameters of the equation must have meaning • Can be used to smooth • Can explain phenomena • Can be used to predict Mathematical Modeling of Serial Data

3. Steps in Mathematical Modeling • Identification of the mechanism • Translation of that phenomenon into a mathematical equation • Testing the fit of the model to actual data • Modification of the model according to the results of the experimental evaluation Mathematical Modeling of Serial Data

4. Criteria of Fit of the Model • Least Sum of Squares • Shape of the curve Mathematical Modeling of Serial Data

5. Examination of Residuals Residual = Actual Y - Predicted Y Ideally there is no pattern to the residuals. In this case there would be a horizontal normal distribution of residuals about a mean of zero. However there is a clear pattern indicating the lack of fit of the model. Mathematical Modeling of Serial Data

6. Ideal Characteristics of a Model • Simple • Fits the experimental data well • Has biologically meaningful parameters Mathematical Modeling of Serial Data

7. Modeling Growth Data

8. National Centre for Health Statistics (N.C.H.S.)1970’srevamped asCenter for Disease ControlC.D.C. charts, 2001 Clinical Growth Charts • Most often used clinical norms for height and weight • Cross-sectional Mathematical Modeling of Serial Data

9. Preece-Baines model I • where h is height at time t, • h1 is final height, • s0 and s1 are rate constants, • q is a time constant and • hq is height at t = q. Mathematical Modeling of Serial Data

10. Smooth curves are the result of fitting Preece-Baines Model 1 to raw data This was achieved using MS EXCEL rather than custom software

11. Examination of Residuals

13. Caribbean Growth Data n =1697