tailieunhanh - Engineering Statistics Handbook Episode 6 Part 3

Tham khảo tài liệu 'engineering statistics handbook episode 6 part 3', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | . Initial Non-Linear Fit Determining an Appropriate Functional Form for the Model Due to the large number of potential functions that can be used for a nonlinear model the determination of an appropriate model is not always obvious. Some guidelines for selecting an appropriate model were given in the analysis chapter. The plot of the data will often suggest a well-known function. In addition we often use scientific and engineering knowledge in determining an appropriate model. In scientific studies we are frequently interested in fitting a theoretical model to the data. We also often have historical knowledge from previous studies either our own data or from published studies of functions that have fit similar data well in the past. In the absence of a theoretical model or experience with prior data sets selecting an appropriate function will often require a certain amount of trial and error. Regardless of whether or not we are using scientific knowledge in selecting the model model validation is still critical in determining if our selected model is adequate. Determining Appropriate Starting Values Nonlinear models are fit with iterative methods that require starting values. In some cases inappropriate starting values can result in parameter estimates for the fit that converge to a local minimum or maximum rather than the global minimum or maximum. Some models are relatively insensitive to the choice of starting values while others are extremely sensitive. If you have prior data sets that fit similar models these can often be used as a guide for determining good starting values. We can also sometimes make educated guesses from the functional form of the model. For some models there may be specific methods for determining starting values. For example sinusoidal models that are commonly used in time series are quite sensitive to good starting values. The beam deflection case study shows an example of obtaining starting values for a sinusoidal model. In the .