SAAM II General Features

General Features of SAAM II


  • Data and Parameters
    • Data may be entered directly in the Data window or loaded from other applications; SAAM II formatting can be added after data is loaded
    • Systems of differential equations (and associated parameters) are automatically generated based on the compartmental model; parameters may be defined as fixed, adjustable or Bayesian; users can easily edit values and types as well as define additional parameters & constants of interest
  • General
    • Flexible, efficient and accurate Optimizer for computational optimization:
      • Choose Data or Model variance as the Variance Model
      • Choose Absolute or Relative for data weighting
      • Choose Forward Derivative (faster) or Central Derivative (smaller total error)
      • Set convergence criteria to control optimization speed versus accuracy
      • Allows use of a Bayesian term to incorporate prior knowledge of an adjustable parameter
    • User Notes can be included in Study Files to document particular items of interest in a model and/or experiment: setup, conclusions, etc.
    • Includes Users Guide with examples and detailed on-line Help
    • Progress Display during analysis
    • Compartmental and Numerical Models are solved and fitted to data automatically
  • Output
    • Study results may be plotted or listed in tables
    • Results may be exported to other applications
    • QuickPlot displays plots for individual Compartmental objects or single defined Numerical variables
    • Complete results may be automatically saved to a text file
    • Statistics for Correlation Matrix, Covariance Matrix and Objective Function are calculated
    • Confidence Intervals on study parameters provide upper and lower bounds on each parameter

Data may be entered directly in the Data window or loaded from other applications

  • The data window uses tables in a specific format that allows sophisticated combinations of values, weighting and unweighting for each of the data elements
  • The data can be listed in multiple columns in one or more tables
  • Each table can include weighting combinations of:
    • Standard Deviation
    • Fractional Standard Deviation
    • Poisson
    • General weighting methods
  • Data constants can also be defined

Model parameters are automatically determined from equation variables

  • The Parameters window lists all the parameters in the model, along with their type (fixed, adjustable, or Bayesian) and values
  • In the SAAM II context, parameters are variables that appear in equations, but are not explicitly defined
  • The parameter values may be modified during optimization to provide an optimal fit to the data
  • The Pop. Mean and SD columns are shown only if the Include Bayesian Term check box in the Computational Settings dialog box has been checked
  • The user modifies a parameter type, value and limits in the boxes at the bottom of the dialog box and then saves the entries back into the parameter list

Flexible, efficient and accurate Optimizer for computational optimization

  • The way in which the Optimizer “fits” the model to the data is determined in the Optimizer pane of the Computational Settings window; the user can limit the number of iterations that the optimizer can use in “fitting” the model to the data
  • The variance model can be based upon model or data; data weighting is used when a measurement of confidence in each particular datum is provided; weights for each datum are calculated from the error model assigned to the data; model weighting expresses the confidence in each of the calculated Sample values rather than in the data
  • Weights in SAAM II can be absolute or relative; absolute weighting assumes that the overall weighting of each data element (variable) is the same, while in relative weighting each data element is given an additional weight that indicates how well that element fits the resulting model sample curve
  • SAAM II uses approximate derivatives of the model function “s(p, ti,j)” during the “fitting” process, and when computing statistics; the optimizer computes a step size for each parameter equal to “d(pU – pL)”, where “pU” and “pL” are the upper and lower limits for “p”, and “d” is the convergence criterion (see below); the step size is used to form either a forward or central difference approximation to the derivative of “s(p, ti,j)” with respect to “p”; central difference approximations have a smaller truncation error, resulting in a smaller total error, but usually require twice the execution time
  • Two different convergence tests are used to terminate the “fitting” process: parameter convergence and objective convergence; the user can specify the value for the convergence criterion “d” in this field or accept the default value of “0.0001”
  • Bayesian estimation incorporates prior knowledge of an adjustable parameter’s value into the fitting process; check Include Bayesian Term to allow Bayesian information to be provided for any adjustable parameters, and Bayesian inference to be used during a fit
  • In Bayesian estimation, a mean value and a standard deviation are specified for one or more adjustable parameters; if the mean value of a parameter is specified but the standard deviation is not specified, lambda is used to assign a default standard deviation to that parameter; if “pU” and “pL” are the upper and lower limits for the parameter, the default standard deviation is “s = lambda(pU – pL)”

User Notes can be included in Study Files

  • The Notes window can be used to create and retain information of interest for a given model or experiment, such as a description of what is being modeled, assumptions, comments on certain aspects of the model, a description of sampling techniques, etc
  • The Notes window is a standard text window
  • Notes are automatically saved with the model; the window may be left open while you are working in other areas

Study results may be plotted or listed in tables

  • SAAM II offers extensive plotting capabilities with the Plot command
  • This allows users to choose plots for several variables
  • Users can customize the plot by choosing a title, labels for the X-axis and Y-axis, and the font size
  • Users can let SAAM II select the plot scale settings or specify them
  • The user can use the Table window to view the values for selected variables at each calculation point; in this window, the data are displayed in columns with the independent variable (time) in the first column

 


QuickPlot displays plots for individual Compartmental objects or single defined Numerical variables

  • In the Numerical application, QuickPlot can be used to plot the values of any selected variable defined explicitly on the left-hand side of an equation
  • In the Compartmental application, QuickPlot can be used to plot the solution values of a selected object

Complete results may be automatically saved to a text file

  • The Save Results option in the Computational Settings window produces a readable summary of results after a “Fit” or “Solve” and stores the results in a user-accessible text file; the file can then be opened in other applications such as spreadsheets, word processors, or report generators; three levels of report details are available:
    • Basic Output, containing the most commonly used results from a Solve or Fit
    • Detailed Output, containing more complete results
    • Model and Detailed Output, containing a complete description of the results and the model itself

Statistics for Correlation Matrix, Covariance Matrix and Objective Function are calculated

  • After a successful fit, the user can open the Statistics window to view:
    • The value, standard deviation, coefficient of variation, and 95% Confidence Interval of each parameter and each derived variable; such confidence intervals provide upper and lower bounds for each parameter/variable
    • The Correlation Matrix and Covariance Matrix for the parameters
    • Information about the Objective Function: the mathematical function (sum of squares) minimized by SAAM II when fitting the model to the data