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# SimBiology

## Estimating Parameters

SimBiology lets you estimate model parameters by fitting the model to experimental time-course data, using either nonlinear regression or nonlinear mixed-effects (NLME) techniques.

### Nonlinear Regression

SimBiology provides nonlinear regression methods to fit data for a single individual or a population. With population data, you can either fit each group independently to generate group-specific estimates or simultaneously fit all groups (pooled approach) to estimate a single set of values.

You can perform nonlinear regression using optimization algorithms from Statistics Toolbox™, Optimization Toolbox™, and Global Optimization Toolbox, including simplex search, interior-point, pattern search, genetic algorithm, and particle swarm optimization. By default, SimBiology performs an ordinary least-squares regression. You can perform a weighted least-squares regression by specifying either a weights vector or a weighting function of observed or predicted responses.

### Nonlinear-Mixed Effects Techniques

SimBiology provides nonlinear mixed-effects (NLME) methods to simultaneously fit population data. The following NLME algorithms are included:

• Stochastic Approximation Expectation-Maximization (SAEM)
• First-order conditional estimate (FOCE)
• First-order estimate (FO)
• Linear mixed-effects approximation (LME)
• Restricted LME approximation (RELME)

### Diagnostic Metrics and Plots

SimBiology provides standard goodness-of-fit statistics and diagnostic plots that can be used to determine the quality of a fit and guide model selection. Goodness-of-fit statistics include:

• Mean squared error (MSE) or weighted MSE
• Residual error model coefficients
• Standard errors for estimated parameters
• Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC)
• Population weighted residuals
Figure 4: Diagnostic plots (clockwise from left): a trellis plot of individual fit over time, a scatter plot of predicted versus observed values, and a probability plot of weighted residuals.