﻿ The six steps of nonlinear regression

# The six steps of nonlinear regression

Before learning how to fit a model using GraphPad Prism (or any program), it is worth first reviewing the necessary steps.

## Step 1. Choose a model

Nonlinear regression fits a model to your data. You must, therefore, choose a model or enter a new model. This is a scientific decision that must be made by someone who understands the scientific goals of the experiment. Why a computer program should not pick a model for you.

## Step 2. Decide whether to constrain any parameters to constant values

When performing nonlinear regression, you don't have to fit each parameter in the equation. Instead, you may fix one or more of the parameters to constant values. It is often helpful to define constants when you have only a few data points. For example, you might fix the bottom plateau of a sigmoid curve or exponential decay to zero.

Don't expect computer programs to have common sense. That is your job! Think about how you did the experiment and prepared the data, and decide whether some of the parameters should be fixed. For example, if a background signal has already been subtracted, it makes sense to fix the bottom plateau of a dose-response curve or an exponential decay curve to zero.

## Step 3. Choose (or review) initial values

Nonlinear regression is an iterative procedure. The program must start with estimated values for each parameter. It then adjusts these initial values to improve the fit. GraphPad Prism supplies initial values automatically if you choose a built-in equation. If you enter your own equation, you will also need to provide initial values, or rules to generate initial values from the range of the data.

You'll find it easy to estimate initial values if you have looked at a graph of the data, understand the model, and understand the meaning of all the parameters in the equation. Remember that you just need an estimate. It doesn't have to be very accurate. If you are having problems estimating initial values, set aside your data and simulate curves using the model. Change the variables one at a time, and see how they influence the shape of the curve. Once you have a better feel for how the parameters influence the curve, you might find it easier to estimate initial values.

When fitting a simple model to clean data, it won't matter much if the initial values are fairly far from the correct values. You'll get the same best-fit curve no matter what initial values you use, unless the initial values are extremely far from correct. Initial values matter more when your data have a lot of scatter or your model has many variables.

## Step 4. If you are fitting two or more data sets at once, decide whether to share any parameters

If you enter data into two or more data set columns, Prism will fit them all in one analysis. But each fit will be independent of the others unless you specify that one or more parameters are shared. When you share parameters, the analysis is called a global nonlinear regression.

## Step 5. Decide on a weighting scheme

Nonlinear regression programs generally weight each point equally. But there are many ways to differentially weight the points.

## Step 6. Choose which results you want reported

Nonlinear regression always reports the best-fit values of the parameters. Beyond that, Prism (and most programs) gives you many choices for which results you want reported.