Method options with Prism

Weighting

Prism offers six choices for weighting your data. See Weighting methods.  

Replicates

If you entered replicate values for each data point, there are two ways to analyze the data. You can count each replicate as an independent data point. Or you can average the replicates, and fit the curve to the mean values. Read about the advantages and disadvantages of each method.

Calculation options

Threshold P value

Prism can compare the fits of two equations using an F test and choose the equation to graph based on the resulting P value. The simpler equation (fewer variables) is chosen unless the P value is less than the threshold P value you enter here. Most investigators leave this set to 0.05.

Derivatives

While performing nonlinear regression, Prism repeatedly evaluates the partial derivative of your equation with respect to each variable. This is the most computer intensive part of nonlinear regression.

If you choose a built-in equation, Prism uses analytical derivatives built-in to the program. There is no choice for you to make. If you enter your own equation (or use a library equation), Prism evaluates the derivatives numerically, and you can choose the method Prism uses.

Ordinarily, Prism uses Richardson's method to evaluate the derivatives. This method calculates the derivative by determining Y after both increasing and decreasing the value of the variable a bit.

Check the option box to use a faster, but potentially less accurate, method (which only evaluates the equation after increasing the value).

In most cases, the results will be identical with both methods. We recommend that you use the slow but accurate method to validate results with a new equation. You can then switch to the quick method for routine analyses if the speed of nonlinear regression matters to you. With small data sets and fast computers, nonlinear regression will seem instantaneous even if you pick the slower method.

Convergence criteria

Prism stops iterating and declares the results to have converged when two iterations in a row change the sum-of-squares by less than 0.01%. If you check the box for strict convergence criteria, Prism will continue the iterations until five consecutive iterations each reduce the sum-of-squares by less than 0.000001%.

We recommend that you use the slow method only when you are having difficulty fitting an equation, or to validate your results. Use the standard method for routine analyses. If you select the standard method, Prism will automatically switch to the stricter criteria if the R2 is less than 0.3

Selecting the stricter criteria rarely affects the results but slows the calculations a bit (only noticeable with huge data sets or slow computers).

Stop calculating after 25 iterations

If this option is checked, Prism will stop nonlinear regression after 25 iterations. In most cases, nonlinear regression converges in fewer than 25 iterations. If the iterations continue beyond 25, it may be because you've picked an inappropriate equation, picked unhelpful initial values, or have very scattered data. This option insures that Prism won't spend a long time on calculations that won't be helpful. It is especially useful when you use a Prism script to fit many data sets.