Why blatant outliers are sometimes not detected by Prism's nonlinear regression.

Prism 5 offers the choice (on the Fit tab of the nonlinear regression tab) to automatically eliminate outliers using the ROUT method. You can also choose (Diagnostics tab of the nonlinear regression tab) to identify and count outliers without eliminating them. 

Surprisingly, in rare cases, Prism can report zero outliers even when an oultier is present. This page explains why.

If you ask Prism to identify or eliminate outliers, here are the steps it uses:

1. Generate the curve defined by the initial parameter values defined in the Initial Values tab.
2. Use least-squares regression to fit the curve as well as possible.
3. Use the results of least-squares regression as initial values for robust nonlinear regression to adjust the values of those parameters to improve the fit of the curve to most of the data points, while giving outliers little weight. 
4. Identify any outliers from that curve defined with robust nonlinear regression.
5. Eliminate those outliers, if that was specified. 
6. Use the best-fit values of the parameters from the robust fit as the starting place for a standard least-squares fit.
7. Fit the curve using standard Marquardt nonlinear regression.

What happens if step #3 does not converge? If robust regression cannot find a best-fit curve, then outlier detection can not proceed. A definition of an outlier is a point that is 'too far' from the robust curve. If robust regression doesn't work, Prism reports zero outliers and fits the curve using standard least-squares regression.

Prism 5.03 and 5.0c add a floating note explaining the problem. Before that, Prism simply reported zero outliers, with no indication that it gave up trying to identify outliers.

This problem should only happen in two situations:

• The initial values defined in the Initial Values tab define a curve that is far from the data. You can view the curve defined by the initial values by checking an option at the top of the Diagnostics tab. Robust regression can be more sensitive to bad initial values than least-squares regression.
• The data don't really define the entire curve. If the data have a lot of scatter, or don't cover a wide enough range of X values, the best-fit curve can be  ambiguous. Robust regression can get more confused by ambiguous fits than least-squares.