Chi square and rmax

Hi Arnoud,
In some of the research articles, I have come across the limit set for chi square. They say it should be less than 10% rmax. What does this mean? How is chi square related to rmax. And why only 10% why not 5%?

Also, while analysing few sensorgrams, I have across instances where the theoretical fit and actual fit are not close enough (wide gap) still the chi square value is less. Shouldn't the chi square value be high so as to match the depicted sensorgram.

Hi

The Chi²-value is an indicator of the goodness of fit but can be difficult to interpret. First, it strongly depends on the average signal level and therefore a generally acceptable Chi² cut-off cannot be established. Second, it is not well adapted for time series data, because there is typically a strong correlation between data points in close temporal proximity. However, the Chi² can be used as a global measure of the residual noise. For a well-defined fit, the square root of Chi² should be of the same magnitude as the (instrument) noise level on the Y-axis. It is recommended to use the Chi² in combination with other validations.

For instance the residual plot can give good insight in the 'goodness' of the fit. A good fit will have absolute residuals that are in the order of the machine noise and the residuals will be randomly scattered in a narrow band around zero. For every fitted curve, there is a set of residuals. Non-randomly distributed residuals are an indication that the model is not adequately explaining the data. Either the model is incorrectly describing the interaction or the experimental conditions are sub- optimal, giving rise to mass transfer, non-specific binding or rebinding during dissociation.

Some other systems are designed to put a value to a fitting such as the T-value and the U-value. The U-value gives a value for the correlation of the fitted parameters. If the U-value is less than 15, there are no correlations. If the U- value is greater than 25, there are correlations and the fitted parameters are not independent and could not be determined uniquely.

To validate a fit: check the fitted line and residuals. Check the rate constants and Rmax, are they logic? Use the Chi² and U-value to make the fit better but do not trust them alone.

Kind regards
Arnoud