Q: How can I change the data weighting method within a data column?

A: Unlike a simple spreadsheet, the contents of the Data window are arranged in a specific format that allows considerable flexibility, but also insures that the Compartmental and Numerical applications can read and interpret it. Each datum is assigned a weight that indicates the measure of confidence in that particular value. As explained in the Manual and Help, weight specifications can be entered using four formats: SD, FSD, POIS and GEN. In each case, the weight for each datum within a data table used internally by the application is determined by converting the weight specification to standard deviation, and calculating:

The short example below shows several different weighting specifications:

The (FSD 0.12) line assigns Fractional Standard Deviation with a value of 0.12 as the weighting method for the entire table. This is applied to each datum in each column unless subsequently modified. In column 1, for smpl1, the weight for the data at time 3.0 would be:

At the next point at time 7.0, the FSD value has been changed to 0.1 for that datum only, so the weight would be:

In column 1, then, the weight for each datum is computed using the weighting method specified globally by (FSD 0.12), except where the FSD value is specifically modified (at time 3.0). 

In column 2, the weighting method for smpl2 has been modified by the (SD 1.0) entry. This tells the application to override the global weighting specified, and to use an SD of 1.0 for all of column 2. At time 3.0, for example, the weight would be:

At time 9.0, however, the SD value has been modified to 2.0 and the corresponding weight would be:

This simple example shows how the weight for each datum can be specified individually, by column, or globally for the entire table. It’s important to note that, while the weighting method can be specified for a table or each column within the table, only the value and not the method can be changed for each datum within the column. The answer to the original question, then, is that the weighting method cannot be changed within a column, but there are workarounds.

Supposing, for example, FSD is the preferred weighting method for data collected for an infusion starting at time zero, as shown in the above example. A measurement at time zero should yield a concentration of 0.0. Unfortunately the value of 0.0 cannot be used with the FSD method because it would yield a weight of infinity. How then can this measured value be included? 

One alternative is to enter a small measurement value instead of 0.0 that would have minimal affect upon the optimization, such as 1.0e-6.  While this would be reasonable computationally, many researchers are hesitant to use “phony” data. 

Another way would be to create an additional sample (e.g. s2) that is attached to the same compartment and is identical to the first, except for the name. Then associate the second sample with a new data element, smpl2, that uses the SD weighting method, and includes only the time zero measurement as shown below:

During a Fit, the two data tables and two samples are computationally equivalent to a single table and single sample when absolute weighting is used (as set in the Computational Settings window). When using relative weighting, an additional weighting factor would be applied for each table that could affect the computed values.

The most foolproof and flexible alternative uses the GEN weighting method. Using GEN, weighting types as well as values can be changed for each datum. Where y is the value at a datum, the GEN method is defined as the following:

To specify an SD of 2.0, use A = SD^2, or:

To specify an FSD of 0.1, use B = 0.1 and C = 2.0, or:

Employing GEN weighting, the data for the previous infusion example could easily be accommodated as:

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