Specialized Models • Nonlinear Regression with Built-In Models • Example Using the Fit Curve Personality
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Example Using the Fit Curve Personality
In this example shows how to build a model for toxicity as a function of the concentration of a drug. You have a standard formulation of the drug and want to compare it to three new formulations.
You are interested in a toxicity ratio of surviving to non-surviving cells at a specific concentration of each drug. From prior research, you know the toxicity ratios for 16 different concentrations of each drug formulation. A lower ratio indicates more toxicity, which could be detrimental to development of the drug. Log concentration was calculated to decrease the range of concentration values and make it easier to detect differences in the curves.
Follow these steps to build the model:
1.
Select Help > Sample Data Library and open Nonlinear Examples/Bioassay.jmp.
2.
Select Analyze > Modeling > Nonlinear.
3.
Assign Toxicity to the Y, Response role.
4.
Assign log Conc to the X, Predictor Formula role.
5.
Assign Formulation to the Group role.
6.
Click OK.
The Fit Curve Report appears as shown in Initial Fit Curve Report. The Plot report contains an overlaid plot of the fitted model of each formulation.
Initial Fit Curve Report
7.
To see a legend identifying each drug formulation, right-click one of the graphs and select Row Legend. Select Formulation for the column and click OK. The plot shown in Fit Curve Report with Plot Legend appears.
Fit Curve Report with Plot Legend
The curves appear S-shaped, so a sigmoid curve would be an appropriate fit. Fit Curve Model Formulas shows formulas and graphical depictions of the different types of models that the Fit Curve personality offers.
8.
Select Sigmoid Curves > Logistic Curves > Fit Logistic 4P from the Fit Curve red triangle menu.
Logistic 4P Report
The Logistic 4P report appears (Logistic 4P Report). There is also a separate plot for each drug formulation. The plot of the fitted curves suggests that formulation B might be different, because the test B curve starts to rise sooner than the others. Inflection point parameters cause this rise.
9.
Select Compare Parameter Estimates from the Logistic 4P red triangle menu.
A portion of the Parameter Comparison report is shown in Parameter Comparison Report.
Parameter Comparison Report
Notice that the Inflection Point parameter for the test B formulation is significantly lower than the average inflection point. This agrees with the plots shown in Logistic 4P Report. Drug formulation B has a lower toxicity ratio than the other formulations.
Launch the Nonlinear Platform
To launch the Nonlinear platform, select Analyze > Modeling > Nonlinear. The launch window is shown in Nonlinear Platform Launch Window.
Nonlinear Platform Launch Window
The Nonlinear platform launch window has the following features:
Y, Response
Select the Y variable.
X, Predictor Formula
Select the X variable (selecting a column containing a model formula launches the Nonlinear platform, as explained in the Nonlinear Regression with Custom Models section).
Group
Specify a grouping variable. The fitted model has separate parameters for each level of the grouping variable. The fitted model has separate parameters for each level of the grouping variable. This enables you to compare fitted models and estimated parameters across the levels of the grouping variable.
Weight
Specify a variable containing the weights of observations.
Freq
Specify a variable representing the frequency of an observation.
Loss
Specify a formula column giving a loss function (only for custom models).
By
Specify a variable to perform a separate analysis for every level of the variable.
The Model Library, formula, and numerical options are only for classic nonlinear analysis. For more details, see the Nonlinear Regression with Custom Models section.