The Fit Curve red triangle menu contains several categories of built-in models. Models that are not available for your particular data are gray menu options. For individual model details and data requirements, see Table 14.1.
Polynomials
Fits first degree to fifth degree polynomials, as well as a Power model.
Sigmoid Curves
Fits Logistic, Probit, Gompertz, and Weibull models. These models are S-shaped and have both upper and lower asymptotes. The Logistic 2P, 3P, and 4P and Probit 2P and 4P models are symmetric. The Logistic 5P, Probit 3P, and both Gompertz models are not symmetric. The Logistic 2P and Probit 2P are available only when the response is between 0 and 1. The Weibull Growth is available only when both the response values and regressor values are nonnegative. Examples of Sigmoid curves include learning curves and modeling tumor growth, both of which increase initially and then taper off.
Exponential Growth and Decay
Fits Exponential, Biexponential, Mechanistic Growth, Hybrid Exponential, and Cell Growth models. The Exponential 2P and 3P are similar, but the 3P model has an asymptote. The Biexponential models assume there are two separate growth or decay processes. The Mechanistic Growth and Exponential 3P models always increase (or decrease), but the rate of growth (or decay) slows so that the model has an asymptote. Examples of exponential growth and decay functions are virus spread and drug half-life, respectively.
Peak Models
Fits Gaussian Peak, Asymmetric Gaussian Peak, Skew Normal Peak, ExGaussian Peak (Exponentially Modified Gaussian Peak), Pseudo-Voigt Peak, Pearson VII Peak and Lorentzian Peak models. These models increase up to a peak and then decrease. The Gaussian Peak model is a scaled version of the Gaussian probability density function (PDF). The ExGaussian Peak model is similar to the Gaussian Peak model, but it can take on a skewed shape. The Lorentzian Peak model is a scaled version of the Cauchy distribution, a continuous probability distribution. These models can be used for some chemical concentration assays and artificial neural networks.
Pharmacokinetic Models
Fits the One Compartment Oral Dose model, the Two Compartment IV Bolus Dose model, and the Biexponential 4P model. This option is used to model the concentration of drugs in the body.
Rate Equations
Fits the Michaelis-Menten and Inverse Michaelis-Menten models, as well as several first order and second order rate models. The Michaelis-Menten model is a biochemical kinetics model, which relates the rate of enzymatic reactions to substrate concentration. The first order and second order rate models are useful in modeling chemical reactions.
Fit Antoine Equation
Fits the Antoine model, which is often used to model vapor pressure as a function of temperature. The Antoine model has both horizontal and vertical asymptotes.
Dissolution Curve Analysis
(Available only if both the response values and the regressor values are nonnegative.) Contains a submenu of options for dissolution curve analysis. A dissolution curve measures the rate at which a tablet dissolves over time. Dissolution curve analysis compares the dissolution curves of a new batch of tablets to the dissolution curves of a standard or reference batch of tablets. A separate analysis is done for each new batch of tablets. The Dissolution Curve Analysis menu provides both parametric and nonparametric techniques for comparing dissolution curves. If you use one of the built-in dissolution curve models, a standard model fit report is created for each individual model that is fit.
Model-Free Comparisons
Provides nonparametric techniques to compare dissolution curves. If you use one of the nonparametric techniques from the Model-Free Comparisons submenu, a method specific dissolution curve report is created. See Model-Free Comparisons Reports.
Note: All of the model-free comparison techniques require that the curves contain no missing values.
F1 Analysis
Performs an analysis using the F1 difference factor, which measures the percent difference between the curves of the reference tablets and the curves of the test tablets at each time point. See Statistical Details for Fit Curve Models. Confidence intervals for F1 are computed using a bootstrapping procedure. The bootstrapping procedure uses the bias-corrected and accelerated (BCa) percentile method. See Efron (1981).
When you select the F1 Analysis option, a Dissolution Curve Specification window appears. Use this window to specify the reference level, the alpha level used to calculate the confidence intervals, the number of bootstrap samples, and a random seed. If the data are in the Stacked Data Format, you must also specify the curve ID column, which identifies the individual curves within the reference group and the test groups.
F2 Analysis
Performs an analysis using the F2 similarity factor, which measures the similarity of percent dissolution between the curves of the reference tablets and the curves of the test tablets. See Statistical Details for Fit Curve Models. Confidence intervals for F2 are computed using a bootstrapping procedure. The bootstrapping procedure uses the bias-corrected and accelerated (BCa) percentile method. See Efron (1981). If the lower limit for F2 is greater than 50, then the conclusion is that the dissolution of the test tablet is similar to the dissolution of the reference tablet (Paixão et al. 2017).
When you select the F2 Analysis option, a Dissolution Curve Specification window appears. Use this window to specify the reference level, the alpha level used to calculate the confidence intervals, the number of bootstrap samples, and a random seed. If the data are in the Stacked Data Format, you must also specify the curve ID column, which identifies the individual curves within the reference group and the test groups.
Multivariate Distance
Performs an analysis using the Mahalanobis distance M, which measures the multivariate distance between the curves of the reference tablets and the curves of the test tablets. See Statistical Details for Fit Curve Models. Confidence intervals are calculated for M using a multivariate normal assumption. If the upper limit for M is less than the maximum difference, then the conclusion is that the dissolution of the test tablet is similar to the dissolution of the reference tablet (Paixão et al. 2017).
When you select the Multivariate Distance option, a Dissolution Curve Specification window appears. Use this window to specify the reference level and the alpha level used to calculate the confidence intervals. If the data are in the Stacked Data Format, you must also specify the curve ID column, which identifies the individual curves within the reference group and the test groups.
T2EQ
Performs an analysis using Wellek’s T2 equivalence (EQ) test. Like the Multivariate Distance option, this test measures the multivariate distance between the curves of the reference tablets and the curves of the test tablets. However, instead of using confidence intervals to determine the similarity, a p-value for the test statistic is calculated. If the p-value is less than the specified alpha level, the test tablets are considered to be similar to the reference tablets. The T2EQ method is particularly useful when the dissolution curves contain a lot of variability. See Hoffelder (2019).
When you select the T2EQ option, a Dissolution Curve Specification window appears. Use this window to specify the reference level and the alpha level used to specify p-value significance. If the data are in the Stacked Data Format, you must also specify the curve ID column, which identifies the individual curves within the reference group and the test groups.
Higuchi Curves
Fits Higuchi models, including models with a time lag component and models with a burst component.
Hixson-Crowell Curves
Fits Hixson-Crowell models, including models with a time lag component.
Korsmeyer-Peppas Curves
Fits Korsmeyer-Peppas models, including models with a time lag component and models with a burst component.
Sigmoid Curves
Fits Logistic, Probit, and Weibull models. See Sigmoid Curves.
See “Local Data Filters in JMP Reports”, “Redo Menus in JMP Reports”, “Group Platform”, and “Save Script Menus in JMP Reports” in Using JMP for more information about the following options:
Local Data Filter
Shows or hides the local data filter that enables you to filter the data used in a specific report.
Redo
Contains options that enable you to repeat or relaunch the analysis. In platforms that support the feature, the Automatic Recalc option immediately reflects the changes that you make to the data table in the corresponding report window.
Platform Preferences
Contains options that enable you to view the current platform preferences or update the platform preferences to match the settings in the current JMP report.
Save Script
Contains options that enable you to save a script that reproduces the report to several destinations.
Save By-Group Script
Contains options that enable you to save a script that reproduces the platform report for all levels of a By variable to several destinations. Available only when a By variable is specified in the launch window.
Note: Additional options for this platform are available through scripting. Open the Scripting Index under the Help menu. In the Scripting Index, you can also find examples for scripting the options that are described in this section.