1	What’s New in Prism 4? Advances in Curve Fitting
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3	"Creates scientific graphs" Creates scientific graphs Performs basic biostatistics Helps you organize your data Fits curves with nonlinear regression Helps you pick analyses and interpret results Easy to learn Efficient to use
4	New features in nonlinear regression Confidence and prediction bands Constraints Fit only to selected range Several standard curves at once Define more complicated models. More parameters. More functions. Define different equations for different data sets. Global fitting (shared parameters) Comparing models. Easier. AICc or F test. New book on nonlinear regression
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8	New features in nonlinear regression Confidence and prediction bands Constraints Fit only to selected range Several standard curves at once Define more complicated models. More parameters. More functions. Define different equations for different data sets. Global fitting (shared parameters) Comparing models. Easier. AICc or F test. New book on nonlinear regression
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10	New features in nonlinear regression Confidence and prediction bands Constraints Fit only to selected range Several standard curves at once Define more complicated models. More parameters. More functions. Define different equations for different data sets. Global fitting (shared parameters) Comparing models. Easier. AICc or F test. New book on nonlinear regression
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12	New features in nonlinear regression Confidence and prediction bands Constraints Fit only to selected range Several standard curves at once Define more complicated models. More parameters. More functions. Define different equations for different data sets. Global fitting (shared parameters) Comparing models. Easier. AICc or F test. New book on nonlinear regression
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14	New features in nonlinear regression Confidence and prediction bands Constraints Fit only to selected range Several standard curves at once Define more complicated models. More parameters. More functions. Define different equations for different data sets. Global fitting (shared parameters) Comparing models. Easier. AICc or F test. New book on nonlinear regression
15	New features in nonlinear regression Confidence and prediction bands Constraints Fit only to selected range Several standard curves at once Define more complicated models. More parameters. More functions. Define different equations for different data sets. Global fitting (shared parameters) Comparing models. Easier. AICc or F test. New book on nonlinear regression
16	What is Global Model-Fitting?
17	"Regular nonlinear regression minimizes the..." Regular nonlinear regression minimizes the sum of the squared vertical distances between points and curve. Global nonlinear regression minimizes the sum of the sum-of-squares for all data sets. Only makes sense when all data sets are expressed in same units (or at least normalized to be comparable).
18	"Prism 4 would not have..." Prism 4 would not have shared parameters if not for the help, and repeated nagging, of Arthur Christopoulos Dept. of Pharmacology, University of Melbourne … who also created initial drafts of many of these slides.
19	Global Model-Fitting
20	Incomplete Data Sets
21	Concentration-Response Curves
22	Concentration-Response Curves
23	Concentration-Response Curves
24	Concentration-Response Curves
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26	Fitting Models where the parameters you care about come from two or more data sets (not one).
27	Example 1: Radioligand Saturation Binding
28	Example 1: Radioligand Saturation Binding
29	Example 1: Radioligand Saturation Binding
30	Example 1: Radioligand Saturation Binding
31	Example 1: Radioligand Saturation Binding
32	Example 1: Radioligand Saturation Binding
33	Example 1: Radioligand Saturation Binding
34	Example 1: Radioligand Saturation Binding
35	Example 1: Radioligand Saturation Binding
36	Example 1: Radioligand Saturation Binding
37	Example 1: Radioligand Saturation Binding
38	Example 2: Homologous Competition Binding
39	Example 2: Homologous Competition Binding
40	Example 2: Homologous Competition Binding
41	Example 2: Homologous Competition Binding
42	In Prism 4
43	Example 2: Homologous Competition Binding
44	Example 2: Homologous Competition Binding
45	Example 2: Homologous Competition Binding
46	Example 3: Agonist-Antagonist C/R Curve Analysis
47	Example 3: Agonist-Antagonist C/R Curve Analysis
48	Example 3: Agonist-Antagonist C/R Curve Analysis
49	Example 3: Agonist-Antagonist C/R Curve Analysis
50	Example 3: Agonist-Antagonist C/R Curve Analysis
51	Example 3: Agonist-Antagonist C/R Curve Analysis
52	How to set constants with different values for each data set in Prism 4
53	Example 3: Agonist-Antagonist C/R Curve Analysis
54	Example 3: Agonist-Antagonist C/R Curve Analysis
55	Example 3: Agonist-Antagonist C/R Curve Analysis
56	Final Example – Kinetic Binding Curves
57	Final Example – Kinetic Binding Curves
58	Final Example – Kinetic Binding Curves
59	Final Example – Kinetic Binding Curves
60	Final Example – Kinetic Binding Curves
61	Global fitting Lets you save time and get better results. Three features in Prism 4 facilitate global fitting: Share one or more parameters between data sets Specify different equations for different data sets (<A> syntax) Specify that one parameter in the equation gets its value from the column title of each data set. So a constant within each data set, but different values for different data sets. You can think of this as a second independent variable.
62	New features in nonlinear regression Confidence and prediction bands Constraints Fit only to selected range Several standard curves at once Define more complicated models. More parameters. More functions. Define different equations for different data sets. Global fitting (shared parameters) Comparing models. Easier. AICc or F test. New book on nonlinear regression
63	Not enough to compare sum-of-squares (goodness of fit) More complicated model (more parameters) almost always fits better. Two-site model fits better than one-site Three-site model fits even better So need to trade-off improvement in fit (lower SS) with more parameters (fewer df) Two ways to do this: F test and AIC
64	F-Test: Standard Example. Comparing fit of two models to one data set
65	F-Test (Extra Sum-Of-Squares Test)
66	Akaike’s Information Criterion Comparing fit of two models to one data set
67	Akaike’s Information Criterion Comparing fit of two models to one data set
68	Akaike’s Information Criterion Comparing fit of two models to one data set
69	Akaike’s Information Criterion Comparing fit of two models to one data set
70	F test or AIC? F test: If the simpler model were correct, what is the chance of obtaining data where the difference in sum-of-squares between the two models is as large or larger than you observed? AICc: How well do the data support each model? Which model is more likely to be correct? How much more likely?
71	F test or AIC? F test: Statistical hypothesis testing (familiar to many, null hypothesis, P value…) Compares nested models only. Requires threshold significance level (0.05) Makes a decision so you don’t have to think. Not straightforward to extend to three or more models. Assumptions: Gaussian independent error….
72	F test or AIC? AICc: Information theory. Unfamiliar to many. Compares nested, or unnested, models. Easy to extend to three or more models. Doesn’t make decision. Tells you how well the data support each model. Assumptions: Gaussian independent error….
73	F test or AIC? If models not nested, use AIC. If comparing three or more models, use AIC. In all other cases (the vast majority) it is a matter of taste. I prefer AIC, as it answers the question you care about: Which model is more likely to be correct and how much more likely?
74	Comparing Curves
75	Comparing Curves
76	Comparing Curves
77	How to answer? Rephrase the question to compare models, with our without sharing.
78	Comparing Curves
79	Comparing Curves
80	Comparing Curves
81	Comparing Curves with F test
82	Comparing Curves with AICc
83	Comparing Parameters
84	Comparing Parameters
85	Comparing Parameters
86	Comparing Parameters
87	Comparing Parameters, with F test
88	Comparing Parameters, with AICc
89	New features in nonlinear regression Confidence and prediction bands Constraints Fit only to selected range Several standard curves at once Define more complicated models. More parameters. More functions. Define different equations for different data sets. Global fitting (shared parameters) Comparing models. Easier. AICc or F test. New book on nonlinear regression
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