<br><font size=2 face="sans-serif">Dear R-users, </font>
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<br><font size=2 face="sans-serif">I'd appreciate your statistical opinion on the following problem. </font>
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<br><font size=2 face="sans-serif">I'm fitting the four parameter logistic model [f(x) = a + (b - a)/(1 + exp((c - x)*d))] to assay data. </font>
<br><font size=2 face="sans-serif">We have a lot of samples to fit and my aim is to classify these samples into following groups:</font><font size=3 face="sans-serif"> </font>
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<br><font size=2 face="sans-serif"> 1. no interrelation </font>
<br><font size=2 face="sans-serif"> all results about =~ 0</font><font size=3 face="sans-serif"> </font>
<br><font size=2 face="sans-serif"> too low concentration </font>
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<br><font size=2 face="sans-serif"> 2. only full saturation </font>
<br><font size=2 face="sans-serif"> all results about =~ 1</font><font size=3 face="sans-serif"> </font>
<br><font size=2 face="sans-serif"> too high concentration </font>
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<br><font size=2 face="sans-serif"> 3. only starting interrelation </font>
<br><font size=2 face="sans-serif"> results going up, not reaching the turning point </font>
<br><font size=2 face="sans-serif"> too low concentration</font><font size=3 face="sans-serif"> </font>
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<br><font size=2 face="sans-serif"> 4. only starting saturation </font>
<br><font size=2 face="sans-serif"> results starting above the turning point, going up, reaching the saturation </font>
<br><font size=2 face="sans-serif"> hence too high concentration</font><font size=3 face="sans-serif"> </font>
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<br><font size=2 face="sans-serif"> 5. only the linear area</font><font size=3 face="sans-serif"> </font>
<br><font size=2 face="sans-serif"> no start and saturation</font><font size=3 face="sans-serif"> </font>
<br><font size=2 face="sans-serif"> hence too low concentration range</font><font size=3 face="sans-serif"> </font>
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<br><font size=2 face="sans-serif"> 6. full interrelation</font><font size=3 face="sans-serif"> </font>
<br><font size=2 face="sans-serif"> including starting interrelation and saturation</font><font size=3 face="sans-serif"> </font>
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<br><font size=2 face="sans-serif">Is there a way to model these classes, and compare their significance by means of an </font>
<br><font size=2 face="sans-serif">analysis of the residuals (ANOVA)?</font><font size=3 face="sans-serif"> </font>
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<br><font size=2 face="sans-serif">Something like</font><font size=3 face="sans-serif"> </font>
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<br><font size=2 face="sans-serif"> model 1 = linear & constant =~ 0 & slope = 0</font><font size=3 face="sans-serif"> </font>
<br><font size=2 face="sans-serif"> model 2 = linear & constant =~ 1 & slope = 0</font><font size=3 face="sans-serif"> </font>
<br><font size=2 face="sans-serif"> model 3 = ???? some curvature</font><font size=3 face="sans-serif"> </font>
<br><font size=2 face="sans-serif"> model 4 = ???? some curvature</font><font size=3 face="sans-serif"> </font>
<br><font size=2 face="sans-serif"> model 5 = linear & slope > 0</font><font size=3 face="sans-serif"> </font>
<br><font size=2 face="sans-serif"> model 6 = full four parameter logistic model</font><font size=3 face="sans-serif"> </font>
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<br><font size=2 face="sans-serif">with the procedure: </font>
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<br><font size=2 face="sans-serif">Starting with the linear model and testing for any curvature.</font><font size=3 face="sans-serif"> </font>
<br><font size=2 face="sans-serif"> -> curvature not significant</font><font size=3 face="sans-serif"> </font>
<br><font size=2 face="sans-serif"> ==> result = model 1, 2 or 3, depending on significance of slope and intercept</font><font size=3 face="sans-serif"> </font>
<br><font size=2 face="sans-serif"> -> curvature significant </font>
<br><font size=2 face="sans-serif"> -> testing for full logistic model</font><font size=3 face="sans-serif"> </font>
<br><font size=2 face="sans-serif"> -> logistic model significant </font>
<br><font size=2 face="sans-serif"> ==> result = logistic model</font><font size=3 face="sans-serif"> </font>
<br><font size=2 face="sans-serif"> -> logistic model not significant </font>
<br><font size=2 face="sans-serif"> ==> result = a curvature model (model 3 or 4), depending on the parameters</font><font size=3 face="sans-serif"> </font>
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<br><font size=2 face="sans-serif">Is this a reasonable and feasible procedure? And if so, what kind of model might be appropriate</font><font size=3 face="sans-serif"> </font>
<br><font size=2 face="sans-serif">for the classes 3 and 4?</font><font size=3 face="sans-serif"> </font>
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<br><font size=2 face="sans-serif">Hope someone has the time to give me an answer or any advice on any other approach. </font>
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<br><font size=2 face="sans-serif">Thanks in advance </font>
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<br><font size=2 face="sans-serif">Maciej Hoffman-Wecker</font><font size=3 face="sans-serif"> </font>
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