Last round of Media Analysis

I spent a fair amount of time noodling around with the problem and then did a quick visualization to confirm my thoughts.  When the points of the full-factorial are shown with the center points, notice they all fall at the origin.  As a result, there's no way to figure out which term is the leading to quadratic behavior.  I'm embarrassed to say the amount of time I spent reaching that conclusion!
Distribution of Coded Points within the Design

What to do?  We're at 35 experiments (32 for the full factorial, 3 for the center points).  What I decided to do was augment, yes, again, but this time I'll add axial points.  However, for which factors?  I decided to stick with the main effects that had the greatest statistical significance: Glutamine, NEAA, and ITS.  In the augmentation, I also included an additional 3 center point runs.  The experimental total is now at 44!

Fitting to a full factorial model that includes square terms for Glutamine, NEAA, and ITS gives some good results.  The ANOVA results aren't spectacular, but the model fits the data better than normal variations.  More importantly, the square term behavior is coming from the NEAA and ITS.
ANOVA for Augmented Design with Axial Components

Source	DF	Sum of Squares	Mean Square	F Ratio
Model	9	296.45290	32.9392	8.2079
Error	34	136.44500	4.0131	Prob > F
C. Total	43	432.89790		<.0001*

Parameter Estimates from Fit

Term		Estimate	Std Error	t Ratio	Prob>|t|
Intercept		10.829294	0.785856	13.78	<.0001*
Glutamine		-0.985914	0.320352	-3.08	0.0041*
NEAA		1.7462562	0.319869	5.46	<.0001*
ITS		0.4912445	0.320681	1.53	0.1348
Glutamine*NEAA		0.2518681	0.35905	0.70	0.4878
Glutamine*ITS		0.2831327	0.357962	0.79	0.4345
NEAA*ITS		-1.104809	0.358561	-3.08	0.0041*
Glutamine*Glutamine		-0.110353	0.392928	-0.28	0.7805
NEAA*NEAA		-1.504103	0.392928	-3.83	0.0005*
ITS*ITS		-1.241603	0.392928	-3.16	0.0033*

After simplifying the model to just the statistically significant terms, the ANOVA improves as well as nearly all the factors are highly relevant.  The outlier factor is the main effect of ITS (p>0.05).  I can rationalize an argument for including and excluding it in the final model to the data; in the end, you'll have to decide which way you'd take the model.

ANOVA from Simplified Model Fit to Augmented Design with Axial Components

Source	DF	Sum of Squares	Mean Square	F Ratio
Model	6	291.39175	48.5653	12.6985
Error	37	141.50615	3.8245	Prob > F
C. Total	43	432.89790		<.0001*

Parameter Estimates from Simplified Model Fit to Augmented Design

Term		Estimate	Std Error	t Ratio	Prob>|t|
Intercept		10.681397	0.599025	17.83	<.0001*
Glutamine		-1.002546	0.311948	-3.21	0.0027*
NEAA		1.7072543	0.309969	5.51	<.0001*
ITS		0.4520094	0.310588	1.46	0.1540
NEAA*ITS		-1.125011	0.348986	-3.22	0.0026*
NEAA*NEAA		-1.485901	0.376752	-3.94	0.0003*
ITS*ITS		-1.223401	0.376752	-3.25	0.0025*

An interesting observation is that my approach leads to a different conclusion about the model that fits the data than the conclusion presented in the paper.  I'll discuss the implications of this in the next, and final, entry about these experiments.

Prediction Profiler from Simplified Model Fit to Augmented Design