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im.sagark ☆ India, 2013-06-06 11:16 (4756 d 08:25 ago) Posting: # 10737 Views: 10,398 |
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Hello, I stuck with calculations of sum of squares for Sequence, Periods, and treatment for Unbalanced 3X3 crossover design. Can you please help on this?? I have 3 periods, 3 treatments and 6 sequences, and 9 subjects. So I don't have exactly 2 subjects in each sequence. Getting wrong calculations for Sum of squares for sequence,period and treatments. Can you please provide me the correct formula for the sum of squares?? — Regards, Sagar Khandagale. |
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ElMaestro ★★★ Denmark, 2013-06-06 13:13 (4756 d 06:27 ago) @ im.sagark Posting: # 10738 Views: 9,231 |
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Hello im.sagark, ❝ I have 3 periods, 3 treatments and 6 sequences, and 9 subjects. So I don't have exactly 2 subjects in each sequence. ❝ Getting wrong calculations for Sum of squares for sequence,period and treatments. ❝ Can you please provide me the correct formula for the sum of squares?? 1. Since you know you that whatever you previously tried gives you the wrong calculation I think you must have access to some sofwtare that gives you the right calculation so why not just use that? 2. It is sometimes a nightmare to derive general non-matrix formulae. Really, truly, honestly, I would rather swim to the South Pole than do it. Assuming you use a normal linear model and not a mixed model where no SS discussion is particularly relevant, in matrix notation you have logPK=y=Xb+e. So if you construct your design matrices X appropriately then you can analytically estimate the maximum likelihood b (max likelihood is here a minimisation of eTe) using for exampleb=(XtX)-1Xtyor some numerically appropriate and stable alternative. That is what the software does also. From such solutions you can always derive for example type I and type III SS estimates. — Pass or fail! ElMaestro |
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im.sagark ☆ India, 2013-06-06 13:20 (4756 d 06:20 ago) (edited on 2013-06-06 13:58) @ ElMaestro Posting: # 10739 Views: 9,235 |
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Thank you ElMaestro!! I am currently trying to do it in MS-Excel. So How can I work over there (In Excel)?? Edit: Full quote removed. Please delete everything from the text of the original poster which is not necessary in understanding your answer; see also this post! [Ohlbe] — Regards, Sagar Khandagale. |
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im.sagark ☆ India, 2013-06-06 13:31 (4756 d 06:10 ago) @ im.sagark Posting: # 10740 Views: 9,331 |
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I have Designed it like this Is it correct?? Subject Period 1 Period 2 Period 3 Regards, Sagar Khandagale — Regards, Sagar Khandagale. |
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Dr_Dan ★★ Germany, 2013-06-06 14:21 (4756 d 05:20 ago) @ im.sagark Posting: # 10743 Views: 9,196 |
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Hi I would design the randomization like this: 1 A B CMakes sense, or do you disagree? Kind regards Dan — Kind regards and have a nice day Dr_Dan |
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im.sagark ☆ India, 2013-06-06 15:38 (4756 d 04:02 ago) @ Dr_Dan Posting: # 10747 Views: 9,175 |
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Thank you Dr_Dan! I agree with the design. Still the question is same how to estimate Sequence sum of squares with this design?? See what i did is, To calculate SS Type III for sequence. I have taken the squared deviation for average of each sequence. Is this a correct way to proceed??? Regards, Sagar Khandagale — Regards, Sagar Khandagale. |
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im.sagark ☆ India, 2013-06-06 13:45 (4756 d 05:56 ago) @ ElMaestro Posting: # 10741 Views: 9,221 |
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❝ Assuming you use a normal linear model and not a mixed model where no SS discussion is particularly relevant, in matrix notation you have ❝ Here I don't have equal number of subjects in each group. So the design is Unbalanced one. How can I deal with this sort of problem?? And Should I consider carryover effect also?? Regards, Sagar Khandagale — Regards, Sagar Khandagale. |
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ElMaestro ★★★ Denmark, 2013-06-06 14:06 (4756 d 05:34 ago) @ im.sagark Posting: # 10742 Views: 9,242 |
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Hi again, 1. I do not have Excel. Try to see if you can invert matrices in a stable manner using inbuilt functions. If you can, then you have a way forward with the analytical solution above. Otherwise you might need to use the solver to optimise ete, or to write some VBA scripts. You need to invest some energy of your own in this. 2. I don't know what you are trying to do so I don't feel able to tell if your design is correct. This looks like a pilot trial, in which case I would personally not bother too much with so many sequences stuff even though three treatments are involved. 3. The matrix equations above apply regardless of imbalance. Re carryover please see above. — Pass or fail! ElMaestro |
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im.sagark ☆ India, 2013-06-06 14:27 (4756 d 05:13 ago) @ ElMaestro Posting: # 10744 Views: 9,228 |
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Thanks again!!! ❝ You need to invest some energy of your own in this.  Actually I did It for Balanced one. Where I have 12 subjects 2 in each sequence. But now I don't know How to manage it for Imbalanced one? ❝ 3. The matrix equations above apply regardless of imbalance. Re carryover please see above. Thats what I did, but sum of squares getting so much different. As we are concern with the average effects. It shouldn't bother the Imbalance stuff. But, Its not true here. Something is going wrong..... Regards, Sagar Khandagale — Regards, Sagar Khandagale. |
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ElMaestro ★★★ Denmark, 2013-06-06 14:55 (4756 d 04:45 ago) @ im.sagark Posting: # 10745 Views: 9,131 |
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Hello again, ❝ Actually I did It for Balanced one. Where I have 12 subjects 2 in each sequence. ❝ But now I don't know How to manage it for Imbalanced one? In that case my guess is that you do not get the right type III SS. You need to fit the whole model and note the SS, then the model without the effect in question and note the SS. The type III SS contribution for the effect in question is the difference of the two SS values. Sequence is a little nasty and peculiar - to get it right you may need to compensate for the nesting. — Pass or fail! ElMaestro |
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im.sagark ☆ India, 2013-06-06 15:17 (4756 d 04:23 ago) @ ElMaestro Posting: # 10746 Views: 9,248 |
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❝ In that case my guess is that you do not get the right type III SS. Yes. I got the right Type III SS as I compared it with Minitab output. ❝ You need to fit the whole model and note the SS, then the model without the effect in question and note the SS. The type III SS contribution for the effect in question is the difference of the two SS values. Sequence is a little nasty and peculiar - to get it right you may need to compensate for the nesting. How can we compensate the SS?? I have still confusion. Please try to elaborate. Regards, Sagar Khandagale. — Regards, Sagar Khandagale. |
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ElMaestro ★★★ Denmark, 2013-06-06 19:25 (4756 d 00:15 ago) @ im.sagark Posting: # 10748 Views: 9,052 |
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Hello Sagar, ❝ How can we compensate the SS?? ❝ I have still confusion. ❝ Please try to elaborate. Lemmefink...from the top of my head containing a walnut-sized brain: Fit the model with Period and Treatment as fixed factors (no subject, no sequence) and note the SS. Fit a new model with Period and Treatment and Sequence as fixed factors (no subject) and note the SS. The sequence type III SS contribution is the difference of the two SS-values. Good luck. — Pass or fail! ElMaestro |
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im.sagark ☆ India, 2013-06-07 07:54 (4755 d 11:46 ago) @ ElMaestro Posting: # 10750 Views: 9,114 |
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Can anybody provide me MAthematical formula for this?? That would be better. Thanks in advance. — Regards, Sagar Khandagale. |
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