[R] Incomplete Factorial design

[Simon Fear]

One could also fit

fit <- lm(y~A*B - 1, data.frame(y=..., A=..., B=..,)

which will give a direct a:b term (as the negative of the
intercept in Spenser's formulation). Arguably this is more
natural in a setting where there is no placebo so that
an intercept term has a less obvious interpretation.

> -----Original Message-----
> From: Spencer Graves [mailto:spencer.graves at pdf.com]
> Sent: 06 February 2004 14:39
> To: parrinel at med.unibs.it
> Cc: R-help at stat.math.ethz.ch
> Subject: Re: [R] Incomplete Factorial design
> 
> 
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>  
>       I assume that means you have two treatments, say A and 
> B, can be 
> either absent or present.  The standard analysis codes them 
> as -1 or +1 
> for absent or present, respectively.  If you have 
> observations in all 4 
> cells, you can write the following equation: 
> 
>       y(A,B) = b0 + b1*A + b2*B + b12*A*B + error. 
> 
>       This equation has 4 unknowns, b1, b1, b2 and b12.  If 
> you have all 
> 4 cells in the 2x2 table, then you can estimate all 4 
> unknowns.  If you 
> have data for only 3 cells, the standard analysis pretends 
> that b12 = 0 
> and estimates the other three.  If you have only 2 cells, say (both 
> absent) and (both present), the standard analysis can 
> estimate b0 plus 
> either of b1 or b2.  However, in fact, these really estimate (b0+b12) 
> and (b1+b2).  To understand this, consult any good book that 
> discusses 
> confounding with 2-level fractional factorial designs. 
> 
>       To do this in R, use "lm", as
> 
>       fit <- lm(y~A+B, data.frame(y=..., A=..., B=..,)
> 
>       hope this helps. 
>       spencer graves
> 
> parrinel at med.unibs.it wrote:
> 
> >Hello,
> >I am planning a study with the main point to evaluate the 
> interaction of two treatments, 
> >but for ethical reasons one cell is empty, that with 
> patients receaving no treatment at all
> >
> >                                                                    
> >                                                                    
> >                            Treatment B
> >                                  
> >                                                                    
> >                                                                    
> >+
> >-
> >
> >Treatment A
> >+
> >a
> >b
> >
> >                                                                    
> >-
> >c
> >-------
> >
> >
> >I am looking for functions in R to estimate the sample size 
> and/or to conduct the 
> >analysis. I have just found an article from Byar in 
> Statistics in Medicine for a 2^3 
> >incomplete factorial design, but I would like not to 
> discover again the wheel..
> >TIA
> >dr. Giovanni Parrinello
> >Section of Medical Statistics
> >Department of Biosciences
> >University of Brescia
> >25127 Viale Europa, 11
> >Brescia Italy
> >Tel: +390303717528
> >Fax: +390303701157
> >
> >
> >
> >	[[alternative HTML version deleted]]
> >
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>  
>

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Simon Fear 
Senior Statistician 
Syne qua non Ltd 
Tel: +44 (0) 1379 644449 
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