[R] Systemfit (was RE: How to force two regression coefficients to be equal but opposite in sign?)

[Woolner, Keith]

Thank you Arne.  Though I didn't detail all of my attempts, I did in
fact try a larger restriction matrix that accounted for the levels of
the factors.  

However, I think my error in those attempts was in adding N columns to
the matrix for an N-level factor (rather than N-1 columns), because I
thought I needed to explicitly constrain all 5 coefficients of each
factor.  I am aware of how lm() returns coefficients for all but the
first level of the factor, but wasn't clear on how that interacted with
the restriction matrix.

A brief sentence in the documentation emphasizing the relationship of
the number of levels of a factor to the number of coefficients
represented in the restriction matrix would have helped me a lot in this
situation, but I would, of course, defer to you as to whether this tip
is of general enough interest to include in the documentation.

Thank you again for your patience and assistance.

Keith


> -----Original Message-----
> From: Arne Henningsen [mailto:arne.henningsen at googlemail.com]
> Sent: Tuesday, June 10, 2008 2:33 AM
> To: r-help at r-project.org
> Cc: Woolner, Keith
> Subject: Re: [R] Systemfit (was RE: How to force two regression
> coefficients to be equal but opposite in sign?)
> 
> Hi Keith!
> 
> On Monday 09 June 2008 16:27, Woolner, Keith wrote:
> > [...]
> > After I sent my initial message, I came across the Systemfit
package,
> > which allows specification of constraints on parameters.  In theory,
> > this should solve my problem perfectly.  However, I was not able to
> > get it to work with my data, as every attempt yielded the following
> error:
> >
> > Error in dimnames(x) <- dn :
> >   length of 'dimnames' [2] not equal to array extent
> >
> > I suspect that it is related to some of my variables being factors
> > rather than numeric.
> 
> Yes and no (see below).
> 
> > library(systemfit)
> >
> > # create data frame - X1, X2, X3, X4 are numeric.  E1 and E2 are
> > factors df <- data.frame(
> > 	X1 =
> > c(.20,.10,.40,.05,.10,.24,.30,.70,.48,.22,.87,.29,.24,.19,.92),
> > 	X2 =
> > c(.25,.12,.45,.01,.19,.50,.30,.40,.50,.40,.68,.30,.16,.02,.70),
> > 	E1 =
> > c("A","A","A","B","B","B","C","C","C","D","D","D","E","E","E"),
> > 	E2 =
> > c("B","C","D","A","D","E","A","B","E","B","C","E","A","B","C")
> > )
> >
> > df$X3 <- sqrt(df$X1)+runif(1)
> > df$X4 <- sqrt(df$X2)+runif(1)
> >
> > # Create constraint matrix such that the last two variables must be
> > equal but opposite in sign
> 
> No. I guess that you mean that the *coefficients* (and not the
> variables) must be equal but opposite in sign.
> 
> > tx <- matrix(0,nrow=1,ncol=4)
> > tx[1,3]<- 1
> > tx[1,4]<- 1
> >
> > # Run systemfit with only numeric variables (works)
> > systemfit(X2 ~ X1 + X3 + X4,"OLS", data=df, restrict.matrix=tx)
> >
> > # Run systemfit with factors but not constraints (works)
> > systemfit(X2 ~ X1 + E1 + E2,"OLS", data=df)
> >
> > # Run systemfit with factors and constraints (this returns an error)
> > systemfit(X2 ~ X1 + E1 + E2,"OLS", data=df, restrict.matrix=tx)
> 
> Run this regression without constraints (works)
>    systemfit(X2 ~ X1 + E1 + E2,"OLS", data=df )
> 
> Take a look at the coefficients: We have *10* coefficients now
(because
> "E1"
> and "E2" are factors. Hence, your restriction matrix must have *10*
> columns.
> For instance, if you want to restrict the coefficients of the "B"s in
> "E1"
> and "E2" (third and seventh coefficient, respectively) to be equal but
> opposite in sign, you could do the following:
>    tx2 <- matrix(0,nrow=1,ncol=10)
>    tx2[1,3]<- 1
>    tx2[1,7]<- 1
>    systemfit(X2 ~ X1 + E1 + E2,"OLS", data=df, restrict.matrix=tx2)
> 
> > Is systemfit able to deal with factors as independent variables
> having
> > constraints, and if so, is there some trick in formulating the
> problem?
> > I searched through the package documentation, but did not see
mention
> > of factors being either supported or unsupported.
> 
> Until now, I thought that it not necessary to say something about
> factors, because they should work in systemfit as in other R functions
> (e.g. lm).
> The documentation says that "restrict.matrix" must be a j x k matrix,
> where k is the number of all parameters (NOT the number of all
> regressors, which differs if some regressors are factors). Hence, I
> think that the documentation is clear enough. However, please tell me
> if you have any suggestions for improving the documentation.
> 
> Best wishes,
> Arne
> 
> --
> Arne Henningsen
> http://www.arne-henningsen.name