Dear List:
I am working to construct a matrix of a particular form. For the most
part, developing the matrix is simple and is built as follows:
vl.mat<-matrix(c(0,0,0,0,0,64,0,0,0,0,64,0,0,0,0,64),nc=4)
Now to expand this matrix to be block-diagonal, I do the following:
sample.size <- 100 # number of individual students
I<- diag(sample.size)
bd.mat<-kronecker(I,vl.mat)
This creates a block-diagonal matrix with variances along the diagonal
and covariances within-student to be zero (I am working with
longitudinal student achievement data). However, across student, I want
to have the correlation equal to 1 for each variance term. To
illustrate, here is a matrix for 2 students. The goal is for the
correlation between the second variance term for student 1 to be
perfectly correlated with the variance term for student 2. In other
words, I need to plug in 64 at position (6,2) and (2,6), another 64 at
position (7,3) and (3,7) and another 64 at positions (8,4) and (4,8).
I'm having some difficulty conceptualizing how to construct this part of
the matrix and would appreciate any thoughts.
Thank you,
Harold
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 0 0 0 0 0 0 0 0
[2,] 0 64 0 0 0 0 0 0
[3,] 0 0 64 0 0 0 0 0
[4,] 0 0 0 64 0 0 0 0
[5,] 0 0 0 0 0 0 0 0
[6,] 0 0 0 0 0 64 0 0
[7,] 0 0 0 0 0 0 64 0
[8,] 0 0 0 0 0 0 0 64
[[alternative HTML version deleted]]
I'm still not clear on exactly what your question is. If you can plug in the numbers you want in, say, the lower triangular portion, you can copy those to the upper triangular part easily; something like: m[upper.tri(m)] <- m[lower.tri(m)] Is that what you're looking for? Andy> From: Doran, Harold > > Dear List: > > I am working to construct a matrix of a particular form. For the most > part, developing the matrix is simple and is built as follows: > > vl.mat<-matrix(c(0,0,0,0,0,64,0,0,0,0,64,0,0,0,0,64),nc=4) > > Now to expand this matrix to be block-diagonal, I do the following: > > sample.size <- 100 # number of individual students > I<- diag(sample.size) > bd.mat<-kronecker(I,vl.mat) > > This creates a block-diagonal matrix with variances along the diagonal > and covariances within-student to be zero (I am working with > longitudinal student achievement data). However, across > student, I want > to have the correlation equal to 1 for each variance term. To > illustrate, here is a matrix for 2 students. The goal is for the > correlation between the second variance term for student 1 to be > perfectly correlated with the variance term for student 2. In other > words, I need to plug in 64 at position (6,2) and (2,6), another 64 at > position (7,3) and (3,7) and another 64 at positions (8,4) and (4,8). > I'm having some difficulty conceptualizing how to construct > this part of > the matrix and would appreciate any thoughts. > > Thank you, > Harold > > > [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] > [1,] 0 0 0 0 0 0 0 0 > [2,] 0 64 0 0 0 0 0 0 > [3,] 0 0 64 0 0 0 0 0 > [4,] 0 0 0 64 0 0 0 0 > [5,] 0 0 0 0 0 0 0 0 > [6,] 0 0 0 0 0 64 0 0 > [7,] 0 0 0 0 0 0 64 0 > [8,] 0 0 0 0 0 0 0 64 > > [[alternative HTML version deleted]] > > ______________________________________________ > R-help at stat.math.ethz.ch mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide! > http://www.R-project.org/posting-guide.html > >
I should probably have explained my data and model a little better. Assume I have student achievement scores across four time points. I estimate the model using gls() as follows fm1 <- gls(score ~ time, long, correlation=corAR1(form=~1|stuid), method='ML') I can now extract the variance-covariance matrix for this model as follows: var.mat<-getVarCov(fm1) Assume for sake of argument I have a sample size of 100 students. I can expand this to the full matrix as follows I<-diag(100) V<-kronecker(I,var.mat) For my particular model, the scores within each student are assumed correlated (AR1), but across student are uncorrelated. Now, for a particular problem I am dealing with I need to make some adjustments to this matrix, V, and reestimate the gls(). The adjustments I need to make cannot be done using any of the existing varFunc classes, so I am having to do this manually. What I need to do is create a new matrix manually, add it to V, then reestimate the gls. Creating this new matrix is the challenge I currently face, let's call it v.prime. The issue at hand is creating v.prime to have non-zero covariance terms across students in very specific places. The matrix I used below is only for two students. But assume I am doing this for thousands of students. My goal is to create a full block-diagonal covariance matrix where the correlation across students at time two is always perfectly correlated and the correlation at time three is always perfectly correlated across students. So, within each block of v.prime, the variances are uncorrelated, but across each block the variances are correlated. So, I need to construct v.prime such that it is one the same order of V to make them conformable for addition. More importantly, I need the off-diagonal elements across students to represent a perfect correlation in very specific places. In the example below, if there was a 64 at position (2,6) this would represent a perfect correlation between student 1 and 2 at this point in time since the variance along the diagonal at time 2 is 64. Since I am doing this for many students, there would need to be a 64 between student 1 and all other students (not just student 2) and so on.>From here I can use R's matrix facilities to reestimate the gls.I hope this clarifies a bit. Harold -----Original Message----- From: Liaw, Andy [mailto:andy_liaw at merck.com] Sent: Thursday, January 20, 2005 8:41 AM To: Doran, Harold; r-help at stat.math.ethz.ch Subject: RE: [R] Constructing Matrices I'm still not clear on exactly what your question is. If you can plug in the numbers you want in, say, the lower triangular portion, you can copy those to the upper triangular part easily; something like: m[upper.tri(m)] <- m[lower.tri(m)] Is that what you're looking for? Andy> From: Doran, Harold > > Dear List: > > I am working to construct a matrix of a particular form. For the most > part, developing the matrix is simple and is built as follows: > > vl.mat<-matrix(c(0,0,0,0,0,64,0,0,0,0,64,0,0,0,0,64),nc=4) > > Now to expand this matrix to be block-diagonal, I do the following: > > sample.size <- 100 # number of individual students > I<- diag(sample.size) > bd.mat<-kronecker(I,vl.mat) > > This creates a block-diagonal matrix with variances along the diagonal> and covariances within-student to be zero (I am working with > longitudinal student achievement data). However, across student, I > want to have the correlation equal to 1 for each variance term. To > illustrate, here is a matrix for 2 students. The goal is for the > correlation between the second variance term for student 1 to be > perfectly correlated with the variance term for student 2. In other > words, I need to plug in 64 at position (6,2) and (2,6), another 64 at> position (7,3) and (3,7) and another 64 at positions (8,4) and (4,8). > I'm having some difficulty conceptualizing how to construct this part > of the matrix and would appreciate any thoughts. > > Thank you, > Harold > > > [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] > [1,] 0 0 0 0 0 0 0 0 > [2,] 0 64 0 0 0 0 0 0 > [3,] 0 0 64 0 0 0 0 0 > [4,] 0 0 0 64 0 0 0 0 > [5,] 0 0 0 0 0 0 0 0 > [6,] 0 0 0 0 0 64 0 0 > [7,] 0 0 0 0 0 0 64 0 > [8,] 0 0 0 0 0 0 0 64 > > [[alternative HTML version deleted]] > > ______________________________________________ > R-help at stat.math.ethz.ch mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide! > http://www.R-project.org/posting-guide.html > >------------------------------------------------------------------------ ------ Notice: This e-mail message, together with any attachments,...{{dropped}}
Does the following do what you want (or at least get you closer)?> tmp <- matrix(0,16,16) > tmp[col(tmp)%%4 == row(tmp)%%4] <- 64 > tmp... Greg Snow, Ph.D. Statistical Data Center greg.snow at ihc.com (801) 408-8111>>> "Doran, Harold" <HDoran at air.org> 01/20/05 07:17AM >>>I should probably have explained my data and model a little better. Assume I have student achievement scores across four time points. I estimate the model using gls() as follows fm1 <- gls(score ~ time, long, correlation=corAR1(form=~1|stuid), method='ML') I can now extract the variance-covariance matrix for this model as follows: var.mat<-getVarCov(fm1) Assume for sake of argument I have a sample size of 100 students. I can expand this to the full matrix as follows I<-diag(100) V<-kronecker(I,var.mat) For my particular model, the scores within each student are assumed correlated (AR1), but across student are uncorrelated. Now, for a particular problem I am dealing with I need to make some adjustments to this matrix, V, and reestimate the gls(). The adjustments I need to make cannot be done using any of the existing varFunc classes, so I am having to do this manually. What I need to do is create a new matrix manually, add it to V, then reestimate the gls. Creating this new matrix is the challenge I currently face, let's call it v.prime. The issue at hand is creating v.prime to have non-zero covariance terms across students in very specific places. The matrix I used below is only for two students. But assume I am doing this for thousands of students. My goal is to create a full block-diagonal covariance matrix where the correlation across students at time two is always perfectly correlated and the correlation at time three is always perfectly correlated across students. So, within each block of v.prime, the variances are uncorrelated, but across each block the variances are correlated. So, I need to construct v.prime such that it is one the same order of V to make them conformable for addition. More importantly, I need the off-diagonal elements across students to represent a perfect correlation in very specific places. In the example below, if there was a 64 at position (2,6) this would represent a perfect correlation between student 1 and 2 at this point in time since the variance along the diagonal at time 2 is 64. Since I am doing this for many students, there would need to be a 64 between student 1 and all other students (not just student 2) and so on.>From here I can use R's matrix facilities to reestimate the gls.I hope this clarifies a bit. Harold -----Original Message----- From: Liaw, Andy [mailto:andy_liaw at merck.com] Sent: Thursday, January 20, 2005 8:41 AM To: Doran, Harold; r-help at stat.math.ethz.ch Subject: RE: [R] Constructing Matrices I'm still not clear on exactly what your question is. If you can plug in the numbers you want in, say, the lower triangular portion, you can copy those to the upper triangular part easily; something like: m[upper.tri(m)] <- m[lower.tri(m)] Is that what you're looking for? Andy> From: Doran, Harold > > Dear List: > > I am working to construct a matrix of a particular form. For the most> part, developing the matrix is simple and is built as follows: > > vl.mat<-matrix(c(0,0,0,0,0,64,0,0,0,0,64,0,0,0,0,64),nc=4) > > Now to expand this matrix to be block-diagonal, I do the following: > > sample.size <- 100 # number of individual students > I<- diag(sample.size) > bd.mat<-kronecker(I,vl.mat) > > This creates a block-diagonal matrix with variances along thediagonal> and covariances within-student to be zero (I am working with > longitudinal student achievement data). However, across student, I > want to have the correlation equal to 1 for each variance term. To > illustrate, here is a matrix for 2 students. The goal is for the > correlation between the second variance term for student 1 to be > perfectly correlated with the variance term for student 2. In other > words, I need to plug in 64 at position (6,2) and (2,6), another 64at> position (7,3) and (3,7) and another 64 at positions (8,4) and(4,8).> I'm having some difficulty conceptualizing how to construct this part> of the matrix and would appreciate any thoughts. > > Thank you, > Harold > > > [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] > [1,] 0 0 0 0 0 0 0 0 > [2,] 0 64 0 0 0 0 0 0 > [3,] 0 0 64 0 0 0 0 0 > [4,] 0 0 0 64 0 0 0 0 > [5,] 0 0 0 0 0 0 0 0 > [6,] 0 0 0 0 0 64 0 0 > [7,] 0 0 0 0 0 0 64 0 > [8,] 0 0 0 0 0 0 0 64 > > [[alternative HTML version deleted]] > > ______________________________________________ > R-help at stat.math.ethz.ch mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide! > http://www.R-project.org/posting-guide.html > >------------------------------------------------------------------------ ------ Notice: This e-mail message, together with any attachments,...{{dropped}} ______________________________________________ R-help at stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html