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		BUGS July 2010
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Subject:
Undefined real result error in longitudinal model with stochastic term
From:
Chaouch Aziz <[log in to unmask]>
Reply-To:
Chaouch Aziz <[log in to unmask]>
Date:
Mon, 26 Jul 2010 10:43:13 +0200
Content-Type:
multipart/mixed
Parts/Attachments:
text/plain (30 lines) , bugsmodel.txt (1 lines)
Dear BUGS users,

I'm trying to build a model for response dY with a fixed slope (beta), a stochastic process which is a difference of the same brownian motion at different times (dW) and measurement error (espilon)

dY_ij=beta*time_ij + dW_ij + espilon_ij

where dW_ij = W_ij - W_is     (j>=s)

dW has a mean 0 and Cov(dW_ij, dW_is) = p*min(j,s)

To implement this model in WinBUGS, I calculated the matrix min(j,s) for each patient i. I then inverted these matrices to get "pseudo-precision matrices" for each patient. I call these "pseudo-precision matrices" because the exact precision matrix is equal to (1/p)*pseudo-precision matrix where p is a scaling parameter to be estimated. Since some patients have more data than others (unbalanced data), these matrices do not all have the same size. So I defined a 2 dimensional array stacking all these pseudo-precision matrices and filling empty cases with 0. This array is stored in the data file as Q. In the model I then compute the precision matrix as Prec[,] <- (1/p)*Q[,].

I use a multivariate normal distribution to model dW for each patient and I retrieve the precision matrix of patient i by correctly indexing Prec. The model loads and compiles correctly but at the first iteration, I get an "Undefined real result" error which I'm not able to debug. I tried different initial values/priors with no success. I found that the error must probably lies in the multivariate normal distribution I defined for dW but I can't find what's the error. The indexing seems to work correctly. The error message writes something about Math.Matrix.LUDecomp so I guess there is some issue with the defined precision matrices. But again I checked several times the code and the calculated precision matrices and I cannot find anything wrong.

Any idea? Please find the model, data and initial value I use in the attached file bugsmodel.txt.

Regards

Aziz Chaouch

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# MODEL

model{

  for(k in 1:K){

    dY[k] ~ dnorm(mu[id[k],visit[k]], tau.e)

    mu[id[k],visit[k]] <- beta*time[k] + dW[id[k],visit[k]]



    #dW Precision matrix

    for(l in 1:colQ){

      Prec[k,l] <- (1/p)*Q[k,l]  #precision matrix = Q/p

    }

  }

  

  # Patients with only 1 visit after first count

  for(i in 1:n1){

    dW[i,1] ~ dnorm(0,Prec[first[i],1])

  }



  # Patients with more than 1 visit after first count

  for(i in (n1+1):N){

    dW[i,1:nvis[i]] ~ dmnorm(zero[first[i]:last[i]],Prec[first[i]:last[i],1:nvis[i]]) # PROBLEM IS SUPPOSED TO LIE HERE!!!

  }

  

  # Priors and parameter transform

  beta ~ dnorm(0,0.01)

  p ~ dnorm(0.001,0.1)I(0.00001,)

  tau.e <- 1/(2*pow(sd.e,2))

  sd.e ~ dunif(0.001,10)

}







# DATA

list(K=2.15000E+02, N=3.00000E+01, id=c(1.00000E+00, 2.00000E+00, 3.00000E+00, 4.00000E+00, 5.00000E+00, 6.00000E+00, 7.00000E+00, 8.00000E+00, 8.00000E+00, 8.00000E+00, 8.00000E+00, 9.00000E+00, 9.00000E+00, 9.00000E+00, 9.00000E+00, 9.00000E+00, 9.00000E+00, 9.00000E+00, 9.00000E+00, 9.00000E+00, 9.00000E+00, 1.00000E+01, 1.00000E+01, 1.00000E+01, 1.00000E+01, 1.00000E+01, 1.00000E+01, 1.00000E+01, 1.10000E+01, 1.10000E+01, 1.10000E+01, 1.20000E+01, 1.20000E+01, 1.20000E+01, 1.20000E+01, 1.20000E+01, 1.20000E+01, 1.20000E+01, 1.20000E+01, 1.30000E+01, 1.30000E+01, 1.30000E+01, 1.40000E+01, 1.40000E+01, 1.40000E+01, 1.40000E+01, 1.40000E+01, 1.40000E+01, 1.40000E+01, 1.50000E+01, 1.50000E+01, 1.50000E+01, 1.50000E+01, 1.50000E+01, 1.50000E+01, 1.60000E+01, 1.60000E+01, 1.60000E+01, 1.60000E+01, 1.60000E+01, 1.60000E+01, 1.60000E+01, 1.60000E+01, 1.60000E+01, 1.60000E+01, 1.60000E+01, 1.60000E+01, 1.60000E+01, 1.70000E+01, 1.70000E+01, 1.70000E+01, 1.70000E+01, 1.70000E+01, 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0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, -1.68980E+00, 2.96600E+00, -1.27620E+00, -0.00000E+00, -0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, -1.27620E+00, 6.01650E+00, -4.74030E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, -4.74030E+00, 6.50350E+00, -1.76330E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, -1.76330E+00, 1.76330E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 1.36070E+00, -7.60400E-01, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, -7.60400E-01, 4.90810E+00, -4.14770E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, -4.14770E+00, 4.14770E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00), .Dim=c(215, 29)), colQ=2.90000E+01, n1=7.00000E+00)





# INITS

list(beta=-2.00000E+00, p=2.00000E+00, dW= structure(.Data= c(3.08248E-02,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA, 1.33929E-02,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA, -3.03328E-01,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA, -3.51237E-01,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA, -3.43182E-01,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA, 4.54347E-01,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA, 9.65200E-02,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA, 1.61660E-01, -3.27370E-01, -1.20127E+00, -1.61627E+00,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA, 2.33569E-01, -8.58759E-02, 5.27440E-01, -1.03470E-01, 8.30400E-01, 1.12983E+00, 2.32350E+00, 2.35452E+00, 1.72084E+00, 1.00353E+00,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA, -1.39237E-01, -8.87124E-02, -1.81546E-01, -6.78574E-01, -1.77873E-01, -4.67309E-01, -1.00366E+00,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA, -7.36502E-02, -1.90006E+00, -8.54800E-01,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA, -2.41248E-01, 1.64026E-01, 6.11873E-01, 1.11717E+00, 1.15946E+00, 1.47427E+00, 1.30351E+00, 1.32970E+00,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA, -1.34790E-01, -1.64597E+00, -2.24981E+00,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA, 3.95943E-01, -6.00653E-02, -3.32821E-01, -2.41459E+00, -9.50386E-01, -9.17894E-01, -5.94216E-01,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA, 4.58430E-01, -3.25769E-01, 7.37499E-01, 1.00258E+00, -4.72807E-01, 4.32355E-01,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA, -2.54943E-01, -3.99153E-01, 5.18248E-02, -4.56741E-02, 7.62842E-01, 9.37917E-01, 6.40796E-01, 3.92325E-01, -9.53643E-02, 2.20137E-01, -8.94970E-01, -3.23460E-01, -6.75223E-01,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA, 8.21205E-02, 1.13347E+00, 2.42707E-01, -7.29239E-01, -5.58735E-01, 5.30774E-01,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA, -5.73251E-01, -7.23278E-01, -4.56124E-01, 6.31132E-01, 8.48356E-01, 5.86576E-01, 4.27184E-01, 4.79025E-01, 1.57020E-01, 8.09259E-01, 1.28435E+00, 2.05537E+00, 2.02213E+00,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA, -6.21892E-01, -1.53842E+00,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA, -9.33575E-02, 4.07775E-02, -4.04268E-01, -1.06059E+00, -6.85078E-01, -9.09288E-01,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA, 6.90484E-01, -1.66548E-01, 5.92764E-01, -6.16499E-01, 4.31184E-02, 4.09833E-01, 6.04463E-01, 6.12299E-01, 6.09909E-02, -1.21558E+00, -1.18180E-01, 4.96584E-02, -4.31358E-01,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA, -1.35333E-01, 5.31710E-02, -1.85671E-01, 4.46611E-01, 1.10617E-01,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA, 3.71876E-01, 8.36634E-01, -3.26373E-01, -1.90189E+00, -7.42277E-01, -5.61647E-01, 3.19011E-02, 3.86233E-02, 7.13463E-01, -5.19993E-01, -1.93227E+00, -4.73710E-01,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA, 9.47070E-01, 1.21211E+00, 1.80264E+00, 2.23973E+00, 1.17175E+00, 9.44242E-01, 1.00791E+00, 3.66650E-01, -9.26284E-01, -5.64570E-01, -3.96292E-01, -3.59109E-01, -4.03890E-01, -1.84039E-01, 4.74717E-01, -5.39913E-02, 5.58235E-01, 9.56422E-01, 1.20438E+00, 1.84965E+00, 3.05221E+00, 3.27577E+00,     NA,     NA,     NA,     NA,     NA,     NA,     NA, -1.43458E-01, 1.51441E-01, 9.06954E-01, -7.07989E-01, 6.80299E-02, 3.08443E-01, -4.26245E-01, 7.19265E-02,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA, 5.88228E-01, 2.25612E-01, -2.78221E-01,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA, -1.00752E+00, -1.39392E+00, -8.63448E-01, -1.04065E+00, -1.56489E+00, -1.14021E+00, -1.43744E+00, -2.06251E+00, -2.04380E+00, -2.45005E+00, -3.52099E+00, -4.00002E+00, -3.42932E+00, -2.98894E+00, -3.62437E+00, -3.68943E+00, -3.85458E+00, -3.91423E+00, -4.17691E+00, -4.46464E+00, -3.44260E+00, -3.83491E+00, -4.10614E+00, -4.75086E+00, -5.12613E+00, -6.19752E+00, -5.69802E+00, -4.98382E+00, -4.72548E+00, 1.34473E-01, 7.51065E-02, -8.78875E-01, 6.90615E-02, -1.12741E+00, -1.01855E+00, -1.19963E+00, -1.37262E+00, -8.53224E-01, -1.37215E+00, -1.07324E+00, -1.47151E+00, -9.40143E-01, -1.00495E+00, -8.73971E-01, -1.52584E+00, -3.00248E+00, -3.63523E+00,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA, -7.21797E-01, 6.84823E-02, 9.64238E-01, 1.97746E+00, 9.48254E-01, 1.17946E+00, 2.78507E+00,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA, 1.33954E+00, 1.20863E+00, 3.60720E-01,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA,     NA), .Dim=c(30, 29)), sd.e=2.00000E+00)









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