<div dir="ltr">See also:<div><br></div><div><a href="http://www.admb-project.org/examples/admb-tricks/parameterization/covariance-matrices/covariance-matrices">http://www.admb-project.org/examples/admb-tricks/parameterization/covariance-matrices/covariance-matrices</a><br></div><div><br></div><div>Hans</div></div><div class="gmail_extra"><br><div class="gmail_quote">On Thu, Nov 6, 2014 at 4:23 PM, dave fournier <span dir="ltr"><<a href="mailto:davef@otter-rsch.com" target="_blank">davef@otter-rsch.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
  
    
  
  <div bgcolor="#FFFFFF" text="#000000">
    <div>On 11/05/2014 05:10 PM, Saang-Yoon
      wrote:<br>
      <br>
      As I said, you should work with the Choleski decomposition of the
      correlation matrix.<br>
      <br>
      In the simple 3x3 case your conditions imply that  it is
      determined by 2 parameters<br>
      <br>
      r and s   with bounds a and b such that   a<=r<=b.  You get
      a and b by solving<br>
      <br>
           0.0<=     r/sqrt(1+r*r)  <=0.7<br>
       <br>
      The matrix is<br>
      <br>
          1                               0                           0<br>
      <br>
           r/sqrt(1+r*r)    1/sqrt(1+r*r)                0<br>
      <br>
            0                     s/sqrt(1+s*s)    1/sqrt(1+s*s)      <br>
      <br>
      <br>
      <br>
      <br>
      <br>
      <br>
      <br>
    </div>
    <blockquote type="cite">
      <div dir="ltr">
        <div>Hi, Dr. Fournier and others.  </div>
        <div>I made some progress.   Exploring many possibilities, I
          found that the following assumptions help, but there is still
          a concern.</div>
        <div>(Assumption 1) Three age classes are not from the same
          cohort, and thus age class 1 and 3 are presumed to be
          independent.    Thus I fix the correlation coefficient between
          age class 1 and 3 as zero.  </div>
        <div>(Assumption 2) If there is a correlation between neighbor
          age classes (e.g., "1 vs. 2", and "2 vs. 3"), the correlation
          should be positive (i.e. autocorrelation over the years).   
          Thus I set bounds of correlation between those neighbor
          classes to be positive: (e.g.,  init_bounded_number
          corp12(0.0,0.7,3);  )</div>
        <div><br>
        </div>
        <div>Then now I have the resultant COR file (i.e., convergence
          was made).  It was good news, but the estimates of correlation
          coefficients between neighbor age classes are stuck to the
          uppder bound, 0.7.  If I allow a wide bound
          (e.g., init_bounded_number corp12(0.0,0.9,3); ), then I failed
          to get positive definite matrices.  </div>
        <div><br>
        </div>
        <div>admb -r -s ssmbr3v4.tpl <br>
          ssmbr3v4 -ind simdataall2.dat -ainp ssmbr3v3.pin -phase 1
          -noinit </div>
        <div><br>
        </div>
        <div>Any advice would be appreciated.    Best Wishes,</div>
        <div>Saang-Yoon<br>
          <br>
          On Tuesday, November 4, 2014 6:30:56 PM UTC-5, dave fournier
          wrote:</div>
        <blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;padding-left:1ex;border-left-color:rgb(204,204,204);border-left-width:1px;border-left-style:solid">
          <div bgcolor="#FFFFFF" text="#000000">
            <div>On 11/04/2014 02:58 PM, Saang-Yoon wrote:<br>
              <br>
              Hmm.  Well its like this. Pick a number between -infinity
              and + infinity. Why would you expect that it would need to
              be positive.<br>
              <br>
              or a matrix like<br>
              <br>
                1 .9 .9<br>
              .9 1 -.50<br>
              .9 -.50 1<br>
              <br>
              If you check you will see that just like -1 is negative,
              this matrix is not positive definite.<br>
              <br>
              What you should be asking is how does one parameterize the
              positive definite matrices in a<br>
              nice way to do nonlinear parameter estimation.  <br>
              <br>
              <br>
              <br>
            </div>
            <blockquote type="cite">
              <div dir="ltr">
                <div>Hi, Dr. Fournier.   Thank you very much for your
                  reply.   Attached is models that reflect the TPL
                  code.   At the moment, I have no clue about why the
                  covariance matrix is not positive definite.    </div>
                <div>Saang-Yoon</div>
                <div><br>
                  On Monday, November 3, 2014 2:58:49 PM UTC-5, dave
                  fournier wrote:</div>
                <blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;padding-left:1ex;border-left-color:rgb(204,204,204);border-left-width:1px;border-left-style:solid">
                  <div dir="ltr">What makes you think the covariance
                    matrix will be positive definite with your
                    parameterization?<br>
                    <br>
                    On Sunday, November 2, 2014 5:49:50 PM UTC-8,
                    Saang-Yoon wrote:
                    <blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;padding-left:1ex;border-left-color:rgb(204,204,204);border-left-width:1px;border-left-style:solid">
                      <div dir="ltr">
                        <div>Hi.   There was no error in compile-link
                          for the attached TPL file; i.e., I got its
                          executable file.    However, I fail to get
                          convergence results.     Would you mind
                          checking the TPL? </div>
                        <div>Following are commands for runs.   </div>
                        <div><br>
                        </div>
                        <div>admb -r -s ssmbr3v4.tpl<br>
                          ssmbr3v4 -ind simdataall2.dat -ainp
                          ssmbr3v3.pin -phase 1 -noinit</div>
                        <div>ssmbr3v4 -ind simdataall2.dat -ainp
                          ssmbr3v3.pin -phase 9 -noinit</div>
                        <div><br>
                        </div>
                        <div>Thank you.</div>
                        <div>Saang-Yoon<br>
                        </div>
                      </div>
                    </blockquote>
                  </div>
                </blockquote>
              </div>
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