Poisson residuals
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Poisson residuals



Hi,
I downloaded the latest version of asreml which provides residuals and
predicted values in a .yht file.  However, how are the residuals
calculated?

For example, I tried a small example of a fixed effects model with a
poisson model with a log link.  Attached are the various files.  For
example, observation one has parity 1 with nlb=1.  The predicted value
is then 0.3185 or 1.375, the latter value is in the .yht file.  Asreml
reports the the residual as -0.2378 and it is not clear how this is
computed.  Is this the residual directly from Schall's approach?

Thanks in advance,
Bruce
 SLOPES FOR LOG(ABS(RES)) on LOG(PV) for Section   1
   0.45
                  
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 * *  *  *        
 * *  *  * *      
 * *  *  * *    **
   
 Min Mean Max-0.45455     0.92519E-16  1.2857     omitting     0 zeros

  ASREML [21 Mar 2000]  Poisson model                                                           
 Wed Apr 12 08:45:06 2000   8.00 Mbyte  Unix   fig
 *****************************************************
 * ASREML 2000  Residuals now written to .yht file,  *
 * convergence monitoring of parameters to .res file *
 *********************************************** ARG *
 QUALIFIERS: !NODISPLAY                                                  
  Reading fig.dat  FREE FORMAT skipping  0  lines
 Univariate analysis of nlb                 
 Using       24 records [of      24 read from      24 lines of fig.dat             ]
  Model term      Size Type    COL   Minimum    Mean      Maximum   #zero #miss
   1 animal          1 Covariat  1  1.000      12.50      24.00         0     0
   2 parity          3 Factor    2      1     1.8333          3         0     0
   3 sire            4 Factor    3      1     2.6667          4         0     0
   4 nlb             1 Variate   4  1.000      1.667      4.000         0     0
   5 mu              1 Constant Term
  Forming  4  equations:  4  dense
 Initial updates will be shrunk by factor    0.010
 Distribution and link: Poisson; Log   Mu=exp(XB) V=Mu                      
 NOTICE:     1 (more) singularities,
 LogL= 2.76751     S2=  1.0000         21 df    1.000    
 LogL= 2.65014     S2=  1.0000         21 df    1.000    
 LogL= 2.65014     S2=  1.0000         21 df    1.000    
 LogL= 2.65014     S2=  1.0000         21 df    1.000    
 Final parameter values                        1.0000    
 Deviance from GLM fit                     -10.49
 Variance heterogenity factor [Deviance/DF]     0.50

 Source                Model  terms     Gamma     Component    Comp/SE   % C
 Variance                 24     21   1.00000       1.00000       0.00   0 F   

 Analysis of Variance       DF     F-incr      F-adj  StndErrDiff
   5 mu                      1      10.77       1.12
   2 parity                  2       0.31       0.31  0.4314    

                     Solution       Standard Error    T-value     T-prev
   2 parity              
                    2   0.287682       0.369274          0.78
                    3   0.241162       0.483494          0.50     -0.11
   5 mu                  
                    4   0.318454       0.301511          1.06
 SLOPES FOR LOG(ABS(RES)) on LOG(PV) for Section   1
   0.45
 Finished: Wed Apr 12 08:45:06 2000   LogL Converged                                              

fig.dat

fig.as

  parity                          1           0.000       0.000    
  parity                          2          0.2877      0.3693    
  parity                          3          0.2412      0.4835    
  mu                              1          0.3185      0.3015    
  Record        Yhat    Residual         Hat
       1      1.3750     -0.2378      0.9091E-01
       2      1.3750     -0.2378      0.9091E-01
       3      1.3750      0.3527      0.9091E-01
       4      1.3750      0.3527      0.9091E-01
       5      1.8333      0.8577E-01  0.4545E-01
       6      1.8333      0.8577E-01  0.4545E-01
       7      1.8333      0.5575      0.4545E-01
       8      1.8333     -0.4767      0.4545E-01
       9      1.8333      0.9767      0.4545E-01
      10      1.3750     -0.2378      0.9091E-01
      11      1.3750     -0.2378      0.9091E-01
      12      1.3750     -0.2378      0.9091E-01
      13      1.8333     -0.4767      0.4545E-01
      14      1.8333     -0.4767      0.4545E-01
      15      1.8333      0.5575      0.4545E-01
      16      1.7500       1.028      0.1429    
      17      1.7500     -0.4363      0.1429    
      18      1.7500     -0.4363      0.1429    
      19      1.3750      0.3527      0.9091E-01
      20      1.8333     -0.4767      0.4545E-01
      21      1.8333     -0.4767      0.4545E-01
      22      1.8333      0.8577E-01  0.4545E-01
      23      1.8333     -0.4767      0.4545E-01
      24      1.7500     -0.4363      0.1429