David Firth, software: QV Calculator

Instructions for using the web-based calculator

The QV Calculator computes quasi-variances for estimates of a group or factor effect in a generalized linear model (including linear models, logistic regression, log linear models, hazard models, etc.) For details (revised 23.9.98) of the methodology click here.

Input to the Calculator is that portion of the variance-covariance matrix which corresponds to the parameters of interest. This information may be provided in one of two ways:

the lower triangle of the variance-covariance matrix, including the variances on the diagonal
a list of standard errors followed by the lower triangle of the correlation matrix, excluding the variances on the diagonal.

Example
(McCullagh & Nelder, "Generalized Linear Models", pp204-8): The main-effects model for the ship damage rates is summarized as follows by GLIM:

? $display e$ ! displays parameter estimates for the model
              ! along with "conventional" standard errors
          estimate        s.e.     parameter
     1      -6.406      0.2827      1
     2     -0.5433      0.2309      TYPE(2)
     3     -0.6874      0.4271      TYPE(3)
     4    -0.07596      0.3779      TYPE(4)
     5      0.3256      0.3067      TYPE(5)
     6      0.6971      0.1946      YEAR(2)
     7      0.8184      0.2208      YEAR(3)
     8      0.4534      0.3032      YEAR(4)
     9      0.3845      0.1538      OP(2)
scale parameter 1.691
 
? $display v$ ! prints the estimated variance-covariance matrix of estimates
  0.0799 
 -0.0530  0.0533
 -0.0458  0.0428  0.1824 
 -0.0396  0.0390  0.0384  0.1428 
 -0.0408  0.0404  0.0412  0.0387  0.0941 
 -0.0266  0.0038  0.0030  0.0020 -0.0002  0.0379 
 -0.0343  0.0138  0.0043  0.0024 -0.0025  0.0272  0.0487 
 -0.0344  0.0160  0.0126 -0.0111  0.0049  0.0281  0.0367  0.0919
 -0.0094  0.0009 -0.0002 -0.0003  0.0013 -0.0036 -0.0089 -0.0147  0.0237

Suppose we are interested in the 5-level factor TYPE (the type of ship). The relevant part of the covariance matrix is highlighted in bold above, and would be input to the QV Calculator as

0 0 0.0533 0 0.0428 0.1824 0 0.0390 0.0384 0.1428 0 0.0404 0.0412 0.0387 0.0941

Notice the column of zeros here, which reflects the fact that GLIM sets the parameter for TYPE(1) to zero and omits the corresponding column from the displayed variance-covariance matrix. Other model-fitting packages have different conventions, and it does not matter which one is used as long as the covariance matrix corresponding to all levels of the factor (i.e, all 5 levels here rather than just 4) is provided.

The alternative representation is in two parts, a list of standard errors followed by the lower triangle of the correlation matrix. For the above example this would be

0  0.2309  0.4271  0.3779  0.3067
0
0  0.4340
0  0.4468  0.2380
0  0.5707  0.3142  0.3338

QV Calculator