Computes the variance-covariance or correlation matrix.

Routine CORVC computes estimates of correlations, covariances, or sums of squares and crossproducts for a data matrix X. Weights and frequencies are allowed but not required. Also allowed are listwise or pairwise deletion of missing values. Routine CORVC is an “IDO routine,” so it may be called with all of the data in one invocation, or it may be called in several invocations with some (or none) of the data input during each call. By setting NROW to a negative integer, observations that have previously been added to the covariance/correlation statistics may be deleted from the statistics. Exercise care with this option, however, since the program may not be able to detect constant variables when negative NROW is used.

The means, (corrected) sums of squares, and (corrected) sums of crossproducts are computed using the method of provisional means. Let

denote the mean based upon i observations for the k-th variable, fi denote the frequency of the i-th observation, wi denote the weight of the i-th observation, and let cjki denote the sum of crossproducts (or sum of squares if j = k) based upon i observations. Then, the method of provisional means finds new means and sums of crossproducts as follows:

The means and crossproducts are initialized as:

where p denotes the number of variables. Letting xk(i+1) denote the k-th variable on observation
i + 1, each new observation leads to the following updates for

and cjki using update constant ri+1:

If there is no weight variable, weights of 1.0 are used. If there is no frequency column, frequencies of 1.0 are used. Means and variances are computed based upon all of the valid data for each variable or, if required, based upon all of the valid data for each pair of variables.

In CORVC, each observation xki with weight wi is assumed to have mean μk and variance

With these assumptions, CORVC uses the following definition of a sample mean:

where nr is the number of cases. The following formula defines the sample covariance, sjk, between variables j and k:

The sample correlation between variables j and k, rjk, is defined as:

The first example illustrates the use of CORVC when inputing all of the data at once. The first 50 observations in the Fisher iris data (see routine GDATA, Chapter 19, “Utilities”) are used. Note in this example that the first variable is constant over the first 50 observations.

In the second example, the IDO option is used. After the initialization step in which IDO = 1, the first 53 observations in the Fisher iris data are input, one observation at a time. The last three observations input are then deleted from the covariances by setting NROW = ‑ 1. Finally, the wrap-up step is accomplished by calling CORVC with IDO = 3. The output is identical to the output above.