What is the Wald statistic?

The wald statistic, outputted in logistic and Cox model regressions, is simply the square of the regression coefficient, B, divided by its variance. This is also calculated as the t-statistic squared.

If the regression coefficient is zero the wald statistic should, for large samples, be asymptotically equal to a chi-square statistics on one df.

Univariate Wald = $$ \frac{\mbox{ B }}{\mbox{variance (B)}}$$

There are problems interpreting Wald statistics in logistic regressions when there is sparse data.

There are multivariate Wald statistics which may be used to compare more than one regression coefficient to zero simultaneously which are approximately chi-squared on p-1 df when testing if p regression estimates are equal to zero.

This uses the Covariance matrix of ther regression estimates (COV). The univariate Wald is a special case.

Multivariate Wald = $$B^T$$ COV B