In handling regression models with set parameters, we may feel that we can streamline the function by dropping variable parameters that don’t provide much significance to the overall model’s performance. The Wald test is essentially a pass or fail surveyor of the coefficients present in the model and see’s if the variables all equal zero. When no variables equal zero, the set is dropped and removed as being null to the model’s overall performance.
Let’s use an example where we have coefficients in a function and want to know if they hold any real value for our end results. This function takes a look at a number of parameters and determines if they meet set limits to be considered relevant to the regression test;
wald.test(Sigma, b, Terms = NULL, L = NULL, H0 = NULL,
df = NULL, verbose = FALSE)
When running the test on a set variable, if a value doesn’t meet the prescribed length for the Terms coefficient, it reads null for fulfillment and moves on until every value in the string is tested. Once in effect, the wald test annexes unnecessary variables to clean up the data set and make sure you don’t waste time on running parameters that hold no real value.
One interesting quirk of the Wald test is its argued similarity to another tool, the z-test. Essentially, the z-test is used to test the one parameter or dual parameters of a function to see if a given population is relevant to the tester’s hypothesis. Appearing like so; z.test(x, y, alternative=’two.sided’, mu=0, sigma.x=NULL, sigma.y=NULL, conf.level=.95), the test function runs the values of the dataset against multiple if then argument paths to see how many match positive to determine the effectiveness of the population.
Possibly the best way to differentiate the two is that the Wald test is a more specialized comparison of populations whose null values have been run through a simpler z-test to filter out some of the early null values. A wald test is even referred to as z-squared in reference to its similar factors and how programmers use z-tested populations as entry parameters for their Wald function.
One way to structure this difference in real-life examples is with this scenario of a credit union’s customer population being run through an attrition predictor model. The various inputs being put into play can be scrutinized by setting the desired factor as a parameter, in this case, the number of families with dependents. Taking a pool of multiple factors like this:
The function can compare lengths of values to see which are relevant to the search parameters and collect relevant data while scrubbing distracting null vectors from the pool. If the credit union wants to look for different factors, they can start with the original data pool and set different parameters to re-assess the dataset and look for a new string of variables that may contain previous null values that become relevant to new search terms. Gaining practice with the Wald test and its near-twin the z test will help in streamlining your regression and sorting modeling projects to make for a more effective data modeling experience.