How to add estimability checking to your model’s predict method

estimability package, Version 1.5.1

The goal of this short vignette is to show how you can easily add estimability checking to your package’s predict() methods. Suppose that you have developed a model class that has elements $coefficients, $formula, etc. Suppose it also has an $env element, an environment that can hold miscellaneous information. This is not absolutely necessary, but handy if it exists. Your model class involves some kind of linear predictor.

We are concerned with models that:

• Allow rank deficiencies (where some predictors may be excluded)
• Allow predictions for new data

For any such model, it is important to add estimability checking to your predict method, because the regression coefficients are not unique – and hence that predictions may not be unique. It can be shown that predictions on new data are unique only for cases that fall within the row space of the model matrix. The estimability package is designed to check for this.

The recommended design for accommodating rank-deficient models is to follow the example of stats::lm objects, where any predictors that are excluded have a corresponding regression coefficient of NA. Please note that this NA code actually doesn’t actually means the coefficient is missing; it is a code that means that that coefficient has been constrained to be zero. In what follows, we assume that this convention is used.

First note that estimability checking is not needed unless you are predicting for new data. So that’s where you need to incorporate estimability checking. The predict method should be coded something like this:

predict.mymod <- function(object, newdata, ...) {
    # ... some setup code ...
    if (!missing(newdata)) {
        X <-  # ... code to set up the model matrix for newdata ...
        
        b <- coef(object)
        if (any(is.na(b))) {  # we have rank deficiency so test estimability
            if (is.null (nbasis <- object$env$nbasis))
                nbasis <- object$nbasis <-
                    estimability::nonest.basis(model.matrix(object))
            b[is.na(b)] <- 0
            pred <- X %*% b
            pred[!estimability::is.estble(X, nbasis)] <- NA
        }
        else
            pred <- X %*% coef(object)
    }
    # ... perhaps more code ...
    pred
}

That’s it – and this is the fancy version, where we can save nbasis for use with possible future predictions. Any non-estimable cases are flagged as NA in the pred vector.

An alternative way to code this would be to exclude the columns of X and elements of b that correspond to NAs in b. But be careful, because you need all the columns in X in order to check estimability.

The only other thing you need to do is add estimability to the Imports list in your `Description file.