idx = fsrftest (X, Y) tests each predictor, a column of the matrix X, with a one-way analysis of variance: whether the response Y has the same mean in every group of observations the predictor forms. It ranks the predictors by the result. idx is a row vector of column indices, from the most important predictor to the least; predictors of equal score keep their order.

X is a real matrix of type double or single with one row per observation, and Y a real vector of type double or single with one response per row of X.

idx = fsrftest (Tbl, ResponseVarName) takes the predictors and the response from the table Tbl: ResponseVarName names the variable holding the response and every other variable is a predictor. idx = fsrftest (Tbl, formula) names them with a model formula instead, 'Y ~ x1 + x2', which holds main effects only, and ranks only the predictors it names, idx indexing them in the order the table holds them. idx = fsrftest (Tbl, Y) takes the predictors from the table and the response from Y. A logical, categorical, text or string variable of the table is a categorical predictor; an ordinal categorical one is continuous, its categories in their order.

[idx, scores] = fsrftest (…) also returns the score of each predictor, a row vector of type double in the order of the predictors, so that scores(idx) is in decreasing order. The score is -log (p), p being the p-value of the predictor’s F-test, so a larger score marks a more important predictor; it is Inf where p is 0. A predictor that forms a single group, or as many groups as observations, scores 0, and so does every predictor when the response is constant.

A continuous predictor is first binned. Its n known values are sorted, the upper edge of bin k is the value at position ceil (k * n / NumBins), and a value goes to the first bin whose edge it does not exceed. The bins so hold equal numbers of observations as nearly as the ties allow, the first ones taking any remainder, and equal values always share a bin, which may leave fewer bins than asked for. A categorical predictor takes its categories as they are. The F-test weighs each observation by its weight, scaling the weights not mattering.

Each predictor is tested on the observations it is known for. An observation whose response is missing is left out of every test.

The following Name-Value pairs are supported:

The option names are not case sensitive but must be given in full. With a matrix, the categorical predictors cannot be named, the predictors having no names, as in MATLAB. The test is computed in double precision whatever the type of the data; MATLAB R2024a gives a different score for a response of type single than for the same values as double, which Octave does not.

See also: fscchi2, relieff, sequentialfs, anova1

Source Code: fsrftest