Table 1 Different steps to compute the effect score

1

fit a machine learning model (for a neural network model, the activation function of the output layer needs to be a sigmoid function)

2

determine a reference value \({x}_{i}^{r}\)

3

\(\left.{es}_{i,j}=logit\left(f\left({x}_{1}^{j},\dots ,{x}_{i}^{j},\dots ,{x}_{n}^{j}\right)\right)-logit(f({x}_{1}^{j},\dots ,{x}_{i}^{r},\dots ,{x}_{n}^{j})\right)\)

- where \(f(.)\) is the prediction of the probability of the positive class by the model

- if \({x}_{i,j}={x}_{i,k}\), then consider the average of them

4

\({ES}_{i}= \sum_{j=1}^{n}|{es}_{i,j}|\)

5

For a continuous feature, plot \({es}_{i,j}\) against the value of \({x}_{i, j \epsilon n \left\{obs\right\}}\) to depict the effect of \({x}_{i}\) at different values on the output with respect to the reference

6

Rank \({ES}_{i}\) of categorial and continuous features to compare strength of different features