ndarray_glm/response/
binomial.rs

1//! Regression with a binomial response function. The N parameter must be known ahead of time.
2#[cfg(feature = "stats")]
3use crate::response::Response;
4use crate::{
5    error::{RegressionError, RegressionResult},
6    glm::{DispersionType, Glm},
7    math::prod_log,
8    num::Float,
9    response::Yval,
10};
11#[cfg(feature = "stats")]
12use statrs::distribution::Binomial as BinDist;
13
14/// Use a fixed type of u16 for the domain of the binomial distribution.
15type BinDom = u16;
16
17/// Binomial regression with a fixed N. Non-canonical link functions are not
18/// possible at this time due to the awkward ergonomics with the const trait
19/// parameter N.
20pub struct Binomial<const N: BinDom>;
21
22impl<const N: BinDom> Yval<Binomial<N>> for BinDom {
23    fn into_float<F: Float>(self) -> RegressionResult<F, F> {
24        F::from(self).ok_or_else(|| RegressionError::InvalidY(self.to_string()))
25    }
26}
27
28#[cfg(feature = "stats")]
29impl<const N: BinDom> Response for Binomial<N> {
30    type DistributionType = BinDist;
31
32    fn get_distribution(mu: f64, _phi: f64) -> Self::DistributionType {
33        use num_traits::ToPrimitive;
34
35        let p = mu / N.to_f64().unwrap();
36        BinDist::new(p, N.into()).unwrap()
37    }
38}
39
40impl<const N: BinDom> Glm for Binomial<N> {
41    /// Only the canonical link function is available for binomial regression.
42    type Link = link::Logit;
43    const DISPERSED: DispersionType = DispersionType::NoDispersion;
44
45    /// The log-partition function for the binomial distribution is similar to
46    /// that for logistic regression, but it is adjusted for the maximum value.
47    fn log_partition<F: Float>(nat_par: F) -> F {
48        let n: F = F::from(N).unwrap();
49        n * num_traits::Float::exp(nat_par).ln_1p()
50    }
51
52    fn variance<F: Float>(mean: F) -> F {
53        let n_float: F = F::from(N).unwrap();
54        mean * (n_float - mean) / n_float
55    }
56
57    fn log_like_sat<F: Float>(y: F) -> F {
58        let n: F = F::from(N).unwrap();
59        prod_log(y) + prod_log(n - y) - prod_log(n)
60    }
61}
62
63pub mod link {
64    use super::*;
65    use crate::link::{Canonical, Link};
66    use num_traits::Float;
67
68    pub struct Logit {}
69    impl Canonical for Logit {}
70    impl<const N: BinDom> Link<Binomial<N>> for Logit {
71        fn func<F: Float>(y: F) -> F {
72            let n_float: F = F::from(N).unwrap();
73            Float::ln(y / (n_float - y))
74        }
75        fn func_inv<F: Float>(lin_pred: F) -> F {
76            let n_float: F = F::from(N).unwrap();
77            n_float / (F::one() + (-lin_pred).exp())
78        }
79    }
80}
81
82#[cfg(test)]
83mod tests {
84    use super::Binomial;
85    use crate::{error::RegressionResult, model::ModelBuilder};
86    use approx::assert_abs_diff_eq;
87    use ndarray::array;
88
89    #[test]
90    fn bin_reg() -> RegressionResult<(), f64> {
91        const N: u16 = 12;
92        let ln2 = f64::ln(2.);
93        let beta = array![0., 1.];
94        let data_x = array![[0.], [0.], [ln2], [ln2], [ln2]];
95        // the first two data points should average to 6 and the last 3 should average to 8.
96        let data_y = array![5, 7, 9, 6, 9];
97        let model = ModelBuilder::<Binomial<N>>::data(&data_y, &data_x).build()?;
98        let fit = model.fit()?;
99        dbg!(&fit.result);
100        dbg!(&fit.n_iter);
101        assert_abs_diff_eq!(beta, fit.result, epsilon = 0.05 * f32::EPSILON as f64);
102        Ok(())
103    }
104}
ndarray_glm/response/binomial.rs

ndarray_glm/response/
binomial.rs
