# \[Feature\] Chained linear regression

**URL:** <https://discuss.hail.is/t/feature-chained-linear-regression/726>\
**Category:** Updates\
**Created:** [October 26, 2018, 1:43am UTC](https://discuss.hail.is/t/feature-chained-linear-regression/726 "2018-10-26T01:43:05Z")\
**Posts on this page:** 1\
**Page:** 1

<div class="post-metadata">

**Author:** ![tpoterba](https://yyz2.discourse-cdn.com/flex036/user_avatar/discuss.hail.is/tpoterba/32/61_2.png) [@tpoterba](https://discuss.hail.is/u/tpoterba)\
**Post date:** [October 26, 2018, 1:43am UTC](https://discuss.hail.is/t/feature-chained-linear-regression/726/1 "2018-10-26T01:43:06Z")

</div>

We’ve added a new capability to [`linear_regression_rows`](https://hail.is/docs/0.2/methods/stats.html#hail.methods.linear_regression_rows): the ability to run multiple regressions with different missingness patterns with one call to the function.

The old (and preserved!) behavior is that passing a list of phenotypes to [`linear_regression_rows`](https://hail.is/docs/0.2/methods/stats.html#hail.methods.linear_regression_rows) will fit the phenotypes in parallel, but **with the caveat that the samples used are the ones for which all phenotypes and covariates are non-missing** , i.e. the “intersection” of samples.

For example, if `pheno1` and `pheno2` are such that no sample has both `pheno1` and `pheno2` defined, then the following code will drop all samples and fail.

```python
result = hl.linear_regression_rows(
    y=[mt.pheno1, mt.pheno2],
    x=mt.GT.n_alt_alleles(),
    covariates=[1, mt.cov1])

```

The **new behavior** is that it is now possible to pass a list of lists (i.e., groups) as the `y` parameter. Each group of phenotypes is run on the intersection of samples as above, but distinct groups are considered independently with respect to sample missing-ness. For example, the following code will instead regress each phenotype on the subset of samples for which that phenotype (alone) and all covariates are defined:

```python
result = hl.linear_regression_rows(
    y=[[mt.pheno1], [mt.pheno2]],
    x=mt.GT.n_alt_alleles(),
    covariates=[1, mt.cov1])

```

Here’s a more interesting example that computes, for a group of phenotypes, the result of linear regression for each phenotype on the intersection of samples overall, as well as results stratified by sex:

```python
phenos = [mt.pheno1, mt.pheno2, mt.pheno3, ...]
male_only = [hl.case().when(~mt.is_female, pheno).or_missing() for pheno in phenos]
female_only = [hl.case().when(mt.is_female, pheno).or_missing() for pheno in phenos]

result = hl.linear_regression_rows(
    y=[phenos, male_only, female_only],
    x=mt.GT.n_alt_alleles(),
    covariates=[1, mt.cov1])

```