gneiss.regression.mixedlm

gneiss.regression.mixedlm(formula, table, metadata, groups, **kwargs)[source]

Linear Mixed Effects Models applied to balances.

Linear mixed effects (LME) models is a method for estimating parameters in a linear regression model with mixed effects. LME models are commonly used for repeated measures, where multiple samples are collected from a single source. This implementation is focused on performing a multivariate response regression with mixed effects where the response is a matrix of balances (table), the covariates (metadata) are made up of external variables and the samples sources are specified by groups.

T-statistics (tvalues) and p-values (pvalues) can be obtained to investigate to evaluate statistical significance for a covariate for a given balance. Predictions on the resulting model can be made using (predict), and these results can be interpreted as either balances or proportions.

Parameters:
  • formula (str) – Formula representing the statistical equation to be evaluated. These strings are similar to how equations are handled in R. Note that the dependent variable in this string should not be specified, since this method will be run on each of the individual balances. See patsy [1] for more details.
  • table (pd.DataFrame) – Contingency table where samples correspond to rows and balances correspond to columns.
  • metadata (pd.DataFrame) – Metadata table that contains information about the samples contained in the table object. Samples correspond to rows and covariates correspond to columns.
  • groups (str) – Column name in metadata that specifies the groups. These groups are often associated with individuals repeatedly sampled, typically longitudinally.
  • **kwargs (dict) – Other arguments accepted into statsmodels.regression.linear_model.MixedLM
Returns:

Container object that holds information about the overall fit. This includes information about coefficients, pvalues and residuals from the resulting regression.
Return type:

LMEModel

References

[1]https://patsy.readthedocs.io/en/latest/

Examples

>>> import pandas as pd
>>> import numpy as np
>>> from gneiss.regression import mixedlm

Here, we will define a table of balances with features Y1, Y2 across 12 samples.

>>> table = pd.DataFrame({
...   'u1': [ 1.00000053,  6.09924644],
...   'u2': [ 0.99999843,  7.0000045 ],
...   'u3': [ 1.09999884,  8.08474053],
...   'x1': [ 1.09999758,  1.10000349],
...   'x2': [ 0.99999902,  2.00000027],
...   'x3': [ 1.09999862,  2.99998318],
...   'y1': [ 1.00000084,  2.10001257],
...   'y2': [ 0.9999991 ,  3.09998418],
...   'y3': [ 0.99999899,  3.9999742 ],
...   'z1': [ 1.10000124,  5.0001796 ],
...   'z2': [ 1.00000053,  6.09924644],
...   'z3': [ 1.10000173,  6.99693644]},
..     index=['Y1', 'Y2']).T

Now we are going to define some of the external variables to test for in the model. Here we will be testing a hypothetical longitudinal study across 3 time points, with 4 patients x, y, z and u, where x and y were given treatment 1 and z and u were given treatment 2.

>>> metadata = pd.DataFrame({
...         'patient': [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4],
...         'treatment': [1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2],
...         'time': [1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3]
...     }, index=['x1', 'x2', 'x3', 'y1', 'y2', 'y3',
...               'z1', 'z2', 'z3', 'u1', 'u2', 'u3'])

Now we can run the linear mixed effects model on the balances. Underneath the hood, the proportions will be transformed into balances, so that the linear mixed effects models can be run directly on balances. Since each patient was sampled repeatedly, we’ll specify them separately in the groups. In the linear mixed effects model time and treatment will be simultaneously tested for with respect to the balances.

>>> res = mixedlm('time + treatment', table, metadata, tree,
...               groups='patient')

See also

statsmodels.regression.linear_model.MixedLM(), ols()