# ---------------------------------------------------------------------------- # Copyright (c) 2013--, scikit-bio development team. # # Distributed under the terms of the Modified BSD License. # # The full license is in the file COPYING.txt, distributed with this software. # ---------------------------------------------------------------------------- from functools import partial import numpy as np import pandas as pd from scipy.stats import f_oneway from scipy.spatial.distance import cdist import hdmedians as hd from ._base import (_preprocess_input_sng, _run_monte_carlo_stats, _build_results, DistanceMatrix) from skbio.stats.ordination import pcoa, OrdinationResults from skbio.util._decorator import experimental @experimental(as_of="0.5.2") def permdisp(distance_matrix, grouping, column=None, test='median', permutations=999, method="eigh", number_of_dimensions=10): """Test for Homogeneity of Multivariate Groups Disperisons using Marti Anderson's PERMDISP2 procedure. PERMDISP is a multivariate analogue of Levene's test for homogeneity of multivariate variances. Distances are handled by reducing the original distances to principal coordinates. PERMDISP calculates an F-statistic to assess whether the dispersions between groups is significant Parameters ---------- distance_matrix : DistanceMatrix or OrdinationResults Distance matrix containing distances between objects (e.g., distances between samples of microbial communities) or result of pcoa on such a matrix. grouping : 1-D array_like or pandas.DataFrame Vector indicating the assignment of objects to groups. For example, these could be strings or integers denoting which group an object belongs to. If `grouping` is 1-D ``array_like``, it must be the same length and in the same order as the objects in `distance_matrix`. If `grouping` is a ``DataFrame``, the column specified by `column` will be used as the grouping vector. The ``DataFrame`` must be indexed by the IDs in `distance_matrix` (i.e., the row labels must be distance matrix IDs), but the order of IDs between `distance_matrix` and the ``DataFrame`` need not be the same. All IDs in the distance matrix must be present in the ``DataFrame``. Extra IDs in the ``DataFrame`` are allowed (they are ignored in the calculations). column : str, optional Column name to use as the grouping vector if `grouping` is a ``DataFrame``. Must be provided if `grouping` is a ``DataFrame``. Cannot be provided if `grouping` is 1-D ``array_like``. test : {'centroid', 'median'} determines whether the analysis is done using centroid or spaitial median. permutations : int, optional Number of permutations to use when assessing statistical significance. Must be greater than or equal to zero. If zero, statistical significance calculations will be skipped and the p-value will be ``np.nan``. method : str, optional Eigendecomposition method to use in performing PCoA. By default, uses SciPy's `eigh`, which computes exact eigenvectors and eigenvalues for all dimensions. The alternate method, `fsvd`, uses faster heuristic eigendecomposition but loses accuracy. The magnitude of accuracy lost is dependent on dataset. Note that using `fsvd` is still considered experimental and should be used with care. Not used if distance_matrix is a OrdinationResults object. number_of_dimensions : int, optional Dimensions to reduce the distance matrix to if using the `fsvd` method. Not used if the `eigh` method is being selected. Returns ------- pandas.Series Results of the statistical test, including ``test statistic`` and ``p-value``. Raises ------ TypeError If, when using the spatial median test, the pcoa ordination is not of type np.float32 or np.float64, the spatial median function will fail and the centroid test should be used instead ValueError If the test is not centroid or median, or if method is not eigh or fsvd TypeError If the distance matrix is not an instance of a ``skbio.DistanceMatrix``. ValueError If there is only one group ValueError If a list and a column name are both provided ValueError If a list is provided for `grouping` and it's length does not match the number of ids in distance_matrix ValueError If all of the values in the grouping vector are unique KeyError If there are ids in grouping that are not in distance_matrix See Also -------- permanova anosim Notes ----- The significance of the results from this function will be the same as the results found in vegan's betadisper, however due to floating point variability the F-statistic results may vary slightly. See [1]_ for the original method reference, as well as ``vegan::betadisper``, available in R's vegan package [2]_. References ---------- .. [1] Anderson, Marti J. "Distance-Based Tests for Homogeneity of Multivariate Dispersions." Biometrics 62 (2006):245-253 .. [2] http://cran.r-project.org/web/packages/vegan/index.html Examples -------- Load a 6x6 distance matrix and grouping vector denoting 2 groups of objects: >>> from skbio import DistanceMatrix >>> dm = DistanceMatrix([[0, 0.5, 0.75, 1, 0.66, 0.33], ... [0.5, 0, 0.25, 0.33, 0.77, 0.61], ... [0.75, 0.25, 0, 0.1, 0.44, 0.55], ... [1, 0.33, 0.1, 0, 0.75, 0.88], ... [0.66, 0.77, 0.44, 0.75, 0, 0.77], ... [0.33, 0.61, 0.55, 0.88, 0.77, 0]], ... ['s1', 's2', 's3', 's4', 's5', 's6']) >>> grouping = ['G1', 'G1', 'G1', 'G2', 'G2', 'G2'] Run PERMDISP using 99 permutations to caluculate the p-value: >>> from skbio.stats.distance import permdisp >>> import numpy as np >>> #make output deterministic, should not be included during normal use >>> np.random.seed(0) >>> permdisp(dm, grouping, permutations=99) method name PERMDISP test statistic name F-value sample size 6 number of groups 2 test statistic ... 1.03... p-value ... number of permutations 99 Name: PERMDISP results, dtype: object The return value is a ``pandas.Series`` object containing the results of the statistical test. To suppress calculation of the p-value and only obtain the F statistic, specify zero permutations: >>> permdisp(dm, grouping, permutations=0) method name PERMDISP test statistic name F-value sample size 6 number of groups 2 test statistic ... 1.03... p-value NaN number of permutations 0 Name: PERMDISP results, dtype: object PERMDISP computes variances based on two types of tests, using either centroids or spatial medians, also commonly referred to as a geometric median. The spatial median is thought to yield a more robust test statistic, and this test is used by default. Spatial medians are computed using an iterative algorithm to find the optimally minimum point from all other points in a group while centroids are computed using a deterministic formula. As such the two different tests yeild slightly different F statistics. >>> np.random.seed(0) >>> permdisp(dm, grouping, test='centroid', permutations=6) method name PERMDISP test statistic name F-value sample size 6 number of groups 2 test statistic ... 3.67... p-value ... 0.42... number of permutations 6 Name: PERMDISP results, dtype: object You can also provide a ``pandas.DataFrame`` and a column denoting the grouping instead of a grouping vector. The following DataFrame's Grouping column specifies the same grouping as the vector we used in the previous examples.: >>> import pandas as pd >>> df = pd.DataFrame.from_dict( ... {'Grouping': {'s1': 'G1', 's2': 'G1', 's3': 'G1', 's4': 'G2', ... 's5': 'G2', 's6': 'G2'}}) >>> permdisp(dm, df, 'Grouping', permutations=6, test='centroid') method name PERMDISP test statistic name F-value sample size 6 number of groups 2 test statistic ... 3.67... p-value ... 0.42... number of permutations 6 Name: PERMDISP results, dtype: object Note that when providing a ``DataFrame``, the ordering of rows and/or columns does not affect the grouping vector that is extracted. The ``DataFrame`` must be indexed by the distance matrix IDs (i.e., the row labels must be distance matrix IDs). If IDs (rows) are present in the ``DataFrame`` but not in the distance matrix, they are ignored. The previous example's ``s7`` ID illustrates this behavior: note that even though the ``DataFrame`` had 7 objects, only 6 were used in the test (see the "Sample size" row in the results above to confirm this). Thus, the ``DataFrame`` can be a superset of the distance matrix IDs. Note that the reverse is not true: IDs in the distance matrix *must* be present in the ``DataFrame`` or an error will be raised. PERMDISP should be used to determine whether the dispersions between the groups in your distance matrix are significantly separated. A non-significant test result indicates that group dispersions are similar to each other. PERMANOVA or ANOSIM should then be used in conjunction to determine whether clustering within groups is significant. """ if test not in ['centroid', 'median']: raise ValueError('Test must be centroid or median') if isinstance(distance_matrix, OrdinationResults): ordination = distance_matrix ids = ordination.samples.axes[0].to_list() sample_size = len(ids) distance_matrix = None # not used anymore, avoid using by mistake elif isinstance(distance_matrix, DistanceMatrix): if method == "eigh": # eigh does not natively support specifying number_of_dimensions # and pcoa expects it to be 0 number_of_dimensions = 0 elif method != "fsvd": raise ValueError('Method must be eigh or fsvd') ids = distance_matrix.ids sample_size = distance_matrix.shape[0] ordination = pcoa(distance_matrix, method=method, number_of_dimensions=number_of_dimensions) else: raise TypeError("Input must be a DistanceMatrix or OrdinationResults.") samples = ordination.samples num_groups, grouping = _preprocess_input_sng( ids, sample_size, grouping, column) test_stat_function = partial(_compute_groups, samples, test) stat, p_value = _run_monte_carlo_stats(test_stat_function, grouping, permutations) return _build_results('PERMDISP', 'F-value', sample_size, num_groups, stat, p_value, permutations) def _compute_groups(samples, test_type, grouping): groups = [] samples['grouping'] = grouping if test_type == 'centroid': centroids = samples.groupby('grouping').aggregate('mean') elif test_type == 'median': centroids = samples.groupby('grouping').apply(_config_med) for label, df in samples.groupby('grouping'): groups.append(cdist(df.values[:, :-1].astype('float64'), [centroids.loc[label].values], metric='euclidean')) stat, _ = f_oneway(*groups) stat = stat[0] return stat def _config_med(x): """ slice the vector up to the last value to exclude grouping column and transpose the vector to be compatible with hd.geomedian """ X = x.values[:, :-1] return pd.Series(np.array(hd.geomedian(X.T)), index=x.columns[:-1])