# DM.MoM: Method-of-Moments (MoM) Estimators of the... In HMP: Hypothesis Testing and Power Calculations for Comparing Metagenomic Samples from HMP

## Description

Method-of-Moments (MoM) estimators of the Dirichlet-multinomial parameters: taxa proportions and overdispersion.

## Usage

 1 DM.MoM(data) 

## Arguments

 data A matrix of taxonomic counts(columns) for each sample(rows).

## Details

Given a set of taxa-count vectors ≤ft\{\textbf{x}_{i},…, \textbf{x}_{P} \right\}, the methods of moments (MoM) estimator of the set of parameters θ and ≤ft\{π_{j} \right\}_{j=1}^K is given as follows (Mosimann, 1962; Tvedebrink, 2010):

\hat{π}_{j}=\frac{∑_{i=1}^P x_{ij}}{∑_{i=1}^P N_{i}},

and

\hat{θ} = ∑_{j=1}^K \frac{S_{j}-G_{j}}{∑_{j=1}^{K}≤ft ( S_{j}+≤ft ( N_{c}-1 \right )G_{j} \right )},

where N_{c}=≤ft( P -1 \right)^{-1} ≤ft(∑_{i=1}^P N_{i}-≤ft (∑_{i=1}^P N_{i} \right )^{-1} ∑_{i=1}^P N_{i}^2\right), and S_{j}=≤ft( P -1 \right)^{-1} ∑_{i=1}^P N_{i} ≤ft ( \hat{π}_{ij} -\hat{π}_{j} \right )^{2}, and G_{j}=≤ft( ∑_{i=1}^P ≤ft (N_i-1 \right ) \right)^{-1} ∑_{i=1}^P N_{i} \hat{π}_{ij} ≤ft (1- \hat{π}_{ij}\right) with \hat{π}_{ij}=\frac{x_{ij}}{N_{i}}.

## Value

A list providing the MoM estimator for overdispersion, the MoM estimator of the RAD-probability mean vector, and the corresponding loglikelihood value for the given data set and estimated parameters.

## References

Mosimann, J. E. (1962). On the compound multinomial distribution, the multivariate β-distribution, and correlations among proportions. Biometrika 49, 65-82.
Tvedebrink, T. (2010). Overdispersion in allelic counts and theta-correction in forensic genetics. Theor Popul Biol 78, 200-210.

## Examples

 1 2 3 4  data(throat) fit.throat <- DM.MoM(throat) fit.throat 

### Example output

Loading required package: dirmult

Attaching package: 'HMP'

The following object is masked from 'package:dirmult':

weirMoM

$loglik [1] -3237.232$gamma
Taxa 1     Taxa 2     Taxa 3     Taxa 4     Taxa 5     Taxa 6     Taxa 7
13.4057765  4.8653659  3.3937428  2.5327106  1.9077238  1.5488983  1.2693338
Taxa 8     Taxa 9    Taxa 10    Taxa 11    Taxa 12    Taxa 13    Taxa 14
1.0673755  0.8849429  0.7353565  0.6178715  0.5285995  0.4326259  0.3748762
Taxa 15    Taxa 16    Taxa 17    Taxa 18    Taxa 19    Taxa 20    Taxa 21
0.3211807  0.2730284  0.2257035  0.2014619  0.1885551  0.1696913  1.8453410

$pi Taxa 1 Taxa 2 Taxa 3 Taxa 4 Taxa 5 Taxa 6 0.364384825 0.132246385 0.092245935 0.068842063 0.051854184 0.042100884 Taxa 7 Taxa 8 Taxa 9 Taxa 10 Taxa 11 Taxa 12 0.034501990 0.029012526 0.024053793 0.019987856 0.016794477 0.014367958 Taxa 13 Taxa 14 Taxa 15 Taxa 16 Taxa 17 Taxa 18 0.011759282 0.010189579 0.008730069 0.007421234 0.006134887 0.005475971 Taxa 19 Taxa 20 Taxa 21 0.005125149 0.004612409 0.050158545$theta
[1] 0.02646191


HMP documentation built on Aug. 31, 2019, 5:05 p.m.