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

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

	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.