Xoc.sevsample {HMP}

Likelihood-Ratio-Test Statistics: Several Sample Overdispersion Test Comparison

Description

This routine provides the value of the likelihood-ratio-test statistic and the corresponding p-value to assess whether the overdispersion observed in multiple groups of microbiome samples are equal.

Usage

Xoc.sevsample(group.data, epsilon = 10^(-4))

Arguments

group.data

A list where each element is a matrix of taxonomic counts(columns) for each sample(rows). (See Notes 1 and 2 in details)

epsilon

Convergence tolerance. To terminate, the difference between two succeeding log-likelihoods must be smaller than epsilon. Default value is 10^(-4).

Details

To assess whether the over dispersion parameter vectors \theta_{\mathrm{m}} observed in J groups of microbiome samples are equal to each other, the following hypothesis \mathrm{H}_{\mathrm{o}}: \theta_{\mathrm{1}} = \cdots =\theta_{\mathrm{m}} =\cdots=\theta_{\mathrm{J}}=\theta_{\mathrm{o}} versus \mathrm{H}_{\mathrm{a}}: \theta_{\mathrm{m}} \ne \theta_{\mathrm{o}}, m=1, \ldots, J can be tested. In particular, the likelihood-ratio test statistic is used (Tvedebrink, 2010), which is given by,

x_{\mathrm{oc}}=-2 \log\left\{\frac{L\left(\theta_{\mathrm{o}}; \mathbf{X}_{\mathrm{1}},\ldots, \mathbf{X}_{\mathrm{J}} \right)}{L\left(\theta_{\mathrm{1}},\ldots, \theta_{\mathrm{J}}; \mathbf{X}_{\mathrm{1}},\ldots, \mathbf{X}_{\mathrm{J}} \right)}\right\} .

The asymptotic null distribution of x_{\mathrm{oc}} follows a Chi-square with degrees of freedom equal to (J-1) (Wilks, 1938).

1. Note 1: The matrices in group.data must contain the same taxa, in the same order.

2. Note 2: Each taxa should be present in at least 1 sample, a column with all 0's may result in errors and/or invalid results.

Value

A list containing the Xoc statistics and p-value.

References

Tvedebrink, T. (2010). Overdispersion in allelic counts and theta-correction in forensic genetics. Theor Popul Biol 78, 200-210.
Wilks, S. S. (1938). The Large-Sample Distribution of the Likelihood Ratio for Testing Composite Hypotheses. The Annals of Mathematical Statistics 9, 60-62.

Examples

	data(saliva) 
	data(tonsils)
	
	### Combine the data sets into a single list
	group.data <- list(saliva, tonsils)
	
	## Not run: 
		xoc <- Xoc.sevsample(group.data)
		xoc
	
## End(Not run)