This routine provides the value of the Likelihood-Ratio-Test Statistics and the corresponding p-value for evaluating the several sample Dirichlet-Multinomial parameter test comparison.
Xdc.sevsample(group.data, epsilon = 10^(-4), est = "mom")A list where each element is a matrix of taxonomic counts(columns) for each sample(rows). (See Notes 1 and 2 in details)
Convergence tolerance. To terminate, the difference between two succeeding log-likelihoods must be smaller than epsilon. Default value is 10^(-4).
The type of parameter estimator to be used with the Likelihood-ratio-test statistics, 'mle' or 'mom'. Default value is 'mom'. (See Note 3 in details)
A list containing the Xdc statistics and p-value.
To assess whether the Dirichlet parameter vector, \(\mathbf{\alpha}_{\mathrm{m}}=\mathbf{\pi}_{\mathrm{m}} \frac{1-\theta_{\mathrm{m}}}{\theta_{\mathrm{m}}}\)(a function of the RAD probability-mean vector and overdispersion), observed in \(J\) groups of microbiome samples are equal to each other, the following hypothesis \(\mathrm{H}_{\mathrm{o}}: \mathbf{\alpha}_{\mathrm{1}} = \cdots =\mathbf{\alpha}_{\mathrm{m}}=\cdots= \mathbf{\alpha}_{\mathrm{J}}=\mathbf{\alpha}_{\mathrm{o}}\) versus \(\mathrm{H}_{\mathrm{a}}: \mathbf{\alpha}_{\mathrm{m}} \ne \mathbf{\alpha}_{\mathrm{o}}, m=1, \ldots, J\) can be tested. The null hypothesis implies that the HMP samples across groups have the same mean and overdispersion, indicating that the RAD models are identical. In particular, the likelihood-ratio test statistic is used, which is given by, $$x_{\mathrm{dc}}=-2 \log\left\{\frac{L\left(\mathbf{\alpha}_{\mathrm{o}}; \mathbf{X}_{\mathrm{1}},\ldots, \mathbf{X}_{\mathrm{J}} \right)}{L\left(\mathbf{\alpha}_{\mathrm{1}},\ldots,\mathbf{\alpha}_{\mathrm{J}}; \mathbf{X}_{\mathrm{1}},\ldots, \mathbf{X}_{\mathrm{J}} \right)}\right\}.$$ The asymptotic null distribution of \(x_{\mathrm{dc}}\) follows a Chi-square with degrees of freedom equal to (J-1)*K, where K is the number of taxa (Wilks, 1938).
Note 1: The matrices in group.data must contain the same taxa, in the same order.
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.
Note 3: 'mle' will take significantly longer time and may not be optimal for small sample sizes; 'mom' will provide more conservative results in such a case.
Wilks, S. S. (1938). The Large-Sample Distribution of the Likelihood Ratio for Testing Composite Hypotheses. The Annals of Mathematical Statistics 9, 60-62.
# NOT RUN {
data(saliva)
data(throat)
### Combine the data sets into a single list
group.data <- list(saliva, throat)
xdc <- Xdc.sevsample(group.data)
xdc
# }
Run the code above in your browser using DataLab