PoisMixSim function

Simulate data from a Poisson mixture model

This function simulates data from a Poisson mixture model, as described by Rau et al. (2011). Data are simulated with varying expression level ($w_i$) for 4 clusters. Clusters may be simulated with high or low separation, and three different options are available for the library size setting: equal , A , and B , as described by Rau et al. (2011).

PoisMixSim(n = 2000, libsize, separation)

Arguments

• n: Number of observations
• libsize: The type of library size difference to be simulated (‘equal’ , ‘A’ , or ‘B’ , as described by Rau et al. (2011))
• separation: Cluster separation (‘high’ or ‘low’ , as described by Rau et al. (2011))

Returns

• y: (n x q) matrix of simulated counts for n observations and q variables

• labels: Vector of length n defining the true cluster labels of the simulated data

• pi: Vector of length 4 (the number of clusters) containing the true value of $\pi$

• lambda: (d x 4) matrix of $\lambda$ values for d conditions (3 in the case of libsize = ‘equal’ or ‘A’ , and 2 otherwise) in 4 clusters (see note below)

• w: Row sums of y (estimate of $\hat{w}$)

• conditions: Vector of length q defining the condition (treatment group) for each variable (column) in y

References

Rau, A., Celeux, G., Martin-Magniette, M.-L., Maugis-Rabusseau, C. (2011). Clustering high-throughput sequencing data with Poisson mixture models. Inria Research Report 7786. Available at https://inria.hal.science/inria-00638082.

Author(s)

Andrea Rau

Note

If one or more observations are simulated such that all variables have a value of 0, those rows are removed from the data matrix; as such, in some cases the simulated data y may have less than n rows.

The PMM-I model includes the parameter constraint $\sum_k \lambda_{jk} r_j = 1$, where $r_j$ is the number of replicates in condition (treatment group) $j$. Similarly, the parameter constraint in the PMM-II model is $\sum_j \sum_l \lambda_{jk}s_{jl} = 1$, where $s_{jl}$ is the library size for replicate l of condition j. The value of lambda corresponds to that used to generate the simulated data, where the library sizes were set as described in Table 2 of Rau et al. (2011). However, due to variability in the simulation process, the actually library sizes of the data y are not exactly equal to these values; this means that the value of lambda may not be directly compared to an estimated value of $\hat{\lambda}$ as obtained from the PoisMixClus function.

Examples

set.seed(12345)

## Simulate data as shown in Rau et al. (2011)
## Library size setting "A", high cluster separation
## n = 200 observations

simulate <- PoisMixSim(n = 200, libsize = "A", separation = "high")
y <- simulate$y
conds <- simulate$conditions