# Simulate data from a Poisson mixture model

### Description

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).

### Usage

1 | ```
PoisMixSim(n = 2000, libsize, separation)
``` |

### Arguments

`n` |
Number of observations |

`libsize` |
The type of library size difference to be simulated (“ |

`separation` |
Cluster separation (“ |

### Value

`y ` |
( |

`labels ` |
Vector of length |

`pi ` |
Vector of length 4 (the number of clusters) containing the true value of |

`lambda ` |
( |

`w ` |
Row sums of |

`conditions ` |
Vector of length |

### 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 *∑_k λ_{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 *∑_j ∑_l λ_{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{λ}* as obtained from the `PoisMixClus`

function.

### Author(s)

Andrea Rau <andrea.rau@jouy.inra.fr>

### 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 http://hal.inria.fr/inria-00638082.

### Examples

1 2 3 4 5 6 7 8 9 | ```
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
``` |

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