glm_gp_impl {glmGamPoi} | R Documentation

## Internal Function to Fit a Gamma-Poisson GLM

### Description

Internal Function to Fit a Gamma-Poisson GLM

### Usage

    glm_gp_impl(
      Y,
      model_matrix,
      offset = 0,
      size_factors = c("normed_sum", "deconvolution", "poscounts"),
      overdispersion = TRUE,
      overdispersion_shrinkage = TRUE,
      ridge_penalty = 0,
      do_cox_reid_adjustment = TRUE,
      subsample = FALSE,
      verbose = FALSE
    )

### Arguments

`Y` | any matrix-like object (e.g. `matrix()`, `DelayedArray()`, `HDF5Matrix()`) with one column per sample and row per gene.
`model_matrix` | a numeric matrix that specifies the experimental design. It can be produced using `stats::model.matrix()`. Default: `NULL`
`offset` | Constant offset in the model in addition to `log(size_factors)`. It can either be a single number, a vector of length `ncol(data)` or a matrix with the same dimensions as `dim(data)`. Note that if data is a DelayedArray or HDF5Matrix, `offset` must be as well. Default: `0`.
`size_factors` | in large scale experiments, each sample is typically of different size (for example different sequencing depths). A size factor is an internal mechanism of GLMs to correct for this effect. `size_factors` is either a numeric vector with positive entries that has the same lengths as columns in the data that specifies the size factors that are used. Or it can be a string that species the method that is used to estimate the size factors (one of `c("normed_sum", "deconvolution", "poscounts")`). Note that `"normed_sum"` and `"poscounts"` are fairly simple methods and can lead to suboptimal results. For the best performance, I recommend to use `size_factors = "deconvolution"` which calls `scran::calculateSumFactors()`. However, you need to separately install the `scran` package from Bioconductor for this method to work. Also note that `size_factors = 1` and `size_factors = FALSE` are equivalent. If only a single gene is given, no size factor is estimated (ie. `size_factors = 1`). Default: `"normed_sum"`.
`overdispersion` | the simplest count model is the Poisson model. However, the Poisson model assumes that variance = mean. For many applications this is too rigid and the Gamma-Poisson allows a more flexible mean-variance relation (variance = mean + mean^2 * overdispersion). `overdispersion` can either be a single boolean that indicates if an overdispersion is estimated for each gene. a numeric vector of length `nrow(data)` fixing the overdispersion to those values. the string `"global"` to indicate that one dispersion is fit across all genes. Note that `overdispersion = 0` and `overdispersion = FALSE` are equivalent and both reduce the Gamma-Poisson to the classical Poisson model. Default: `TRUE`.
`overdispersion_shrinkage` | the overdispersion can be difficult to estimate with few replicates. To improve the overdispersion estimates, we can share information across genes and shrink each individual overdispersion estimate towards a global overdispersion estimate. Empirical studies show however that the overdispersion varies based on the mean expression level (lower expression level => higher dispersion). If `overdispersion_shrinkage = TRUE`, a median trend of dispersion and expression level is fit and used to estimate the variances of a quasi Gamma Poisson model (Lund et al. 2012). Default: `TRUE`.
`ridge_penalty` | to avoid overfitting, we can penalize fits with large coefficient estimates. Instead of directly minimizing the deviance per gene (Sum dev(y_i, X_i b)), we will minimize Sum dev(y_i, X_i b) + N * Sum (penalty_p * b_p)^2. `ridge_penalty` can be a scalar in which case all parameters except the intercept are penalized. a vector which has to have the same length as columns in the model matrix a matrix with the same number of columns as columns in the model matrix. This gives maximum flexibility for expert users and allows for full Tikhonov regularization. Default: `ridge_penalty = 0`, which is internally replaced with a small positive number for numerical stability.
`do_cox_reid_adjustment` | the classical maximum likelihood estimator of the `overdisperion` is biased towards small values. McCarthy et al. (2012) showed that it is preferable to optimize the Cox-Reid adjusted profile likelihood. `do_cox_reid_adjustment` can be either be `TRUE` or `FALSE` to indicate if the adjustment is added during the optimization of the `overdispersion` parameter. Default: `TRUE`.
`subsample` | the estimation of the overdispersion is the slowest step when fitting a Gamma-Poisson GLM. For datasets with many samples, the estimation can be considerably sped up without loosing much precision by fitting the overdispersion only on a random subset of the samples. Default: `FALSE` which means that the data is not subsampled. If set to `TRUE`, at most 1,000 samples are considered. Otherwise the parameter just specifies the number of samples that are considered for each gene to estimate the overdispersion.
`verbose` | a boolean that indicates if information about the individual steps are printed while fitting the GLM. Default: `FALSE`.

### Value

a list with four elements

- `Beta` the coefficient matrix

- `overdispersion` the vector with the estimated overdispersions

- `Mu` a matrix with the corresponding means for each gene and sample

- `size_factors` a vector with the size factor for each sample

- `ridge_penalty` a vector with the ridge penalty

### See Also

`glm_gp()` and `overdispersion_mle()`

[Package glmGamPoi version 1.6.0 Index]