weitrix_sd_confects | R Documentation |

Find rows with confident excess standard deviation beyond what is expected based on the weights of a calibrated weitrix. This may be used, for example, to find potential marker genes.

```
weitrix_sd_confects(
weitrix,
design = ~1,
fdr = 0.05,
step = 0.001,
assume_normal = TRUE
)
```

`weitrix` |
A weitrix object, or an object that can be converted to a weitrix
with |

`design` |
A formula in terms of |

`fdr` |
False Discovery Rate to control for. |

`step` |
Granularity of effect sizes to test. |

`assume_normal` |
Assume weighted residuals are normally distributed? Assumption of normality is quite a strong assemption here. If TRUE, tests are based on the weighted squared residuals following a chi-squared distribution. If FALSE, tests are based on assuming the dispersion follows an asymptotically normal distribution, with variance estimated from the weighted squared residuals. If FALSE, a reasonably large number of columns is required. Defaults to TRUE. |

Important note: With the default setting of `assume_normal=TRUE`

, the "confect" values produced by this method are only valid if the weighted residuals are close to normally distributed. If you have a reasonably large number of columns (eg single cell data), you can and should relax this assumption by specifying `assume_normal=FALSE`

.

This is a conversion of the "dispersion" statistic for each row into units that are more readily interpretable, accompanied by confidence bounds with a multiple testing correction.

We are looking for further perturbation of observed values beyond what is accounted for by a linear model and, further, beyond what is expected based on the observation weights (assumed to be calibrated and so interpreted as 1/variance). We are seeking to estimate the standard deviation of this further perturbation.

The weitrix must have been calibrated for results to make sense.

Top confident effect sizes are found using the `topconfects`

method, based on the model that the observed weighted sum of squared residuals being non-central chi-square distributed.

Note that all calculations are based on weighted residuals, with a rescaling to place results on the original scale. When a row has highly variable weights, this is an approximation that is only sensible if the weights are unrelated to the values themselves.

A topconfects result. The `$table`

data frame contains columns:

effect Estimated excess standard deviation, in the same units as the observations themselves. 0 if the dispersion is less than 1.

confect A lower confidence bound on effect.

row_mean Weighted mean of observations in this row.

typical_obs_err Typical accuracy of each observation.

dispersion Dispersion. Weighted sum of squared residuals divided by residual degrees of freedom.

n_present Number of observations with non-zero weight.

df Degrees of freedom. n minus the number of coefficients in the model.

fdr_zero FDR-adjusted p-value for the null hypothesis that effect is zero.

Note that `dispersion = effect^2/typical_obs_err^2 + 1`

for non-zero effect values.

```
# weitrix_sd_confects should only be used with a calibrated weitrix
calwei <- weitrix_calibrate_all(simwei, ~1, ~1)
weitrix_sd_confects(calwei, ~1)
```

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