# weitrix_sd_confects: Find rows with confidently excessive variability in a... In weitrix: Tools for matrices with precision weights, test and explore weighted or sparse data

## Description

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.

## Usage

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

## Arguments

 `weitrix` A weitrix object, or an object that can be converted to a weitrix with `as_weitrix`. `design` A formula in terms of `colData(weitrix` or a design matrix, which will be fitted to the weitrix on each row. Can also be a pre-existing Components object, in which case the existing fits (`design\$row`) are used. `fdr` False Discovery Rate to control for. `step` Granularity of effect sizes to test.

## Details

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.

## Value

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.

## Examples

 ```1 2 3 4``` ```# weitrix_sd_confects should only be used with a calibrated weitrix calwei <- weitrix_calibrate_all(simwei, ~1, ~1) weitrix_sd_confects(calwei, ~1) ```

weitrix documentation built on Nov. 8, 2020, 8:10 p.m.