mrfrequentist {mrregression}

Fitting frequentist linear models using Merge and Reduce

Description

mrfrequentist is used to conduct frequentist linear regression on very large data sets using Merge and Reduce as described in Geppert et al. (2020).

Usage

mrfrequentist(
  formula,
  fileMr = NULL,
  dataMr = NULL,
  obsPerBlock,
  approach = c("1", "3"),
  sep = "auto",
  dec = ".",
  header = TRUE,
  naStrings = "NA",
  colNames = NULL,
  naAction = na.fail
)

Arguments

formula

(formula)
See formula. Note that mrfrequentist currently supports numeric predictors only.

fileMr

(character)
The name of a file, including the filepath, to be read in blockwise. Either fileMr or dataMr needs to be specified. When using this argument, the arguments sep, dec, header, naStrings, colNames (as in fread) are of relevance. Further options from fread are currently not supported. Also note that defaults might differ. In case the data to be read in has row names, note that these will be read in as regular column. This may need special treatment.

dataMr

(data.frame)
The data to be used for the regression analysis. Either fileMr or dataMr needs to be specified. Note that the arguments sep, dec, header, naStrings, and colNames are ignored when dataMr is specified.

obsPerBlock

(numeric)
Value specifying the number of observations in each block. This number has to be larger than the number of regression coefficients. Moreover, for approach 1 the recommended ratio of observations per regression coefficient is larger than 25 (Geppert et al., 2020). Note that the last block may contain less observations than specified depending on the sample size. If the number of observations in this last block is too small it is not included in the model and a warning is issued.

approach

(character)
Approach specifying the merge technique. One of either "1" or "3". Approach "1" is based on a weighted mean procedure whereas approach "3" is an exact method based on blockwise calculations of X'X, y'X and y'y. See Geppert et al. (2020) for details on the approaches and section Details below for comments on approach "3".

sep

See documentation of fread. Default is "auto". Ignored when dataMr is specified.

dec

See documentation of fread. Default is ".". Ignored when dataMr is specified.

header

(logical)
See documentation of fread. Defaults to TRUE. Ignored when dataMr is specified. If header is set to FALSE and no colNames are given, then column names default to "V" followed by the column number.

naStrings

(character)
Optional argument. See argument na.strings of fread. Default is "NA". Ignored when dataMr is specified and optional when fileMr is used.

colNames

(character vector)
Same as argument col.names of fread. Ignored when dataMr is specified and optional when fileMr is used.

naAction

(function)
Action to be taken when missing values are present in the data. Currently only na.fail is supported.

Value

Returns an object of class "mrfrequentist" which is a list containing the following components for both approaches "1" and "3":

approach

The approach used for merging the models. Either "1" or "3".

formula

The model's formula.

level

Number of level of the final model in Merge and Reduce. This is equal to \lceil \log_2{(\code{numberObs}/\code{obsPerBlock})} \rceil + 1 and corresponds to the number of buckets in Figure 1 of Geppert et al. (2020).

numberObs

The total number of observations.

summaryStats

Summary statistics reporting the estimated regression coefficients and their unbiased standard errors. Estimates are based on the merge technique as specified in the argument approach. For approach "1" the estimates of the standard errors are corrected dividing by \sqrt \lceil \code{numberObs / obsPerBlock} \rceil . For further details see Geppert et al. (2020). For approach "3" the unbiased estimates of the standard errors are given.

dataHead

First six rows of the data in the first block. This serves as a sanity check, especially when using the argument fileMr.

terms

Terms object.

Additionally for approach "3" only:

XTX

The final model's crossprod(X, X).

yTX

The final model's crossprod(y, X).

yTy

The final model's crossprod(y, y).

Details

In approach "3" the estimated regression coefficients and their unbiased standard errors are calculated via qr decompositions on X'X (as in speedlm with argument method = "qr"). Moreover, the merge step uses the same idea of blockwise addition for X'X, y'y and y'X as speedglm's updating procedure updateWithMoreData. Conceptually though, Merge and Reduce is not an updating algorithm as it merges models based on a comparable amount of data along a tree structure to obtain a final model.

References

Geppert, L.N., Ickstadt, K., Munteanu, A., & Sohler, C. (2020). Streaming statistical models via Merge & Reduce. International Journal of Data Science and Analytics, 1-17,
doi: https://doi.org/10.1007/s41060-020-00226-0

Examples

## run mrfrequentist() with dataMr
data(exampleData)
fit1 = mrfrequentist(dataMr = exampleData, approach = "1", obsPerBlock = 300,
formula = V11 ~ .)

## run mrfrequentist() with fileMr
filepath = system.file("extdata", "exampleFile.txt", package = "mrregression")
fit2 = mrfrequentist(fileMr = filepath, approach = "3", header = TRUE,
obsPerBlock = 100, formula = y ~ .)