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Weighted Two-Way (Tukey) Decomposition of Log Odds Ratios

Source: R/woolf_twoway.R
woolf_twoway.Rd

For a \(2 \times 2 \times R \times C\) table, computes an additive row + column decomposition of the stratum log odds ratios tested by woolf_test(), following Tukey's two-way ("median polish"-style) fit as implemented in the twoway package.

Usage

woolf_twoway(
  x,
  weighted = TRUE,
  name = deparse(substitute(x)),
  responseName = "log odds ratio",
  varNames = NULL
)

Arguments

x

A \(2 \times 2 \times R \times C\) array, as used by woolf_test().

weighted

Logical. If TRUE (the default), fit by weighted least squares using Woolf inverse-variance weights. If FALSE, fit an ordinary (unweighted) Tukey mean-polish via twoway::twoway().

name

A label for the data, used in the print/plot titles. Defaults to the deparsed expression passed as x.

responseName

Label for the response (log odds ratio) axis.

varNames

Character vector of length 2 giving row/column variable names. Defaults to the strata variable names from x's dimnames.

Value

An object of class "twoway" (see twoway::twoway()), with components overall, roweff, coleff, residuals, name, rownames, colnames, method, responseName, varNames, compValue, slope, and power. The weighted fit additionally includes weights (the Woolf weights used) and fit (the underlying lm object).

Details

Unlike twoway::twoway(), which weights every stratum equally, woolf_twoway() weights each stratum's log odds ratio by its inverse variance (the Woolf weight), so that strata with more precise log odds ratios contribute more to the fitted row and column effects.

twoway::twoway() has no weight argument, so the additive model \(y_{ij} = \mu + \alpha_i + \beta_j + \epsilon_{ij}\) is instead fit directly by weighted least squares (stats::lm() with weights = w and sum-to-zero contrasts), where \(y_{ij}\) is the log odds ratio and \(w_{ij}\) its inverse variance in stratum \((i,j)\), exactly as used internally by woolf_test(). The resulting fit is repackaged as an object of class "twoway", so that print.twoway() and plot.twoway() from twoway (which = "fit" or "diagnose") work on it unchanged.

Set weighted = FALSE to instead get the ordinary (unweighted) Tukey mean-polish fit, via twoway::twoway() directly, for comparison.

This is a purely descriptive decomposition: it does not attempt to partition the woolf_test() homogeneity statistic itself (see issues/woolf.md for why a naive row/column/residual split of that statistic is not generally valid). It is intended for visualizing how the log odds ratio varies additively (or not) across the row and column stratifying variables.

See also

woolf_test(), twoway::twoway(), twoway::plot.twoway()

Other association tests: CMHtest(), GKgamma(), HLtest(), breslow_day_test(), woolf_test(), zero.test()

Examples

if (requireNamespace("twoway", quietly = TRUE)) {
  data(Fungicide, package = "vcdExtra")

  tw <- woolf_twoway(Fungicide)
  print(tw)
  plot(tw, which = "fit")
  plot(tw, which = "diagnose")

  # compare with the unweighted (plain mean-polish) decomposition
  tw0 <- woolf_twoway(Fungicide, weighted = FALSE)
  rbind(mean = tw0$roweff, Woolf = tw$roweff)
  rbind(mean = tw0$coleff, Woolf = tw$coleff)
}
#> 
#> Initial data (Dataset: "Fungicide"; Response: log odds ratio)
#> Residuals bordered by row effects, column effects, and overall
#> 
#>         strain
#> sex        1          2            roweff    
#>          + ---------- ---------- + ----------
#>   M      | -0.0024449  0.0019400 : -0.1015887
#>   F      |  0.0040983 -0.0063370 :  0.1015887
#>          + .......... .......... + ..........
#>   coleff | -0.3824757  0.3824757 : -1.1095056
#> 


#> Slope of Residual on comparison value:  0.1 
#> Suggested power transformation:         0.9 
#> Ladder of powers transformation:        no transformation 
#>                1         2
#> mean  -0.3809631 0.3809631
#> Woolf -0.3824757 0.3824757