Binned residuals for binomial logistic regression — binned

Check model quality of binomial logistic regression models.

Usage

binned_residuals(model, term = NULL, n_bins = NULL, ...)

Arguments

model: A glm-object with binomial-family.
term: Name of independent variable from x. If not NULL, average residuals for the categories of term are plotted; else, average residuals for the estimated probabilities of the response are plotted.
n_bins: Numeric, the number of bins to divide the data. If n_bins = NULL, the square root of the number of observations is taken.
...: Currently not used.

Value

A data frame representing the data that is mapped in the accompanying plot. In case all residuals are inside the error bounds, points are black. If some of the residuals are outside the error bounds (indicated by the grey-shaded area), blue points indicate residuals that are OK, while red points indicate model under- or over-fitting for the relevant range of estimated probabilities.

Details

Binned residual plots are achieved by “dividing the data into categories (bins) based on their fitted values, and then plotting the average residual versus the average fitted value for each bin.” (Gelman, Hill 2007: 97). If the model were true, one would expect about 95% of the residuals to fall inside the error bounds.

If term is not NULL, one can compare the residuals in relation to a specific model predictor. This may be helpful to check if a term would fit better when transformed, e.g. a rising and falling pattern of residuals along the x-axis is a signal to consider taking the logarithm of the predictor (cf. Gelman and Hill 2007, pp. 97-98).

Note

binned_residuals() returns a data frame, however, the print() method only returns a short summary of the result. The data frame itself is used for plotting. The plot() method, in turn, creates a ggplot-object.

References

Gelman, A., and Hill, J. (2007). Data analysis using regression and multilevel/hierarchical models. Cambridge; New York: Cambridge University Press.

Examples

model <- glm(vs ~ wt + mpg, data = mtcars, family = "binomial")
result <- binned_residuals(model)
result
#> Warning: Probably bad model fit. Only about 50% of the residuals are inside the error bounds.
#> 

# look at the data frame
as.data.frame(result)
#>         xbar        ybar n       x.lo       x.hi         se   ci_range
#> 1 0.03786483 -0.03786483 5 0.01744776 0.06917366 0.01899089 0.00968941
#> 2 0.09514191 -0.09514191 5 0.07087498 0.15160143 0.02816391 0.01436960
#> 3 0.25910531  0.07422802 6 0.17159955 0.35374001 0.42499664 0.21683901
#> 4 0.47954643 -0.07954643 5 0.38363314 0.54063600 0.49728294 0.25372045
#> 5 0.71108931  0.28891069 5 0.57299903 0.89141359 0.10975381 0.05599787
#> 6 0.97119262 -0.13785929 6 0.91147360 0.99815623 0.30361062 0.15490623
#>        CI_low     CI_high group
#> 1 -0.05685572 -0.01887394    no
#> 2 -0.12330581 -0.06697800    no
#> 3 -0.35076862  0.49922466   yes
#> 4 -0.57682937  0.41773650   yes
#> 5  0.17915688  0.39866451    no
#> 6 -0.44146992  0.16575133   yes

# plot
if (require("see")) {
  plot(result)
}
#> Loading required package: see
#> Warning: Computation failed in `stat_smooth()`
#> Caused by error in `smooth.construct.tp.smooth.spec()`:
#> ! A term has fewer unique covariate combinations than specified maximum degrees of freedom