Quantile Crossing Detection

Returns a logical from testing whether an object such as an extlogF1() VGLM object has crossing quantiles.

is.crossing.vglm(object, ...)

Arguments

object

an object such as a vglm object with family function extlogF1.

...

additional optional arguments. Currently unused.

Details

This function was specifically written for a vglm with family function extlogF1. It examines the fitted quantiles to see if any cross. Note that if one uses regression splines such as bs and ns then it is possible that they cross at values of the covariate space that are not represented by actual data. One could use linear interpolation between fitted values to get around this problem.

Value

A logical. If TRUE then one can try fit a similar model by combining columns of the constraint matrices so that crossing no longer holds; see fix.crossing. For LMS-Box-Cox type quantile regression models it is impossible for the quantiles to cross, by definition, hence FALSE is returned; see lms.bcn.

See also

extlogF1, fix.crossing, lms.bcn. vglm.

Examples

if (FALSE)  ooo <- with(bmi.nz, order(age))
bmi.nz <- bmi.nz[ooo, ]  # Sort by age
#> Error: object 'ooo' not found
with(bmi.nz, plot(age, BMI, col = "blue"))

mytau <- c(50, 93, 95, 97) / 100  # Some quantiles are quite close
fit1 <- vglm(BMI ~ ns(age, 7), extlogF1(mytau), bmi.nz, trace = TRUE)
#> Taking a modified step.
#> Iteration  2 :  loglikelihood = -9827.2672
#> Taking a modified step.
#> Iteration  3 :  loglikelihood = -9821.8497
#> Taking a modified step.
#> Iteration  4 :  loglikelihood = -9817.6926
#> Taking a modified step.
#> Iteration  5 :  loglikelihood = -9814.6062
#> Taking a modified step.
#> Iteration  6 :  loglikelihood = -9812.2572
#> Taking a modified step.
#> Iteration  7 :  loglikelihood = -9810.5167
#> Taking a modified step.
#> Iteration  8 :  loglikelihood = -9809.2165
#> Taking a modified step.
#> Iteration  9 :  loglikelihood = -9808.2009
#> Taking a modified step.
#> Iteration  10 :  loglikelihood = -9807.4706
#> Taking a modified step.
#> Iteration  11 :  loglikelihood = -9807.0344
#> Taking a modified step.
#> Iteration  12 :  loglikelihood = -9806.7858
#> Taking a modified step.
#> Iteration  13 :  loglikelihood = -9806.6309
#> Taking a modified step.
#> Iteration  14 :  loglikelihood = -9806.5045
#> Taking a modified step.
#> Iteration  15 :  loglikelihood = -9806.3928
#> Taking a modified step.
#> Iteration  16 :  loglikelihood = -9806.2922
#> Taking a modified step.
#> Iteration  17 :  loglikelihood = -9806.2011
#> Taking a modified step.
#> Iteration  18 :  loglikelihood = -9806.1193
#> Taking a modified step.
#> Iteration  19 :  loglikelihood = -9806.047
#> Taking a modified step.
#> Iteration  20 :  loglikelihood = -9805.9853
#> Taking a modified step.
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#> Taking a modified step.
#> Iteration  22 :  loglikelihood = -9805.8964
#> Taking a modified step.
#> Iteration  23 :  loglikelihood = -9805.8694
#> Taking a modified step.
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#> Taking a modified step.
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#> Taking a modified step.
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#> Taking a modified step.
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#> Taking a modified step.
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#> Taking a modified step.
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#> Taking a modified step.
#> Iteration  30 :  loglikelihood = -9805.8316
#> Taking a modified step.
#> Iteration  31 :  loglikelihood = -9805.8309
#> Taking a modified step.
#> Iteration  32 :  loglikelihood = -9805.8304
#> Taking a modified step.
#> Iteration  33 :  loglikelihood = -9805.83
#> Taking a modified step.
#> Iteration  34 :  loglikelihood = -9805.8297
#> Taking a modified step.
#> Iteration  35 :  loglikelihood = -9805.8295
#> Taking a modified step.
#> Iteration  36 :  loglikelihood = -9805.8293
#> Taking a modified step.
#> Iteration  37 :  loglikelihood = -9805.8291
#> Taking a modified step.
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#> Taking a modified step.
#> Iteration  39 :  loglikelihood = -9805.8289
#> Taking a modified step.
#> Iteration  40 :  loglikelihood = -9805.8289
#> Taking a modified step.
#> Iteration  41 :  loglikelihood = -9805.8288
#> Taking a modified step.
#> Iteration  42 :  loglikelihood = -9805.8288
#> Taking a modified step.
#> Iteration  43 :  loglikelihood = -9805.8288
plot(BMI ~ age, bmi.nz, col = "blue", las = 1,
     main = "Partially parallel (darkgreen) & nonparallel quantiles",
     sub = "Crossing quantiles are orange")
is.crossing(fit1)
#> [1] TRUE
matlines(with(bmi.nz, age), fitted(fit1), lty = 1, col = "orange")  # \dontrun{}