cNORM (version 3.6.1)

checkConsistency: Check the consistency of the norm data model

Description

While abilities increase and decline over age, within one age group, the norm scores always have to show a monotonic increase or decrease with increasing raw scores. Violations of this assumption are an indication for problems in modeling the relationship between raw and norm scores. There are several reasons, why this might occur:

1. Vertical extrapolation: Choosing extreme norm scores, e. g. values -3 <= x and x >= 3. In order to model these extreme values, a large sample dataset is necessary.

2. Horizontal extrapolation: Taylor polynomials converge in a certain radius. Using the model values outside the original dataset may lead to inconsistent results.

3. The data cannot be modeled with Taylor polynomials, or you need another power parameter (k) or R2 for the model.

Usage

checkConsistency(
  model,
  minAge = NULL,
  maxAge = NULL,
  minNorm = NULL,
  maxNorm = NULL,
  minRaw = NULL,
  maxRaw = NULL,
  stepAge = NULL,
  stepNorm = 1,
  method = c("analytic", "grid"),
  warn = FALSE,
  silent = FALSE
)

Value

Boolean, indicating model violations (TRUE) or no problems (FALSE)

Arguments

model

The model from the bestModel function or a cnorm object

minAge

Age to start with checking

maxAge

Upper end of the age check

minNorm

Lower end of the norm value range

maxNorm

Upper end of the norm value range

minRaw

clipping parameter for the lower bound of raw scores

maxRaw

clipping parameter for the upper bound of raw scores

stepAge

Stepping parameter for the age check. If NULL, 8 equidistant age points are used. Lower values indicate higher precision.

stepNorm

Stepping parameter for the norm table check within age (only used with method = "grid")

method

Either "analytic" (default; exact within age via polynomial derivative roots) or "grid" (numerical check on a norm score grid)

warn

Retained for backwards compatibility (violations below numerical tolerance are always suppressed)

silent

turn off messages

Details

In general, extrapolation (point 1 and 2) can carefully be done to a certain degree outside the original sample, but it should in general be handled with caution. Please note that at extreme values, the models most likely become independent and it is thus recommended to restrict the norm score range to the relevant range of abilities, e.g. +/- 2.5 SD via the minNorm and maxNorm parameter.

With method = "analytic" (default), monotonicity within each age is verified exactly: since the model is polynomial in the norm score L, the real roots of its derivative are computed via polyroot and the sign of the derivative is checked between consecutive roots. This detects even narrow violations that a coarse norm score grid can miss. Age remains discretized; violations that are entirely clipped by the raw score bounds are ignored. method = "grid" reproduces the classical numerical check and is used automatically as a fallback for models with non-Taylor predictors.

See Also

Other model: bestModel(), cnorm.cv(), derive(), modelSummary(), print.cnorm(), printSubset(), rangeCheck(), regressionFunction(), summary.cnorm(), weightedAverageModel()

Examples

if (FALSE) {
  model <- cnorm(raw = elfe$raw, group = elfe$group, plot = FALSE)
  modelViolations <- checkConsistency(model, minNorm = 25, maxNorm = 75)
  plotDerivative(model, minNorm = 25, maxNorm = 75)
}