checkConsistency function

Check the consistency of the norm data model

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.

checkConsistency(
  model,
  minAge = NULL,
  maxAge = NULL,
  minNorm = NULL,
  maxNorm = NULL,
  minRaw = NULL,
  maxRaw = NULL,
  stepAge = NULL,
  stepNorm = 1,
  warn = FALSE,
  silent = 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. values indicate higher precision / closer checks
• stepNorm: Stepping parameter for the norm table check within age with lower scores indicating a higher precision. The choice depends of the norm scale used. With T scores a stepping parameter of 1 is suitable
• warn: If set to TRUE, already minor violations of the model assumptions are displayed (default = FALSE)
• silent: turn off messages

Returns

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

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.

Examples

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

See Also

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