cnorm: Continuous Norming

Description

Conducts continuous norming in one step and returns an object including ranked raw data and the continuous norming model. Please consult the function description ' of 'rankByGroup', 'rankBySlidingWindow' and 'bestModel' for specifics of the steps in the data preparation and modelling process. In addition to the raw scores, either provide

a numeric vector for the grouping information (group)
a numeric vector for both grouping and age (group, age)
a numeric age vector and the width of the sliding window (age, width)

for the ranking of the raw scores. You can adjust the grade of smoothing of the regression modell by setting the k and terms parameter. In general, increasing k to more than 4 and the number of terms lead to a higher fit, while lower values lead to more smoothing.

Usage

cnorm(
  raw = NULL,
  group = NULL,
  age = NULL,
  width = NA,
  weights = NULL,
  scale = "T",
  method = 4,
  descend = FALSE,
  k = 4,
  terms = 0,
  R2 = NULL
)

Arguments

raw

Numeric vector of raw scores

group

Numeric vector of grouping variable, e. g. grade

age

Numeric vector with chronological age, please additionally specify width of window

width

Size of the moving window in case an age vector is used

weights

Vector or variable name in the dataset with weights to compensate imbalances due to insufficient norm data stratification. All weights have to be numerical and positive. The code to compute weighted percentiles originates from the Hmisc package (functions) wtd.rank and wtd.table) and is provided by the courtesy of Frank Harrell. Please note, that this feature is currently EXPERIMENTAL!

scale

type of norm scale, either T (default), IQ, z or percentile (= no transformation); a double vector with the mean and standard deviation can as well, be provided f. e. c(10, 3) for Wechsler scale index points

method

Ranking method in case of bindings, please provide an index, choosing from the following methods: 1 = Blom (1958), 2 = Tukey (1949), 3 = Van der Warden (1952), 4 = Rankit (default), 5 = Levenbach (1953), 6 = Filliben (1975), 7 = Yu & Huang (2001)

descend

ranking order (default descent = FALSE): inverses the ranking order with higher raw scores getting lower norm scores; relevant for example when norming error scores, where lower scores mean higher performance

The power constant. Higher values result in more detailed approximations but have the danger of over-fit (default = 4, max = 6)

terms

Selection criterion for model building. The best fitting model with this number of terms is used

Adjusted R square as a stopping criterion for the model building (default R2 = 0.99)

Value

cnorm object including the ranked raw data and the regression model

References

Gary, S. & Lenhard, W. (2021). In norming we trust. Diagnostica.
Harrel, F. (2020). Hmisc: Harrell Miscellaneous (v. 4.4-1). available https://CRAN.R-project.org/package=Hmisc (code for weighted ranking adapted from wtd.rank & wtd.table by courtesy of Frank Harrell)
Lenhard, A., Lenhard, W., Suggate, S. & Segerer, R. (2016). A continuous solution to the norming problem. Assessment, Online first, 1-14. doi:10.1177/1073191116656437
Lenhard, A., Lenhard, W., Gary, S. (2018). Continuous Norming (cNORM). The Comprehensive R Network, Package cNORM, available: https://CRAN.R-project.org/package=cNORM
Lenhard, A., Lenhard, W., Gary, S. (2019). Continuous norming of psychometric tests: A simulation study of parametric and semi-parametric approaches. PLoS ONE, 14(9), e0222279. doi:10.1371/journal.pone.0222279
Lenhard, W., & Lenhard, A. (2020). Improvement of Norm Score Quality via Regression-Based Continuous Norming. Educational and Psychological Measurement(Online First), 1-33. https://doi.org/10.1177/0013164420928457

Examples

Run this code

# NOT RUN {
# Using this function with the example dataset 'elfe'
cnorm.elfe <- cnorm(raw = elfe$raw, group = elfe$group)

# return norm tables including 90% confidence intervals for a
# test with a reliability of r = .85; table are set to mean of quartal
# in grade 3 (children completed 2 years of schooling)
normTable(c(2.125, 2.375, 2.625, 2.875), cnorm.elfe, CI = .90, reliability = .95)

# ... or instead of raw scores for norm scores, the other way round
rawTable(c(2.125, 2.375, 2.625, 2.875), cnorm.elfe, CI = .90, reliability = .95)

# }