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 modeling process. In addition to the raw scores, either provide

a numeric vector for the grouping information (group)
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 model 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. The power parameter for the age trajectory can be specified independently by 't'. If both parameters are missing, cnorm uses k = 5 and t = 3 by default.

Usage

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

Value

cnorm object including the ranked raw data and the regression model

Arguments

raw: Numeric vector of raw scores
group: Numeric vector of grouping variable, e. g. grade. If no group or age variable is provided, conventional norming is applied
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 for each individual case. It can be used to compensate for moderate imbalances due to insufficient norm data stratification. Weights should be numerical and positive.
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
k: The power constant. Higher values result in more detailed approximations but have the danger of over-fit (max = 6). If not set, it uses t and if both parameters are NULL, k is set to 5.
t: The age power parameter (max = 6). If not set, it uses k and if both parameters are NULL, k is set to 3, since age trajectories are most often well captured by cubic polynomials.
terms: Selection criterion for model building. The best fitting model with this number of terms is used
R2: Adjusted R square as a stopping criterion for the model building (default R2 = 0.99)
plot: Default TRUE; plots the regression model and prints report
extensive: If TRUE, screen models for consistency and - if possible, exclude inconsistent ones

References

Gary, S. & Lenhard, W. (2021). In norming we trust. Diagnostica.
Gary, S., Lenhard, W. & Lenhard, A. (2021). Modelling Norm Scores with the cNORM Package in R. Psych, 3(3), 501-521. https://doi.org/10.3390/psych3030033
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

if (FALSE) {
# Using this function with the example dataset 'elfe'

# Conventional norming (no modelling over age)
cnorm(raw=elfe$raw)

# Continuous norming
# You can use the 'getGroups()' function to set up grouping variable in case,
# you have a continuous age variable.
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), 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), cnorm.elfe, CI = .90, reliability = .95)


# Using a continuous age variable instead of distinct groups, using a sliding
# window for percentile estimation. Please specify continuos variable for age
# and the sliding window size.
cnorm.ppvt.continuous <- cnorm(raw = ppvt$raw, age = ppvt$age, width=1)


# In case of unbalanced datasets, deviating from the census, the norm data
# can be weighted by the means of raking / post stratification. Please generate
# the weights with the computeWeights() function and pass them as the weights
# parameter. For computing the weights, please specify a data.frame with the
# population margins (further information is available in the computeWeights
# function). A demonstration based on sex and migration status in vocabulary
# development (ppvt dataset):
margins <- data.frame(variables = c("sex", "sex",
                                    "migration", "migration"),
                      levels = c(1, 2, 0, 1),
                      share = c(.52, .48, .7, .3))
weights <- computeWeights(ppvt, margins)
model <- cnorm(raw = ppvt$raw, group=ppvt$group, weights = weights)
}