D-score estimation

The function dscore() function estimates the D-score, a numeric score that measures child development, from PASS/FAIL observations on milestones.

dscore(
  data,
  items = names(data),
  xname = "age",
  xunit = c("decimal", "days", "months"),
  key = NULL,
  itembank = dscore::builtin_itembank,
  metric = c("dscore", "logit"),
  prior_mean = NULL,
  prior_sd = NULL,
  transform = NULL,
  qp = -10:100,
  population = NULL,
  dec = c(2L, 3L),
  relevance = c(-Inf, Inf)
)

dscore_posterior(
  data,
  items = names(data),
  xname = "age",
  xunit = c("decimal", "days", "months"),
  key = NULL,
  itembank = dscore::builtin_itembank,
  metric = c("dscore", "logit"),
  prior_mean = NULL,
  prior_sd = NULL,
  transform = NULL,
  qp = -10:100,
  population = NULL,
  dec = c(2L, 3L),
  relevance = c(-Inf, Inf)
)

Arguments

data: A data.frame with the data. A row collects all observations made on a child on a set of milestones administered at a given age. The function calculates a D-score for each row. Different rows correspond to different children or different ages.
items: A character vector containing names of items to be included into the D-score calculation. Milestone scores are coded numerically as 1 (pass) and 0 (fail). By default, D-score calculation is done on all items found in the data that have a difficulty parameter under the specified key.
xname: A string with the name of the age variable in data. The default is "age".
xunit: A string specifying the unit in which age is measured (either "decimal", "days" or "months"). The default ("decimal") means decimal age in years.
key: A string that selects a subset in the itembank that makes up the key, the set of difficulty estimates from a fitted Rasch model. The built-in keys are: "gsed2212" (default), "gsed2208" (deprecated), "gsed2206" (deprecated), "gsed1912", "lf2206", "sf2206", "gcdg", and "dutch". Since version 1.5.0, the key = "gsed" selects the latest key starting with the string "gsed". Use key = "" to use all item names, which should only be done if there are no duplicate itemnames in the itembank.
itembank: A data.frame with columns key, item, tau, instrument, domain, mode, number and label. Only columns item and tau are required. The function uses dscore::builtin_itembank by default.
metric: A string, either "dscore" (default) or "logit", signalling the metric in which ability is estimated.
prior_mean: A string specifying where the mean of the prior for the D-score calculation should come from. It could be a column name in data (when you want your own prior for every row), but normally this is one of the keywords ".dutch", ".gcdg" or ".phase1". The default depends on the key. If key == "dutch" then prior_mean = ".dutch". The choice prior_mean = ".dutch" calculates prior_mean from the Count model coded in dscore:::count_mu_dutch()). If key is #' "gcdg", "gsed1912", "gsed2206", "lf2206" or "sf2206" then prior_mean = ".gcdg". This setting calculates an age-dependent prior mean internally according to function dscore:::count_mu_gcdg(). In other cases, prior_mean = ".phase1" which uses the function dscore:::count_mu_phase1(). Normally, you should not touch this parameter, but feel free to use prior_mean to override the automatic choices.
prior_sd: A string specifying a column name in data with the standard deviation of the prior for the D-score calculation. If not specified, the standard deviation is taken as 5 for every row.
transform: Vector of length 2, signalling the intercept and slope respectively of the linear transform that converts an observation in the logit scale to the the D-score scale. Only needed if metric == "logit".
qp: Numeric vector of equally spaced quadrature points. This vector should span the range of all D-score values. The default (qp = -10:100) is suitable for age range 0-4 years.
population: A string describing the population. Currently supported are "phase1" (default), "dutch", "gcdg".
dec: A vector of two integers specifying the number of decimals for rounding the D-score and DAZ, respectively. The default is dec = c(2L, 3L).
relevance: A numeric vector of length with the lower and upper bounds of the relevance interval. The procedure calculates a dynamic EAP for each item. If the difficulty level (tau) of the next item is outside the relevance interval around EAP, the procedure ignore the score on the item. The default is c(-Inf, +Inf) does not ignore scores.

Value

The dscore() function returns a data.frame with nrow(data) rows and the following columns:

Name	Label
`a`	Decimal age
`n`	Number of items with valid (0/1) data
`p`	Percentage of passed milestones
`d`	Ability estimate, mean of posterior
`sem`	Standard error of measurement, standard deviation of the posterior
`daz`	D-score corrected for age, calculated in Z-scale

The dscore_posterior() function returns a numeric matrix with nrow(data) rows and length(qp) columns with the density at each quadrature point. The vector represents the full posterior ability distribution. If no valid responses were obtained, dscore_posterior() returns the prior.

Details

The algorithm is based on the method by Bock and Mislevy (1982). The method uses Bayes rule to update a prior ability into a posterior ability.

The item names should correspond to the "gsed" lexicon.

A key is defined by the set of estimated item difficulties.

Key	Model	Quadrature	Instruments	Direct/Caregiver	Reference
`"dutch"`	`75_0`	`-10:80`	1	direct	Van Buuren, 2014/2020
`"gcdg"`	`565_18`	`-10:100`	14	direct	Weber, 2019
`"gsed1912"`	`807_17`	`-10:100`	20	mixed	GSED Team, 2019
`"gsed2206"`	`818_17`	`-10:100`	22	mixed	GSED Team, 2022
`"gsed2208"`	`818_6`	`-10:100`	22	mixed	GSED Team, 2022
`"gsed2212"`	`818_6`	`-10:100`	22	mixed	GSED Team, 2022
`"lf2206"`	`155_0`	`-10:100`	1	direct	GSED Team, 2022
`"sf2206"`	`139_0`	`-10:100`	1	caregiver	GSED Team, 2022

As a general rule, one should only compare D-scores that are calculated using the same key and the same set of quadrature points. For calculating D-scores on new data, the advice is to use the default, which currently links to "gsed2212".

The default starting prior is a mean calculated from a so-called "Count model" that describes mean D-score as a function of age. The Count models are stored as internal functions dscore:::count_mu_phase1(), dscore:::count_mu_gcdg() and dscore:::count_mu_dutch(). The spread of the starting prior is 5 D-score points around this mean D-score, which corresponds to approximately 1.5 to 2 times the normal spread of child of a given age. The starting prior is thus somewhat informative for low numbers of valid items, and uninformative for large number of items (say >10 items).

References

Bock DD, Mislevy RJ (1982). Adaptive EAP Estimation of Ability in a Microcomputer Environment. Applied Psychological Measurement, 6(4), 431-444.

Van Buuren S (2014). Growth charts of human development. Stat Methods Med Res, 23(4), 346-368. https://stefvanbuuren.name/publication/van-buuren-2014-gc/

Weber AM, Rubio-Codina M, Walker SP, van Buuren S, Eekhout I, Grantham-McGregor S, Caridad Araujo M, Chang SM, Fernald LCH, Hamadani JD, Hanlon A, Karam SM, Lozoff B, Ratsifandrihamanana L, Richter L, Black MM (2019). The D-score: a metric for interpreting the early development of infants and toddlers across global settings. BMJ Global Health, BMJ Global Health 4: e001724. https://gh.bmj.com/content/bmjgh/4/6/e001724.full.pdf

Author

Stef van Buuren, Iris Eekhout, Arjan Huizing (2022)

Examples

data <- data.frame(
  age = rep(round(21 / 365.25, 4), 10),
  ddifmd001 = c(NA, NA, 0, 0, 0, 1, 0, 1, 1, 1),
  ddicmm029 = c(NA, NA, NA, 0, 1, 0, 1, 0, 1, 1),
  ddigmd053 = c(NA, 0, 0, 1, 0, 0, 1, 1, 0, 1)
)
items <- names(data)[2:4]

# third item is not part of default key
get_tau(items)
#> ddifmd001 ddicmm029 ddigmd053 
#>      8.61      8.47        NA 

# calculate D-score
dscore(data)
#>         a n   p     d      sem    daz
#> 1      NA 0  NA    NA       NA     NA
#> 2      NA 0  NA    NA       NA     NA
#> 3  0.0575 1 0.0  6.61 2.763004 -2.019
#> 4  0.0575 2 0.0  5.60 2.459750 -2.235
#> 5  0.0575 2 0.5  9.09 1.695326 -1.447
#> 6  0.0575 2 0.5  9.09 1.695326 -1.447
#> 7  0.0575 2 0.5  9.09 1.695326 -1.447
#> 8  0.0575 2 0.5  9.09 1.695326 -1.447
#> 9  0.0575 2 1.0 15.30 3.851173  0.277
#> 10 0.0575 2 1.0 15.30 3.851173  0.277

# calculate full posterior
p <- dscore_posterior(data)

# plot posterior for row 7
plot(x = -10:100, y = p[7, ], type = "l", xlab = "D-score",
 ylab = "Density", xlim = c(0, 30))