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 = "gsed",
itembank = dscore::builtin_itembank,
metric = c("dscore", "logit"),
prior_mean = ifelse(key == "dutch", ".dutch", ".gcdg"),
prior_sd = NULL,
transform = NULL,
qp = -10:100,
population = key,
dec = c(2L, 3L)
)

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

## 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. 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. A string with the name of the age variable in data. The default is "age". A string specifying the unit in which age is measured (either "decimal", "days" or "months"). The default ("decimal") means decimal age in years. A string that sets the key, the set of difficulty estimates from a fitted Rasch model. The built-in keys are: "gsed" (default), "gcdg", and "dutch". Use key = "" to use all item names, which should only be done if there are no duplicate itemnames. 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. A string, either "dscore" (default) or "logit", signalling the metric in which ability is estimated. A string specifying a column name in data with the mean of the prior for the D-score calculation. The default depends on the key. If key == "dutch" then prior_mean = "dutch", else it is ".gcdg". These settings calculate an age-dependent prior mean internally according to function dscore:::count_mu_gcdg(). The choice prior_mean = ".dutch" calculates prior_mean from the Count model coded in dscore:::count_mu_dutch()). 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. 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". 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. A string describing the population. Currently supported are "dutch" and "gcdg" (default). 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).

## 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.

The built-in itembank (object builtin_itembank()) supports keys "gsed" (default), "gcdg" and "dutch". 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 "gsed" 807_17 -10:100 20 mixed GSED Team, 2019

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 most general key, "gsed".

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_gcdg() (default) 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 twice the normal spread of child of a given age. The starting prior is thus somewhat informative for low numbers of valid items, and unformative 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

get_tau(), builtin_itembank(), posterior(), builtin_references()

## Author

Stef van Buuren, Iris Eekhout, Arjan Huizing (2020)

## 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
#>      5.51      2.43        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  3.46 2.772368 -2.138
#> 4  0.0575 2 0.0  0.96 2.375263 -2.843
#> 5  0.0575 2 0.5  4.82 1.881393 -1.754
#> 6  0.0575 2 0.5  4.82 1.881393 -1.754
#> 7  0.0575 2 0.5  4.82 1.881393 -1.754
#> 8  0.0575 2 0.5  4.82 1.881393 -1.754
#> 9  0.0575 2 1.0 11.81 3.970219  0.219
#> 10 0.0575 2 1.0 11.81 3.970219  0.219
# 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))