z2y {AGD}R Documentation

Convert standard deviation scores (SDS) to measurements


Converts standard deviation score (SDS) into measurements using an age- and sex-conditional external reference.


z2y(z = c(-2, 0, 2), x = 1, sex = "M", sub = "N",
  ref = get("nl4.hgt"), dist = "LMS", dec = 3, sex.fallback = NA,
  sub.fallback = NA)



A numerical vector containing standard deviation scores that are to be converted. The length length(z) determines the size of the output vector.


A vector containing the values of the numerical covariate (typically decimal age or height) at which conversion is desired. Values are replicated to match length(y).


A character vector indicating whether the male ("M") of female ("F")reference should be used. Values are replicated to match length(y).


A character vector indicating the level of the sub field of the reference standard defined in ref


A data frame containing a factor sex, a numerical variable age containing the tabulated decimal point ages, and two or more numerical variables with reference values. See details.


A string identifying the type of distribution. Values values are: "NO", "BCCG", "LMS", "BCPE" and "BCT". The default is "LMS".


A scalar value indicating the number of decimals used to round the value.


The level of the sex field used when no match is found. The default sex.fallback=NA specifies that unmatched entries should receive a NA value.


The level of the sub field used when no match is found. The default sub.fallback=NA specifies that unmatched entries should receive a NA value.


Functions z2y() and y2z() are the inverse of each other.

The argument dist determines the statistical distribution. The possibilities are as follows:


ref should contain columns mean and sd, containing the mean and the standard deviation in the external reference population.


ref should contain columns L, S and M containing the LMS parameters.


ref should contain columns mu, sigma and nu containing the Box-Cox Cole-Green parameters.


ref should contain columns mu, sigma, nu and tau containing the Box-Cox Power Exponential parameters.


ref should contain columns mu, sigma, nu and tau containing the Box-Cox T distribution parameters.


For y2z(): A vector with length(y) elements containing the standard deviation score. For z2y(): A vector with length(z) elements containing quantiles.


Stef van Buuren, 2010

See Also



boys <- boys7482

# quantile at SD=0 of age 2 years, 
# height Dutch boys
z2y(z=0, x=2)

# same for Dutch girls
z2y(z=0, x=2, sex="F")

# quantile at SD=c(-1,0,1) of age 2 years, BMI Dutch boys
z2y(z=c(-1,0,+1), x=2, ref=nl4.bmi)

# 0SD line (P50) in kg of weight for age in 5-10 year, Dutch boys
z2y(z=rep(0,6), x=5:10, ref=nl4.wgt)

# 95th percentile (P95), age 10 years, wfa, Dutch boys
z2y(z=qnorm(0.95), x=10, ref=nl4.wgt)

# table of P3, P10, P50, P90, P97 of weight for 5-10 year old dutch boys
# age per year
age <- 5:10
p <- c(0.03,0.1,0.5,0.9,0.97)
z <- rep(qnorm(p), length(age))
x <- rep(age, each=length(p))
w <- matrix(z2y(z, x=x, sex="M", ref=nl4.wgt), ncol=length(p),
dimnames(w) <- list(age, p)

# standard set of Z-scores of weight for all tabulated ages, boys & girls
# and three etnicities
sds <- c(-2.5, -2, -1, 0, 1, 2, 2.5)
age <- nl4.wgt$x
z <- rep(sds, times=length(age))
x <- rep(age, each=length(sds))
sex <- rep(c("M","F"), each=length(z)/2)
w <- z2y(z=z, x=x, sex=sex, ref=nl4.wgt)
w <- matrix(w, ncol=length(sds), byrow=TRUE)
dimnames(w) <- list(age, sds)
data.frame(sub=nl4.wgt$sub,sex=nl4.wgt$sex,round(w,2), row.names=NULL)

# P85 of BMI in 5-8 year old Dutch boys and girls
e <- expand.grid(age=5:8, sex=c("M","F"))
w <- z2y(z=rep(qnorm(0.85),nrow(e)), x=e$age, sex=e$sex, ref=nl4.bmi)
w <- matrix(w, nrow=2, byrow=TRUE)
dimnames(w) <- list(c("boys","girls"),5:8)

# data transformation of height z-scores to cm-scale
z <- c(-1.83, 0.09, 2.33, 0.81, -1.20)
x <- c(8.33,  0.23, 19.2, 24.3, 10)
sex <- c("M", "M", "F", "M", "F")
round(z2y(z=z, x=x, sex=sex, ref=nl4.hgt), 1)

# interpolate published height standard 
# to daily values, days 0-31, boys
# on centiles -2SD, 0SD and +2SD 
days <- 0:31
sds  <- c(-2, 0, +2)
z    <- rep(sds, length(days))
x    <- rep(round(days/365.25,4), each=length(sds))
w    <- z2y(z, x, sex="M", ref=nl4.hgt)
w    <- matrix(w, ncol=length(sds), byrow=TRUE)
dimnames(w) <- list(days, sds)

[Package AGD version 0.39 Index]