Computing Designmatrix for Splines

Description

This function computes the design matrix for Bayesian P-splines as it would be done in BayesX. The implementation currently on works properly for default values (knots=20, degree=3).

Usage

DesignM(x, degree = 3, m = 20, min_x = min(x), max_x = max(x))

Arguments

Value

a list with design matrix at distinct covariates, design matrix at all observations, index of sorted observations, the difference matrix, precision matrix and the knots used.

Author(s)

Nadja Klein

References

Stefan Lang and Andy Brezger (2004). Bayesian P-Splines. Journal of Computational and Graphical Statistics, 13, 183–212.

Belitz, C., Brezger, A., Klein, N., Kneib, T., Lang, S., Umlauf, N. (2015): BayesX - Software for Bayesian inference in structured additive regression models. Version 3.0.1. Available from http://www.bayesx.org.

Compute Density Function of Approximated (Differentiably) Uniform Distribution.

Description

Compute Density Function of Approximated (Differentiably) Uniform Distribution.

Usage

dapprox_unif(x, scale, tildec = 13.86294)

Arguments

Details

The density of the uniform distribution for \tau is approximated by

p(\tau)=(1/(1+exp(\tau\tilde{c}/\theta-\tilde{c})))/(\theta(1+log(1+exp(-\tilde{c}))))

. This results in

p(\tau^2)=0.5*(\tau^2)^(-1/2)(1/(1+exp((\tau^2)^(1/2)\tilde{c}/\theta-\tilde{c})))/(\theta(1+log(1+exp(-\tilde{c}))))

for tau^2. \tilde{c} is chosen such that P(\tau<=\theta)>=0.95.

Value

the density.

Author(s)

Nadja Klein

References

Nadja Klein and Thomas Kneib (2015). Scale-Dependent Priors for Variance Parameters in Structured Additive Distributional Regression. Working Paper.

See Also

rapprox_unif,papprox_unif

Find Scale Parameter for (Scale Dependent) Hyperprior

Description

This function implements a optimisation routine that computes the scale parameter \theta of the scale dependent hyperprior for a given design matrix and prior precision matrix such that approximately P(|f(x_{k}|\le c,k=1,\ldots,p)\ge 1-\alpha

Usage

get_theta(alpha = 0.01, method = "integrate", Z, c = 3,
  eps = .Machine$double.eps, Kinv)

Arguments

Value

an object of class list with values from uniroot.

Author(s)

Nadja Klein

References

Nadja Klein and Thomas Kneib (2015). Scale-Dependent Priors for Variance Parameters in Structured Additive Distributional Regression. Working Paper.

Examples

## Not run: 

set.seed(91179)
library(BayesX)
library(MASS)
# prior precision matrix to zambia data set
K <- read.gra(system.file("examples/zambia.gra", package="sdPrior"))
# generalised inverse of K
Kinv <- ginv(K)

# read data
dat <- read.table(system.file("examples/zambia_height92.raw", package="sdPrior"), header = TRUE)

# design matrix for spatial component
Z <- t(sapply(dat$district, FUN=function(x){1*(x==rownames(K))}))

# get scale parameter
theta <- get_theta(alpha = 0.01, method = "integrate", Z = Z, 
                            c = 3, eps = .Machine$double.eps, Kinv = Kinv)$root

## End(Not run) 

Find Scale Parameter for Hyperprior for Variances Where the Standard Deviations have an Approximated (Differentiably) Uniform Distribution.

Description

This function implements a optimisation routine that computes the scale parameter \theta of the prior \tau^2 (corresponding to a differentiably approximated version of the uniform prior for \tau) for a given design matrix and prior precision matrix such that approximately P(|f(x_{k}|\le c,k=1,\ldots,p)\ge 1-\alpha

Usage

get_theta_aunif(alpha = 0.01, method = "integrate", Z, c = 3,
  eps = .Machine$double.eps, Kinv)

Arguments

Value

an object of class list with values from uniroot.

Author(s)

Nadja Klein

References

Nadja Klein and Thomas Kneib (2015). Scale-Dependent Priors for Variance Parameters in Structured Additive Distributional Regression. Working Paper.

Andrew Gelman (2006). Prior Distributions for Variance Parameters in Hierarchical Models. Bayesian Analysis, 1(3), 515–533.

Examples

set.seed(123)
library(MASS)
# prior precision matrix (second order differences) 
# of a spline of degree l=3 and with m=20 inner knots
# yielding dim(K)=m+l-1=22
K <- t(diff(diag(22), differences=2))%*%diff(diag(22), differences=2)
# generalised inverse of K
Kinv <- ginv(K)
# covariate x
x <- runif(1)
Z <- matrix(DesignM(x)$Z_B,nrow=1)
theta <- get_theta_aunif(alpha = 0.01, method = "integrate", Z = Z, 
                            c = 3, eps = .Machine$double.eps, Kinv = Kinv)$root

Find Scale Parameter for Gamma (Half-Normal) Hyperprior

Description

This function implements a optimisation routine that computes the scale parameter \theta of the gamma prior for \tau^2 (corresponding to a half-normal prior for \tau) for a given design matrix and prior precision matrix such that approximately P(|f(x_{k}|\le c,k=1,\ldots,p)\ge 1-\alpha

Usage

get_theta_ga(alpha = 0.01, method = "integrate", Z, c = 3,
  eps = .Machine$double.eps, Kinv)

Arguments

Value

an object of class list with values from uniroot.

Author(s)

Nadja Klein

References

Nadja Klein and Thomas Kneib (2015). Scale-Dependent Priors for Variance Parameters in Structured Additive Distributional Regression. Working Paper.

Andrew Gelman (2006). Prior Distributions for Variance Parameters in Hierarchical Models. Bayesian Analysis, 1(3), 515–533.

Examples

set.seed(123)
require(MASS)
# prior precision matrix (second order differences) 
# of a spline of degree l=3 and with m=20 inner knots
# yielding dim(K)=m+l-1=22
K <- t(diff(diag(22), differences=2))%*%diff(diag(22), differences=2)
# generalised inverse of K
Kinv <- ginv(K)
# covariate x
x <- runif(1)
Z <- matrix(DesignM(x)$Z_B,nrow=1)
theta <- get_theta_ga(alpha = 0.01, method = "integrate", Z = Z, 
                            c = 3, eps = .Machine$double.eps, Kinv = Kinv)$root

## Not run: 

set.seed(91179)
library(BayesX)
library(MASS)
# prior precision matrix to zambia data set
K <- read.gra(system.file("examples/zambia.gra", package="sdPrior"))
# generalised inverse of K
Kinv <- ginv(K)

# read data
dat <- read.table(system.file("examples/zambia_height92.raw", package="sdPrior"), header = TRUE)

# design matrix for spatial component
Z <- t(sapply(dat$district, FUN=function(x){1*(x==rownames(K))}))

# get scale parameter
theta <- get_theta_ga(alpha = 0.01, method = "integrate", Z = Z, 
                            c = 3, eps = .Machine$double.eps, Kinv = Kinv)$root

## End(Not run) 

Find Scale Parameter for Generalised Beta Prime (Half-Cauchy) Hyperprior

Description

This function implements a optimisation routine that computes the scale parameter \theta of the gamma prior for \tau^2 (corresponding to a half cauchy for \tau) for a given design matrix and prior precision matrix such that approximately P(|f(x_{k}|\le c,k=1,\ldots,p)\ge 1-\alpha

Usage

get_theta_gbp(alpha = 0.01, method = "integrate", Z, c = 3,
  eps = .Machine$double.eps, Kinv)

Arguments

Value

an object of class list with values from uniroot.

Author(s)

Nadja Klein

References

Nadja Klein and Thomas Kneib (2015). Scale-Dependent Priors for Variance Parameters in Structured Additive Distributional Regression. Working Paper.

Andrew Gelman (2006). Prior Distributions for Variance Parameters in Hierarchical Models. Bayesian Analysis, 1(3), 515–533.

Examples

set.seed(123)
require(MASS)
# prior precision matrix (second order differences) 
# of a spline of degree l=3 and with m=20 inner knots
# yielding dim(K)=m+l-1=22
K <- t(diff(diag(22), differences=2))%*%diff(diag(22), differences=2)
# generalised inverse of K
Kinv <- ginv(K)
# covariate x
x <- runif(1)
Z <- matrix(DesignM(x)$Z_B,nrow=1)
theta <- get_theta_gbp(alpha = 0.01, method = "integrate", Z = Z, 
                            c = 3, eps = .Machine$double.eps, Kinv = Kinv)$root

## Not run: 

set.seed(91179)
library(BayesX)
library(MASS)
# prior precision matrix to zambia data set
K <- read.gra(system.file("examples/zambia.gra", package="sdPrior"))
# generalised inverse of K
Kinv <- ginv(K)

# read data
dat <- read.table(system.file("examples/zambia_height92.raw", package="sdPrior"), header = TRUE)

# design matrix for spatial component
Z <- t(sapply(dat$district, FUN=function(x){1*(x==rownames(K))}))

# get scale parameter
theta <- get_theta_gbp(alpha = 0.01, method = "integrate", Z = Z, 
                            c = 3, eps = .Machine$double.eps, Kinv = Kinv)$root

## End(Not run) 

Find Scale Parameter for Inverse Gamma Hyperprior

Description

This function implements a optimisation routine that computes the scale parameter b of the inverse gamma prior for \tau^2 when a=b=\epsilon with \epsilon small for a given design matrix and prior precision matrix such that approximately P(|f(x_{k}|\le c,k=1,\ldots,p)\ge 1-\alpha When a unequal to a the shape parameter a has to be specified.

Usage

get_theta_ig(alpha = 0.01, method = "integrate", Z, c = 3,
  eps = .Machine$double.eps, Kinv, equals = FALSE, a = 1,
  type = "marginalt")

Arguments

Details

Currently, the implementation only works properly for the cases a unequal b.

Value

an object of class list with values from uniroot.

Author(s)

Nadja Klein

References

Nadja Klein and Thomas Kneib (2015). Scale-Dependent Priors for Variance Parameters in Structured Additive Distributional Regression. Working Paper.

Stefan Lang and Andreas Brezger (2004). Bayesian P-Splines. Journal of Computational and Graphical Statistics, 13, 183-212.

Examples

set.seed(123)
library(MASS)
# prior precision matrix (second order differences) 
# of a spline of degree l=3 and with m=20 inner knots
# yielding dim(K)=m+l-1=22
K <- t(diff(diag(22), differences=2))%*%diff(diag(22), differences=2)
# generalised inverse of K
Kinv <- ginv(K)
# covariate x
x <- runif(1)
Z <- matrix(DesignM(x)$Z_B,nrow=1)
theta <- get_theta_ig(alpha = 0.01, method = "integrate", Z = Z, 
                      c = 3, eps = .Machine$double.eps, Kinv = Kinv, 
					 equals = FALSE, a = 1, type="marginalt")$root

Find Scale Parameter for Inverse Gamma Hyperprior of Linear Effects with Spike and Slab Prior

Description

This function implements a optimisation routine that computes the scale parameter v_2 and selection parameter r of the inverse gamma prior IG(v_1,v_2) for \tau^2 when \tau^2\sim N(0,r(\delta)\tau^2) and given shape paramter such that approximately P(\beta\le c_2|spike)\ge 1-\alpha_2 and P(\beta\ge c_1|slab)\ge 1-\alpha1.
\alpha_1 and \alpha_2 should not be smaller than 0.1 due to numerical sensitivity and possible instability. Better change c_1, c_2.

Usage

get_theta_linear(alpha1 = 0.1, alpha2 = 0.1, c1 = 0.1, c2 = 0.1,
  eps = .Machine$double.eps, v1 = 5)

Arguments

Value

an object of class list with values from uniroot.

Warning

\alpha_1 and \alpha_2 should not be smaller than 0.1 due to numerical sensitivity and possible instability. Better change c_1, c_2.

Author(s)

Nadja Klein

References

Nadja Klein, Thomas Kneib, Stefan Lang and Helga Wagner (2016). Automatic Effect Selection in Distributional Regression via Spike and Slab Priors. Working Paper.

Examples

set.seed(123)
result <- get_theta_linear()
r <- result$r
v2 <- result$v2

get_theta_linear(alpha1=0.1,alpha2=0.1,c1=0.5,c2=0.1,v1=5) 

Find Scale Parameters for Inverse Gamma Hyperprior of Nonlinear Effects with Spike and Slab Prior (Simulation-based)

Description

This function implements a optimisation routine that computes the scale parameter b and selection parameter r. . Here, we assume an inverse gamma prior IG(a,b) for \psi^2 and \tau^2\sim N(0,r(\delta)\psi^2) and given shape paramter a, such that approximately P(f(x)\le c|spike,\forall x\in D)\ge 1-\alpha1 and P(\exists x\in D s.t. f(x)\ge c|slab)\ge 1-\alpha2.

Usage

hyperpar(Z, Kinv, a = 5, c = 0.1, alpha1 = 0.1, alpha2 = 0.1,
  R = 10000, myseed = 123)

Arguments

Value

an object of class list with root values r, b from uniroot.

Author(s)

Nadja Klein

References

Nadja Klein, Thomas Kneib, Stefan Lang and Helga Wagner (2016). Spike and Slab Priors for Effect Selection in Distributional Regression. Working Paper.

Examples

set.seed(123)
library(MASS)
# prior precision matrix (second order differences) 
# of a spline of degree l=3 and with m=22 inner knots
# yielding dim(K)=m+l-1=22
K <- t(diff(diag(22), differences=2))%*%diff(diag(22), differences=2)
# generalised inverse of K (same as if we used mixed model representation!)
Kinv <- ginv(K)
# covariate x
x <- runif(1)
Z <- matrix(DesignM(x)$Z_B,nrow=1)
fgrid <- seq(-3,3,length=1000)
mdf <- hyperpar(Z,Kinv,a=5,c=0.1,alpha1=0.05,alpha2=0.05,R=10000,myseed=123)

Find Scale Parameter for modular regression

Description

Find Scale Parameter for modular regression

Usage

hyperpar_mod(Z, K1, K2, A, c = 0.1, alpha = 0.1, omegaseq, omegaprob,
  R = 10000, myseed = 123, thetaseq = NULL, type = "IG",
  lowrank = FALSE, k = 5, mc = FALSE, ncores = 1, truncate = 1)

Arguments

Value

the optimal value for theta

Author(s)

Nadja Klein

References

Kneib, T., Klein, N., Lang, S. and Umlauf, N. (2017) Modular Regression - A Lego System for Building Structured Additive Distributional Regression Models with Tensor Product Interactions Working Paper.

Find Scale Parameter for Inverse Gamma Hyperprior of Linear Effects with Spike and Slab Prior

Description

This function implements a optimisation routine that computes the scale parameter b and selection parameter r. Here, we assume an inverse gamma prior IG(a,b) for \tau^2 and \beta|\delta,\tau^2\sim N(0,r(\delta)\tau^2). For given shape paramter a the user gets b, r such that approximately P(\beta\le c2|spike)\ge 1-\alpha2 and P(\beta\ge c1|slab)\ge 1-\alpha1 hold.
Note that if you observe numerical instabilities try not to specify \alpha1 and \alpha2 smaller than 0.1.

Usage

hyperparlin(alpha1 = 0.1, alpha2 = 0.1, c1 = 0.1, c2 = 0.1,
  eps = .Machine$double.eps, a = 5)

Arguments

Value

an object of class list with root values r, b from uniroot.

Warning

\alpha1 and \alpha2 should not be smaller than 0.1 due to numerical sensitivity and possible instability. Better change c1, c2.

Author(s)

Nadja Klein

References

Nadja Klein, Thomas Kneib, Stefan Lang and Helga Wagner (2016). Automatic Effect Selection in Distributional Regression via Spike and Slab Priors. Working Paper.

Examples

set.seed(123)
result <- hyperparlin()
r <- result$r
b <- result$b

hyperparlin(alpha1=0.1,alpha2=0.1,c1=0.5,c2=0.1,a=5) 

Marginal Density of \beta

Description

This function computes the marginal density of \beta and for \beta on an equidistant grid specified by the user. Currently only implemented for dim(\beta)=1,2.

Usage

mdbeta(D = 1, rangebeta, ngridbeta, a = 5, b = 25, r = 0.00025,
  a0 = 0.5, b0 = 0.5, plot = FALSE, log = FALSE)

Arguments

Value

the marginal density, the sequence of \beta and depending on specified plot, log arguments also the log-density and plot functions.

Author(s)

Nadja Klein

References

Nadja Klein, Thomas Kneib, Stefan Lang and Helga Wagner (2016). Spike and Slab Priors for Effect Selection in Distributional Regression. Working Paper.

Examples

set.seed(123)
#1-dimensional example
D = 1
ngridbeta = 1000
rangebeta = c(0.000001,1)
a0 = b0 = 0.5
a = 5
b = 50
r = 0.005
mdf <- mdbeta(D=1,rangebeta,ngridbeta,a=a,b=b,r=r,a0=a0,b0=b0) 

#2-dimensional example
D = 2
ngridbeta = 100
rangebeta = c(0.000001,8)
a0 = b0 = 0.5
a = 5
b = 50
r = 0.005
mdf <- mdbeta(D=2,rangebeta,ngridbeta,a=a,b=b,r=r,a0=a0,b0=b0,plot=TRUE,log=TRUE) 
mdf$logpl()

Marginal Density for Given Scale Parameter and Approximated Uniform Prior for \tau

Description

This function computes the marginal density of z_p'\beta for approximated uniform hyperprior for \tau

Usage

mdf_aunif(f, theta, Z, Kinv)

Arguments

Value

the marginal density evaluated at point x.

Author(s)

Nadja Klein

References

Nadja Klein and Thomas Kneib (2015). Scale-Dependent Priors for Variance Parameters in Structured Additive Distributional Regression. Working Paper.

Examples

set.seed(123)
library(MASS)
# prior precision matrix (second order differences) 
# of a spline of degree l=3 and with m=20 inner knots
# yielding dim(K)=m+l-1=22
K <- t(diff(diag(22), differences=2))%*%diff(diag(22), differences=2)
# generalised inverse of K
Kinv <- ginv(K)
# covariate x
x <- runif(1)
Z <- matrix(DesignM(x)$Z_B,nrow=1)
fgrid <- seq(-3,3,length=1000)
mdf <- mdf_aunif(fgrid,theta=0.0028,Z=Z,Kinv=Kinv)

Marginal Density for Given Scale Parameter and Half-Normal Prior for \tau

Description

This function computes the marginal density of z_p'\beta for gamma priors for \tau^2 (referring to a half-normal prior for \tau).

Usage

mdf_ga(f, theta, Z, Kinv)

Arguments

Value

the marginal density evaluated at point x.

Author(s)

Nadja Klein

References

Nadja Klein and Thomas Kneib (2015). Scale-Dependent Priors for Variance Parameters in Structured Additive Distributional Regression. Working Paper.

Examples

set.seed(123)
library(MASS)
# prior precision matrix (second order differences) 
# of a spline of degree l=3 and with m=20 inner knots
# yielding dim(K)=m+l-1=22
K <- t(diff(diag(22), differences=2))%*%diff(diag(22), differences=2)
# generalised inverse of K
Kinv <- ginv(K)
# covariate x
x <- runif(1)
Z <- matrix(DesignM(x)$Z_B,nrow=1)
fgrid <- seq(-3,3,length=1000)
mdf <- mdf_ga(fgrid,theta=0.0028,Z=Z,Kinv=Kinv)

Marginal Density for Given Scale Parameter and Half-Cauchy Prior for \tau

Description

This function computes the marginal density of z_p'\beta for generalised beta prior hyperprior for \tau^2 (half-Chauchy for \tau)

Usage

mdf_gbp(f, theta, Z, Kinv)

Arguments

Value

the marginal density evaluated at point x.

Author(s)

Nadja Klein

References

Nadja Klein and Thomas Kneib (2015). Scale-Dependent Priors for Variance Parameters in Structured Additive Distributional Regression. Working Paper.

Examples

set.seed(123)
library(MASS)
# prior precision matrix (second order differences) 
# of a spline of degree l=3 and with m=20 inner knots
# yielding dim(K)=m+l-1=22
K <- t(diff(diag(22), differences=2))%*%diff(diag(22), differences=2)
# generalised inverse of K
Kinv <- ginv(K)
# covariate x
x <- runif(1)
Z <- matrix(DesignM(x)$Z_B,nrow=1)
fgrid <- seq(-3,3,length=1000)
mdf <- mdf_gbp(fgrid,theta=0.0028,Z=Z,Kinv=Kinv)

Marginal Density for Given Scale Parameter and Inverse Gamma Prior for \tau^2

Description

This function computes the marginal density of z_p'\beta for inverse gamma hyperpriors with shape parameter a=1.

Usage

mdf_ig(f, theta, Z, Kinv)

Arguments

Value

the marginal density evaluated at point x.

Author(s)

Nadja Klein

References

Nadja Klein and Thomas Kneib (2015). Scale-Dependent Priors for Variance Parameters in Structured Additive Distributional Regression. Working Paper.

Examples

set.seed(123)
library(MASS)
# prior precision matrix (second order differences) 
# of a spline of degree l=3 and with m=20 inner knots
# yielding dim(K)=m+l-1=22
K <- t(diff(diag(22), differences=2))%*%diff(diag(22), differences=2)
# generalised inverse of K
Kinv <- ginv(K)
# covariate x
x <- runif(1)
Z <- matrix(DesignM(x)$Z_B,nrow=1)
fgrid <- seq(-3,3,length=1000)
mdf <- mdf_ig(fgrid,theta=0.0028,Z=Z,Kinv=Kinv)

Marginal Density for Given Scale Parameter and Scale-Dependent Prior for \tau^2

Description

This function computes the marginal density of z_p'\beta for scale-dependent priors for \tau^2

Usage

mdf_sd(f, theta, Z, Kinv)

Arguments

Value

the marginal density evaluated at point x.

Author(s)

Nadja Klein

References

Nadja Klein and Thomas Kneib (2015). Scale-Dependent Priors for Variance Parameters in Structured Additive Distributional Regression. Working Paper.

Examples

set.seed(123)
library(MASS)
# prior precision matrix (second order differences) 
# of a spline of degree l=3 and with m=20 inner knots
# yielding dim(K)=m+l-1=22
K <- t(diff(diag(22), differences=2))%*%diff(diag(22), differences=2)
# generalised inverse of K
Kinv <- ginv(K)
# covariate x
x <- runif(1)
Z <- matrix(DesignM(x)$Z_B,nrow=1)
fgrid <- seq(-3,3,length=1000)
mdf <- mdf_sd(fgrid,theta=0.0028,Z=Z,Kinv=Kinv)

Compute Cumulative Distribution Function of Approximated (Differentiably) Uniform Distribution.

Description

Compute Cumulative Distribution Function of Approximated (Differentiably) Uniform Distribution.

Usage

papprox_unif(x, scale, tildec = 13.86294)

Arguments

Details

The cumulative distribution function of dapprox_unif is given by

(1/(log(1+exp(-\tilde{c}))+\tilde{c}))*(\tilde{c}*(\tau^2)^(1/2)/\theta-log(exp((\tau^2)^(1/2)*\tilde{c}/\theta)+exp(\tilde{c})))

\tilde{c} is chosen such that P(\tau^2<=\theta)>=0.95.

Value

the cumulative distribution function.

Author(s)

Nadja Klein

References

Nadja Klein and Thomas Kneib (2015). Scale-Dependent Priors for Variance Parameters in Structured Additive Distributional Regression. Working Paper.

See Also

rapprox_unif,dapprox_unif

Draw Random Numbers from Approximated (Differentiably) Uniform Distribution.

Description

Draw Random Numbers from Approximated (Differentiably) Uniform Distribution.

Usage

rapprox_unif(n = 100, scale, tildec = 13.86294, seed = 123)

Arguments

Details

The method is based on the inversion method and the quantile function is computed numerically using uniroot.

Value

n draws with density papprox_unif.

Author(s)

Nadja Klein

References

Nadja Klein and Thomas Kneib (2015). Scale-Dependent Priors for Variance Parameters in Structured Additive Distributional Regression. Working Paper.

See Also

rapprox_unif,papprox_unif

Prior precision matrix for spatial variable in Zambia data set

Description

This is a 57x57 matrix containing row- and columwise the regions of Zambia, and the entries define the neighbourhoodstructure. The corresponding map sambia.bnd can be downloaded from http://www.stat.uni-muenchen.de/~kneib/regressionsbuch/daten_e.html. from the bnd file the prior precision matrix is obtained by library(BayesX) map <- read.bnd("zambia.bnd") K <- bnd2gra(map)

Malnutrition in Zambia

Description

The primary goal of a statistical analysis is to determine the effect of certain socioeconomic variables of the child, the mother, and the household on the child's nutritional condition

• zscore child's Z-score

• c _breastf duration of breastfeeding in months

• c_age child's age in months

• m_agebirth mother's age at birth in years

• m_height mother's height in centimeter

• m_bmi mother's body mass index

• m_education mother's level of education

• m_work mother's work status

• region region of residence in Zambia

• district district of residence in Zambia

Format

A data frame with 4421 rows and 21 variables

Source

http://www.stat.uni-muenchen.de/~kneib/regressionsbuch/daten_e.html