tdVA {modernVA}

R wrapper that accesses C code to fit temporal dependent value-added models for two cohorts

Description

tdVA is the main function used to fit the temporally dependent value-added model for two cohorts

Usage

tdVA(y1, xmat1,
     y2, xmat2,
     school1, school2,
     groupID=NULL,
     model=0,
     priors=c(0, 100^2, 1, 1, 1, 1, 0, 100^2, -1, 1, 0, 100^2, 0, 100^2),
     var.global=TRUE,
     MHsd=c(0.2),
     nchains=1,
     draws=50000, burn=40000, thin=10,
     verbose=FALSE)

Arguments

y1

numeric vector (response variable) of length N1 for cohort 1. Must be in long format.

y2

numeric vector (response variable) of Length N2 for cohort 2. Must be in long format.

xmat1

N1 x p matrix of covariates for cohort 1 (column of 1's must NOT be included).

xmat2

N2 x p matrix of covariates for cohort 2 (column of 1's must NOT be included).

school1

numeric vector indicating to which school each student belongs for cohort 1. These labels must be contiguous labels and start with 1

school2

numeric vector indicating to which school each student belongs for cohort 2. These labels must be contiguous labels and start with 1

groupID

Optional vector that identifies to which group a school belongs. If NULL there is no grouping

model

Integer indicating which value-added model is to be fit

0 - Independent school effects between the two cohorts.

1 - Temporally dependent school effects between two cohorts based on a non-statinary AR(1) process,

2 - Temporally dependent school effects based on previous cohorts post-test performance.

3 - Full model that includes both an AR(1) type correlation and one based on previous cohorts post-test performance.

priors

Vector of prior distribution parameter values.

mb - prior mean for beta1 and beta2, default is 0.

s2b - prior variance for beta1 and beta2, default is 100^2.

at - prior shape for tau22 and tau21, default is 1.

bt - prior rate for tau22 and tau21, default is 1.

as - prior shape for sigma2, default is 1.

bs - prior rate for sigma2, default is 1.

mg - prior mean for gamma2, default is 0. (only used if model = 2)

s2g - prior variance for gamma2, default is 100^2. (only used if model = 2)

lp12 - prior lower bound for for phi12, default is -1. (only used if model = 1)

up12 - prior upper bound for for phi12, default is 1. (only used if model = 1)

mp02 - prior mean for phi02, default is 0.

s202 - prior variance for phi02, default is 100^2.

mp01 - prior mean for phi01, default is 0.

s201 - prior variance for phi01, default is 100^2.

var.global

Logical argument. If true, then a model with common sigma21 and sigma22 among schools is fit. If false, then a model with school-specific sigma21i and sigma22i is fit.

MHsd

Tuning parameter associated with M-H step of phi12. Default is 0.2

nchains

number of MCMC chains to run. Default is 1

draws

number of MCMC iterates to be collected. default is 50,000

burn

number of MCMC iterates discared as burn-in. default is 40,000

thin

number by which the MCMC chain is thinne. default is 10

verbose

Logical indicating if progress of MCMC algorithm should be printed to screen along with other data summaries

Value

This function returns a list that contains MCMC iterates for all the model parameters in addition to the value-added estimates and intervals for each of the two cohorts

Examples

# Generate data from model 1 of San Martin el al.
m <- 25 # number of schools
ni <- 20 # number of students per school
N <- m*ni

# specify parameter values to generate data
beta1 <- 0.6
beta2 <- 0.75;
sig21 <- 100;
sig22 <- 100;
tau2 <- 100
phi02 <- 0;
phi12 <- 0.75;
phi01 <- 0

X1 <- rnorm(N, 0, sqrt(200))
X2 <- rnorm(N, 0, sqrt(200))

alpha1 <- rnorm(m, phi01, sqrt(tau2))
alpha2 <- rnorm(m, phi02 + phi12*alpha1, sqrt(tau2*(1-phi12^2)))

Y1 <- rep(alpha1, each=ni) + X1*beta1 + rnorm(N, 0, sqrt(sig21))
Y2 <- rep(alpha2, each=ni) + X2*beta2 + rnorm(N, 0, sqrt(sig22))

# Create school vector indicating to which school each observation belongs
school1 <- rep(1:m, each=ni)
school2 <- rep(1:m, each=ni)


# design matrix only one covariate and no intercept
X1i <- cbind(X1)
X2i <- cbind(X2)


fit <- tdVA(y1=Y1,xmat1=X1i,y2=Y2,xmat2=X2i,
              school1=school1,school2=school2, groupID=NULL, model=2,
              var.global=TRUE, nchains=1)

# Value-added estimates of cohort 1 and 2 with 95% credible intervals.  See paper for details
cbind(fit$VA1.estimate,t(fit$VA1.intervals))
cbind(fit$VA2.estimate,t(fit$VA2.intervals))