mandd {lazy.tools}

R Documentation

Calculates mean vector and dispersion matrix with case weight

Description

Calculates mean vector and dispersion matrix with case weight

Usage

mandd(
  data,
  weight = 1,
  by = NULL,
  byvarname = NULL,
  vardef = "n",
  nocov = 0,
  cor = 0,
  print = 0,
  simplify = 0
)

Arguments

data	data matrix or data frame.
weight	case weight vector of length nrow(data) or 1.
by	a factor or a list of factors, each of length nrow(data) to be used as the INDICES of by function.
byvarname	vector containing the names of by varialbes to be used. (Not Yet Implemented.)
vardef	= "n-1" to use n-1 as denominator for variance.
nocov	= 1 to skip the calculation of the variance/covariance matrix. mands function will be used.
cor	= 1 to return the correlation matrix as well.
print	= 1 to print the result
simplify	= 1 to simplify the rewult when by= is given

Details

When the dispersion matrix is not needed (nocov=1) use mands function.
When simplified=0 is given, the result is a list consisting of
vectors: mean, var, std, nobs
matrix: cov, nobspair
scalars: n, vardef
where nobspair is a matrix of the same size as cov containing the weighted # of observations used to calculate cov.
When cor=1 is given, correlation matrix will also be returned.

When by is specified, the result is a class by list if simplify=0, Otherwise, it is a list consisting of
matrices: mean, var, std, nobs
lists: cov, nobspair
scalars: n, vardef

To convert the list of covariance matrices to an array or stacked matrix, use:
library(lazy.mat)
cov_array=l2a(res1$cov)
cov_mat=a2m(cov_array,method=2)

Value

list of:
mean vector, var vector, std vector, nobs vector,
where nobs is sum(weights) for nonmissing obs and n=nrow(data).
cov matrix, nobspair matrix which contains # of obs. per pair , or NULL,
n (# of rows), and vardef.

Examples

##################################
# data matrix with by group
##################################
nobs <- 1000
ndims <- 2

# covariance matrix
cov <- 0.2
C1 <- matrix(cov,ndims,ndims)+(1-cov)*diag(ndims)
C1[1,1] <- .5
C2 <- -C1; diag(C2) <- diag(C1)
C3 <- diag(ndims)
Print(C1,C2,C3)

# random numbers
seed=1701
set.seed(seed)

# X1 ~ N(0,C1),  X2 ~ N(0,C2),   X3 ~ N(0,C3)
X1=matrix(rnorm(nobs*ndims),nobs)
ev <- eigen(C1); eva <- diag(ev$values); eve <- ev$vectors
X1 <- X1%*%diag(sqrt(ev$values))%*%t(ev$vectors)
X2 <- matrix(rnorm(nobs*ndims),nobs)
ev <- eigen(C2); eva <- diag(ev$values); eve <- ev$vectors
X2 <- X2%*%diag(sqrt(ev$values))%*%t(ev$vectors)
X3 <- matrix(rnorm(nobs*ndims),nobs)

X <- rbind(X1,X2,X3)
byvar <- rep(c("pos","neg","zero"), each=nobs)

# missing values
locmiss <- sample(1:length(X), 0.2*length(X))
X[locmiss]=NA

# statistics w/o by-group
res0 <- mandd( X )
# statistics by by-group
res1 <- mandd( X, 1, byvar, simplify=1 )
Print(res1$mean, res1$std, res1$cov)


#############################
# grid points and weight
#############################
# C1, C2, C3 are defined above.
npoints <- 11; thmin <- -3; thmax <- 3; nobs2 <- 10000
theta <- seq(thmin,thmax,length.out=npoints)
theta <- cprod(theta,theta)
if( ndims > 2 )
 for( i in 2:ndims )
  theta <- cprod(theta,theta)

# weight:  pdf of N(0,C1)
thdist1 <- exp( -0.5*diag( theta%*%solve(C1)%*%t(theta) ) )
thdist1 <- thdist1/sum(thdist1)
n1 <- round(nobs2*thdist1+.5)

# statistics
res20 <- mandd( theta, n1 )
res200 <- mandd( theta )
Print(res20$mean, res200$mean)
Print(res20$var, res200$var)
Print(C1, res20$cov, res200$cov)


# missing values
seed <- 1701
set.seed(seed)
locmiss1 <- sample( 1:(npoints^ndims), max(1,(npoints^ndims)/10) )
theta[locmiss1] <- NA

# statistics
res2 <- mandd( theta, n1 )
Print(res2$mean, res2$std, res2$cov)


# grid points and weight with by group
# theta, nobs2, C1, C2, C3 are defined above.
# weight:  pdf of N(0,C2)
thdist2 <- exp( -0.5*diag( theta%*%solve(C2)%*%t(theta) ) )
thdist2[is.na(thdist2)] <- 0
thdist2 <- thdist2/sum(thdist2)
n2 <- round(nobs2*thdist2+.5)
# weight:  pdf of N(0,C3)
thdist3 <- exp( -0.5*diag( theta%*%solve(C3)%*%t(theta) ) )
thdist3[is.na(thdist3)] <- 0
thdist3 <- thdist3/sum(thdist3)
n3 <- round(nobs2*thdist3+.5)

Theta=rbind(theta,theta,theta)
n=c(n1,n2,n3)
byvar2=rep(c("pos","neg","zero"),each=nrow(theta))

# statistics
res3 <- mandd( Theta, n, byvar2, simplify=1 )
Print(res3$mean, res3$std, res3$cov)

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