Create a database for gross flows.

Description

Create a database based on \xi model.

Usage

createBase(x)

Arguments

Value

createBase returns data.table,data.frame that contains the data base based on \xi model.

Examples

candidates_t0 <- c("Candidate1","Candidate2","Candidate3","Candidate4",
	"Candidate5","WhiteVote", "NoVote")
candidates_t1 <- c("Candidate3","Candidate5","WhiteVote", "NoVote")

N 	   <- 100000
nCanT0  <- length(candidates_t0)
nCanT1  <- length(candidates_t1)

eta <- matrix(c(0.10, 0.10, 0.20, 0.17, 0.28, 0.1, 0.05),
			   byrow = TRUE, nrow = nCanT0)
P <- matrix(c(0.10, 0.60, 0.15, 0.15,
			  0.30, 0.10, 0.25,	0.35,
			  0.34, 0.25, 0.16, 0.25,
			  0.25,	0.05, 0.35,	0.35,
			  0.10, 0.25, 0.45,	0.20,
			  0.12, 0.36, 0.22, 0.30,
			  0.10,	0.15, 0.30,	0.45),
	 byrow = TRUE, nrow = nCanT0)

citaModel <- matrix(, ncol = nCanT1, nrow = nCanT0)
row.names(citaModel) <- candidates_t0
colnames(citaModel) <- candidates_t1

for(ii in 1:nCanT0){ 
 citaModel[ii,] <- c(rmultinom(1, size = N * eta[ii,], prob = P[ii,]))
}

# # Model I
psiI   <- 0.9
rhoRRI <- 0.9
rhoMMI <- 0.5

citaModI <- matrix(nrow = nCanT0 + 1, ncol = nCanT1 + 1)
rownames(citaModI) <- c(candidates_t0, "Non_Resp")
colnames(citaModI) <- c(candidates_t1, "Non_Resp")

citaModI[1:nCanT0, 1:nCanT1] 		 <- P * c(eta) * rhoRRI * psiI  
citaModI[(nCanT0 + 1), (nCanT1 + 1)]  <- rhoMMI * (1-psiI) 
citaModI[1:nCanT0, (nCanT1 + 1)]  	 <-  (1-rhoRRI) * psiI * rowSums(P * c(eta))
citaModI[(nCanT0 + 1), 1:nCanT1 ] 	 <-  (1-rhoMMI) * (1-psiI) * colSums(P * c(eta))
citaModI   <- round_preserve_sum(citaModI * N)
DBmodCitaI <- createBase(citaModI)
DBmodCitaI

Gross Flows estimation

Description

Gross Flows under complex electoral surveys.

Usage

estGF(
  sampleBase = NULL,
  niter = 100,
  model = NULL,
  colWeights = NULL,
  nonrft = FALSE
)

Arguments

Details

The population size N must satisfy the condition:

N = \sum_{j}\sum_{i} N_{ij} + \sum_{j} C_{j} + \sum_{i} R_{i} + M

where, N_{ij} is the amount of people interviewed who have classification i at first time and classification j at second time, R_{i} is the amount of people who did not respond at second time, but did at first time, C_{j} is the amount of people who did not respond at first time, but they did at second time and M is the number of people who did not respond at any time or could not be reached. Let \eta_{i} the initial probability that a person has classification i in the first time, and let p_{ij} the vote transition probability for the cell (i,j), where \sum_{i} \eta_{i} = 1 and \sum_{j} p_{ij} = 1. Thus, four possibles models for the gross flows are given by:

1. Model I: This model assumes that a person's initial probability of being classified as i at first time is the same for everyone, that is, \psi(i,j) = \psi. Besides, transition probabilities between respond and non response not depend of the classification (i,j), that is \rho_{MM}(i,j) = \rho_{MM} and \rho_{RR}(i,j) = \rho_{RR}.

2. Model II: Unlike 'Model I', this model assumes that person initial probability that person has classification (i,j), only depends of his classification at first time, that is \psi(i,j) = \psi(i).

3. Model III: Unlike 'Model I', this model assumes that transition probabilities between response and non response only depends of probability classification at first time, that is \rho_{MM}(i,j) = \rho_{MM}(i) and \rho_{RR}(i,j) = \rho_{RR}(i).

4. Model IV: Unlike 'Model I', this model assumes that transition probabilities between response and non response only depends of probability classification at second time, that is \rho_{MM}(i,j) = \rho_{MM}(j) and \rho_{RR}(i,j) = \rho_{RR}(j).

Value

estGF returns a list containing:

1. Est.CIV: a data.frame containing the gross flows estimation.

2. Params.Model: a list that contains the \hat{\eta}_{i}, \hat{p}_{ij}, \hat{\psi}(i,j), \hat{\rho}_{RR}(i,j), \hat{\rho}_{MM}(i,j) parameters for the estimated model.

3. Sam.Est: a list containing the sampling estimators \hat{N}_{ij}, \hat{R}_{i}, \hat{C}_{j}, \hat{M}, \hat{N}.

References

Stasny, E. (1987), ‘Some markov-chain models for nonresponse in estimating gross’, Journal of Oficial Statistics 3, pp. 359-373.
Sarndal, C.-E., Swensson, B. & Wretman, J. (1992), Model Assisted Survey Sampling, Springer-Verlag, New York, USA.
Gutierrez, A., Trujillo, L. & Silva, N. (2014), ‘The estimation of gross ows in complex surveys with random nonresponse’, Survey Methodology 40(2), pp. 285-321.

Examples

library(TeachingSampling)
library(data.table)
# Colombia's electoral candidates in 2014
candidates_t0 <- c("Clara","Enrique","Santos","Martha","Zuluaga","WhiteVote", "NoVote")
candidates_t1 <- c("Santos","Zuluaga","WhiteVote", "NoVote")

N <- 100000
nCanT0 <- length(candidates_t0)
nCanT1 <- length(candidates_t1)
# Initial probabilities
eta <- matrix(c(0.10, 0.10, 0.20, 0.17, 0.28, 0.1, 0.05),
				byrow = TRUE, nrow = nCanT0)
# Transition probabilities
P <- matrix(c(0.10, 0.60, 0.15, 0.15,
				 0.30, 0.10, 0.25,0.35,
				 0.34, 0.25, 0.16, 0.25,
				 0.25,0.05, 0.35,0.35,
				 0.10, 0.25, 0.45,0.20,
				 0.12, 0.36, 0.22, 0.30,
				 0.10,0.15, 0.30,0.45),
		byrow = TRUE, nrow = nCanT0)
citaMod <- matrix(, ncol = nCanT1, nrow = nCanT0)
row.names(citaMod) <- candidates_t0
colnames(citaMod) <- candidates_t1

for(ii in 1:nCanT0){
		citaMod[ii,] <- c(rmultinom(1, size = N * eta[ii,], prob = P[ii,]))
}

# # Model I
psiI   <- 0.9
rhoRRI <- 0.9
rhoMMI <- 0.5

citaModI <- matrix(nrow = nCanT0 + 1, ncol = nCanT1 + 1)
rownames(citaModI) <- c(candidates_t0, "Non_Resp")
colnames(citaModI) <- c(candidates_t1, "Non_Resp")
citaModI[1:nCanT0, 1:nCanT1] <- P * c(eta) * rhoRRI * psiI
citaModI[(nCanT0 + 1), (nCanT1 + 1)] <- rhoMMI * (1-psiI)
citaModI[1:nCanT0, (nCanT1 + 1)] <- (1-rhoRRI) * psiI * rowSums(P * c(eta))
citaModI[(nCanT0 + 1), 1:nCanT1 ] <- (1-rhoMMI) * (1-psiI) * colSums(P * c(eta))
citaModI <- round_preserve_sum(citaModI * N)
DBcitaModI <- createBase(citaModI)

# Creating auxiliary information
DBcitaModI[,AuxVar := rnorm(nrow(DBcitaModI), mean = 45, sd = 10)]

# Selects a sample with unequal probabilities
res <- S.piPS(n = 3200, as.data.frame(DBcitaModI)[,"AuxVar"])
sam <- res[,1]
pik <- res[,2]
DBcitaModISam <- copy(DBcitaModI[sam,])
DBcitaModISam[,Pik := pik]

# Gross Flows estimation
estima <- estGF(sampleBase = DBcitaModISam, niter = 500, model = "I", colWeights = "Pik")
estima

Gross flows variance estimation.

Description

Gross flows variance estimation according to resampling method (Bootstrap or Jackknife).

Usage

reSamGF(
  sampleBase = NULL,
  nRepBoot = 500,
  model = "I",
  niter = 100,
  type = "Bootstrap",
  colWeights = NULL,
  nonrft = FALSE
)

Arguments

Details

The resampling methods for variance estimation are:

Bootstrap:

This technique allows to estimate the sampling distribution of almost any statistic by using random sampling methods. Bootstrapping is the practice of estimating properties of an statistic (such as its variance) by measuring those properties from it's approximated sample.

Jackknife:

The jackknife estimate of a parameter is found by systematically leaving out each observation from a dataset and calculating the estimate and then finding the average of these calculations. Given a sample of size n, the jackknife estimate is found by aggregating the estimates of each n-1-sized sub-sample.

Value

reSamGF returns a list that contains the variance of each parameter of the selected model.

References

Efron, B. (1979), ‘Computers and the theory of statistics: Thinking the unthinkable’, SIAM review 21(4), pp. 460-480.
Quenouille, M. H. (1949), ‘Problems in plane sampling’, The Annals of Mathematical Statistics pp. 355-375.
Tukey, J. W. (1958), ‘Bias and confidence in not-quite large samples’, Annals of Mathematical Statistics 29, pp. 614.

Examples

library(TeachingSampling)
library(data.table)
# Colombia's electoral candidates in 2014
candidates_t0 <- c("Clara","Enrique","Santos","Martha","Zuluaga","Blanco", "NoVoto")
candidates_t1 <- c("Santos","Zuluaga","Blanco", "NoVoto")

N 	   <- 100000
nCanT0  <- length(candidates_t0)
nCanT1  <- length(candidates_t1)

# Initial probabilities 
eta <- matrix(c(0.10, 0.10, 0.20, 0.17, 0.28, 0.1, 0.05),
			   byrow = TRUE, nrow = nCanT0)
# Transition probabilities
P <- matrix(c(0.10, 0.60, 0.15, 0.15,
			  0.30, 0.10, 0.25,	0.35,
			  0.34, 0.25, 0.16, 0.25,
			  0.25,	0.05, 0.35,	0.35,
			  0.10, 0.25, 0.45,	0.20,
			  0.12, 0.36, 0.22, 0.30,
			  0.10,	0.15, 0.30,	0.45),
	 byrow = TRUE, nrow = nCanT0)

citaMod <- matrix(, ncol = nCanT1, nrow = nCanT0)
row.names(citaMod) <- candidates_t0
colnames(citaMod) <- candidates_t1

for(ii in 1:nCanT0){ 
 citaMod[ii,] <- c(rmultinom(1, size = N * eta[ii,], prob = P[ii,]))
}

# # Model I
psiI   <- 0.9
rhoRRI <- 0.9
rhoMMI <- 0.5

citaModI <- matrix(nrow = nCanT0 + 1, ncol = nCanT1 + 1)
rownames(citaModI) <- c(candidates_t0, "Non_Resp")
colnames(citaModI) <- c(candidates_t1, "Non_Resp")

citaModI[1:nCanT0, 1:nCanT1] 		 <- P * c(eta) * rhoRRI * psiI  
citaModI[(nCanT0 + 1), (nCanT1 + 1)]  <- rhoMMI * (1-psiI) 
citaModI[1:nCanT0, (nCanT1 + 1)]  	 <-  (1-rhoRRI) * psiI * rowSums(P * c(eta))
citaModI[(nCanT0 + 1), 1:nCanT1 ] 	 <-  (1-rhoMMI) * (1-psiI) * colSums(P * c(eta))
citaModI   <- round_preserve_sum(citaModI * N)
DBcitaModI <- createBase(citaModI)

# Creating auxiliary information
DBcitaModI[,AuxVar := rnorm(nrow(DBcitaModI), mean = 45, sd = 10)]
# Selects a sample with unequal probabilities
res <- S.piPS(n = 1200, as.data.frame(DBcitaModI)[,"AuxVar"])
sam <- res[,1]
pik <- res[,2]
DBcitaModISam <- copy(DBcitaModI[sam,])
DBcitaModISam[,Pik := pik]

# Gross flows estimation
estima <- estGF(sampleBase = DBcitaModISam, niter = 500, model = "II", colWeights = "Pik")
# gross flows variance estimation
varEstima <- reSamGF(sampleBase = DBcitaModISam, type = "Bootstrap", nRepBoot = 100,
						model = "II", niter = 101,  colWeights = "Pik")
varEstima

Round preserve sum.

Description

Rounds a vector of numbers while preserving the sum of them.

Usage

round_preserve_sum(x, digits = 0)

Arguments

Value

round_preserve_sum returns y with round vector.

Source

https://www.r-bloggers.com/2016/07/round-values-while-preserve-their-rounded-sum-in-r/ and https://stackoverflow.com/questions/32544646/round-vector-of-numerics-to-integer-while-preserving-their-sum

Examples

sum(c(0.333, 0.333, 0.334))
round(c(0.333, 0.333, 0.334), 2)
sum(round(c(0.333, 0.333, 0.334), 2))
round_preserve_sum(c(0.333, 0.333, 0.334), 2)
sum(round_preserve_sum(c(0.333, 0.333, 0.334), 2))