Package 'PracTools'

Description

Compute components of relvariance for a sample design where primary sampling units (PSUs) are selected with probability proportional to size (pps) and elements are selected via simple random sampling (srs). The input is an entire sampling frame.

Usage

BW2stagePPS(X, pp, psuID, lonely.SSU = "mean")

Arguments

Details

BW2stagePPS computes the between and within population relvariance components appropriate for a two-stage sample in which PSUs are selected with varying probabilities and with replacement. Elements within PSUs are selected by simple random sampling. The components are appropriate for approximating the relvariance of the probability-with-replacement (pwr)-estimator of a total when the same number of elements are selected within each sample PSU. The function requires that an entire frame of PSUs and elements be input.

If a PSU contains multiple SSUs, some of which have missing data, or contains only one SSU, a value is imputed. If lonely.SSU = "mean", the mean of the non-missing PSU contributions is imputed. If lonely.SSU = "zero", a 0 is imputed. The former would be appropriate if a PSU contains multiple SSUs but one or more of them has missing data in which case R will normally calculate an NA. The latter would be appropriate if the PSU contains only one SSU which would be selected with certainty in any sample.

If any PSUs have one-draw probabilities of 1 (pp=1), they will be excluded from all computations.

(Use BW2stagePPSe if only a sample of PSUs and elements is available.)

Value

List object with values:

Author(s)

Richard Valliant, Jill A. Dever, Frauke Kreuter

References

Cochran, W.G. (1977, pp.308-310). Sampling Techniques. New York: John Wiley & Sons.

Saerndal, C.E., Swensson, B., and Wretman, J. (1992). Model Assisted Survey Sampling. New York: Springer.

Valliant, R., Dever, J., Kreuter, F. (2018, sect. 9.2.3). Practical Tools for Designing and Weighting Survey Samples, 2nd edition. New York: Springer.

See Also

BW2stagePPSe, BW2stageSRS, BW3stagePPS, BW3stagePPSe

Examples

data(MDarea.popA)
MDsub <- MDarea.popA[1:100000,]
    # Use PSU and SSU variables to define psu's
pp.PSU <- table(MDsub$PSU) / nrow(MDsub)
pp.SSU <- table(MDsub$SSU) / nrow(MDsub)
    # components with psu's defined by the PSU variable
BW2stagePPS(MDsub$y1, pp=pp.PSU, psuID=MDsub$PSU, lonely.SSU="mean")
    # components with psu's defined by the SSU variable
BW2stagePPS(MDsub$y1, pp=pp.SSU, psuID=MDsub$SSU, lonely.SSU="mean")

    # Use census tracts and block groups to define psu's
trtBG <- 10*MDsub$TRACT + MDsub$BLKGROUP
pp.trt <- table(MDsub$TRACT) / nrow(MDsub)
pp.BG <- table(trtBG) / nrow(MDsub)
    # components with psu's defined by tracts
BW2stagePPS(MDsub$ins.cov, pp=pp.trt, psuID=MDsub$TRACT, lonely.SSU="mean")
    # components with psu's defined by block groups
BW2stagePPS(MDsub$ins.cov, pp=pp.BG, psuID=trtBG, lonely.SSU="mean")

Description

Estimate components of relvariance for a sample design where primary sampling units (PSUs) are selected with pps and elements are selected via srs. The input is a sample selected in this way.

Usage

BW2stagePPSe(Ni, ni, X, psuID, w, m, pp, lonely.SSU = "mean")

Arguments

Details

BW2stagePPSe computes the between and within population variance and relvariance components appropriate for a two-stage sample in which PSUs are selected with varying probabilities and with replacement. Elements within PSUs are selected by simple random sampling. The number of elements selected within each sample PSU can vary but must be at least two. The estimated components are appropriate for approximating the relvariance of the pwr-estimator of a total when the same number of elements are selected within each sample PSU. This function can also be used if PSUs are selected by srswr by appropriate definition of pp.

If a PSU contains multiple SSUs, some of which have missing data, or contains only one SSU, a value is imputed. If lonely.SSU = "mean", the mean of the non-missing PSU contributions is imputed. If lonely.SSU = "zero", a 0 is imputed. The former would be appropriate if a PSU contains multiple SSUs but one or more of them has missing data in which case R will normally calculate an NA. The latter would be appropriate if the PSU contains only one SSU which would be selected with certainty in any sample.

If any PSUs have one-draw probabilities of 1 (pp=1), the function will be halted. Any such PSUs should be removed before calling the function.

Value

List with values:

Author(s)

Richard Valliant, Jill A. Dever, Frauke Kreuter

References

Cochran, W.G. (1977, pp.308-310). Sampling Techniques. New York: John Wiley & Sons.

Valliant, R., Dever, J., Kreuter, F. (2018, sect. 9.4.1). Practical Tools for Designing and Weighting Survey Samples, 2nd edition. New York: Springer.

See Also

BW2stagePPS, BW2stageSRS, BW3stagePPS, BW3stagePPSe

Examples

require(sampling)
require(plyr)      # has function that allows renaming variables
data(MDarea.popA)
Ni <- table(MDarea.popA$TRACT)
m <- 20
probi <- m*Ni / sum(Ni)
    # select sample of clusters
sam <- cluster(data=MDarea.popA, clustername="TRACT", size=m, method="systematic",
                pik=probi, description=TRUE)
    # extract data for the sample clusters
samclus <- getdata(MDarea.popA, sam)
samclus <- rename(samclus, c("Prob" = "pi1"))


    # treat sample clusters as strata and select srswor from each
s <- strata(data = as.data.frame(samclus), stratanames = "TRACT",
            size = rep(50,m), method="srswor")
# extracts the observed data
samdat <- getdata(samclus,s)
samdat <- rename(samdat, c("Prob" = "pi2"))

    # extract pop counts for PSUs in sample
pick <- names(Ni) %in% sort(unique(samdat$TRACT))
Ni.sam <- Ni[pick]
pp <- Ni.sam / sum(Ni)
wt <- 1/samdat$pi1/samdat$pi2

BW2stagePPSe(Ni = Ni.sam, ni = rep(50,20), X = samdat$y1,
            psuID = samdat$TRACT, w = wt,
            m = 20, pp = pp, lonely.SSU="mean")

Description

Compute components of relvariance for a sample design where primary sampling units (PSUs) and elements are selected via srs. The input is an entire sampling frame.

Usage

BW2stageSRS(X, psuID, lonely.SSU)

Arguments

Details

BW2stageSRS computes the between and within population relvariance components appropriate for a two-stage sample in which PSUs are selected via srs (either with or without replacement). Elements within PSUs are assumed to be selected by srswor. The same number of elements is assumed to be selected within each sample PSU. The function requires that an entire frame of PSUs and elements be input.

If a PSU contains multiple SSUs, some of which have missing data, or contains only one SSU, a value is imputed. If lonely.SSU = "mean", the mean of the non-missing PSU contributions is imputed. If lonely.SSU = "zero", a 0 is imputed. The former would be appropriate if a PSU contains multiple SSUs but one or more of them has missing data in which case R will normally calculate an NA. The latter would be appropriate if the PSU contains only one SSU which would be selected with certainty in any sample.

(Use BW2stagePPSe if only a sample of PSUs and elements are available.)

Value

List with values:

Author(s)

Richard Valliant, Jill A. Dever, Frauke Kreuter

References

Cochran, W.G. (1977, chap. 11). Sampling Techniques. New York: John Wiley & Sons.

Valliant, R., Dever, J., Kreuter, F. (2018, sect. 9.2.1). Practical Tools for Designing and Weighting Survey Samples, 2nd edition. New York: Springer.

See Also

BW2stagePPS, BW2stagePPSe, BW3stagePPS, BW3stagePPSe

Examples

data(MDarea.popA)
MDsub <- MDarea.popA[1:100000,]
    # psu's are defined by PSU variable
BW2stageSRS(abs(MDsub$Hispanic-2), psuID=MDsub$PSU, lonely.SSU="mean")
    # psu's are defined by SSU variable
BW2stageSRS(abs(MDsub$Hispanic-2), psuID=MDsub$SSU, lonely.SSU="mean")

Description

Compute components of relvariance for a sample design where primary sampling units (PSUs) are selected with ppswr and secondary sampling units (SSUs) and elements within SSUs are selected via srs. The input is an entire sampling frame.

Usage

BW3stagePPS(X, pp, psuID, ssuID, lonely.SSU = "mean", lonely.TSU = "mean")

Arguments

Details

BW3stagePPS computes the between and within population relvariance components appropriate for a three-stage sample in which PSUs are selected with varying probabilities and with replacement. SSUs and elements within SSUs are selected by simple random sampling. The components are appropriate for approximating the relvariance of the pwr-estimator of a total when the same number of SSUs are selected within each PSU, and the same number of elements are selected within each sample SSU. The function requires that an entire sampling frame of PSUs and elements be input.

If a PSU contains multiple SSUs, some of which have missing data, or contains only one SSU, a value is imputed. If lonely.SSU = "mean", the mean of the non-missing PSU contributions is imputed. If lonely.SSU = "zero", a 0 is imputed. The former would be appropriate if a PSU contains multiple SSUs but one or more of them has missing data in which case R will normally calculate an NA. The latter would be appropriate if the PSU contains only one SSU which would be selected with certainty in any sample. lonely.TSU has a similar purpose for third-stage units.

(Use BW2stagePPSe if only a sample of PSUs, SSUs, and elements is available.)

Value

List with values:

Author(s)

Richard Valliant, Jill A. Dever, Frauke Kreuter

References

Hansen,M.H., Hurwitz,W.N., and Madow,W.G. (1953, chap. 9, p.211). Sample Survey Methods and Theory, Vol.I. John Wiley & Sons.

Saerndal, C.E., Swensson, B., and Wretman, J. (1992, p.149). Model Assisted Survey Sampling. Springer.

Valliant, R., Dever, J., Kreuter, F. (2018, sect. 9.2.4). Practical Tools for Designing and Weighting Survey Samples, 2nd edition. New York: Springer.

See Also

BW2stagePPS, BW2stagePPSe, BW2stageSRS, BW3stagePPSe

Examples

data(MDarea.popA)
MDsub <- MDarea.popA[1:100000,]
M <- length(unique(MDsub$PSU))
    # srs/srs/srs design
pp.PSU <- rep(1/M,M)
BW3stagePPS(X=MDsub$y1, pp=pp.PSU, psuID=MDsub$PSU, ssuID=MDsub$SSU,
    lonely.SSU = "mean", lonely.TSU = "mean")
    # ppswr/srs/srs design
pp.PSU <- table(MDsub$PSU) / nrow(MDsub)
BW3stagePPS(X=MDsub$y1, pp=pp.PSU, psuID=MDsub$PSU, ssuID=MDsub$SSU,
    lonely.SSU = "mean", lonely.TSU = "mean")

Description

Estimate components of relvariance for a sample design where primary sampling units (PSUs) are selected with probability proportional to size with replacement (ppswr) and secondary sampling units (SSUs) and elements within SSUs are selected via simple random sampling (srs). The input is a sample selected in this way.

Usage

BW3stagePPSe(dat, v, Ni, Qi, Qij, m, lonely.SSU = "mean", lonely.TSU = "mean")

Arguments

Details

BW3stagePPSe computes the between and within population relvariance components appropriate for a three-stage sample in which PSUs are selected with varying probabilities and with replacement. SSUs and elements within SSUs are selected by simple random sampling. The estimated components are appropriate for approximating the relvariance of the pwr-estimator of a total when the same number of SSUs are selected within each PSU, and the same number of elements are selected within each sample SSU.

If a PSU contains multiple SSUs, some of which have missing data, or contains only one SSU, a value is imputed. If lonely.SSU = "mean", the mean of the non-missing PSU contributions is imputed. If lonely.SSU = "zero", a 0 is imputed. The former would be appropriate if a PSU contains multiple SSUs but one or more of them has missing data in which case R will normally calculate an NA. The latter would be appropriate if the PSU contains only one SSU which would be selected with certainty in any sample. lonely.TSU has a similar purpose for third-stage units.

Value

List with values:

Author(s)

Richard Valliant, Jill A. Dever, Frauke Kreuter

References

Hansen, M.H., Hurwitz, W.N., and Madow, W.G. (1953, chap. 9, sect. 10). Sample Survey Methods and Theory, Vol.II. New York: John Wiley & Sons.

Valliant, R., Dever, J., Kreuter, F. (2018, sect. 9.4.2). Practical Tools for Designing and Weighting Survey Samples, 2nd edition. New York: Springer.

See Also

BW2stagePPS, BW2stagePPSe, BW2stageSRS, BW3stagePPS

Examples

# select 3-stage sample from Maryland population
set.seed(-780087528)
data(MDarea.popA)
MDpop <- MDarea.popA
require(sampling)
require(plyr)      # has function that allows renaming variables
    # make counts of SSUs and elements per PSU
xx <- do.call("rbind",list(by(1:nrow(MDpop),MDpop$SSU,head,1)))
pop.tmp <- MDpop[xx,]
Ni <- table(pop.tmp$PSU)
Qi <- table(MDarea.popA$PSU)
Qij <- table(MDpop$SSU)
m <- 30         # no. of PSUs to select
probi <- m*Qi / sum(Qi)
    # select sample of clusters
sam <- cluster(data=MDpop, clustername="PSU", size=m, method="systematic",
               pik=probi, description=TRUE)
    # extract data for the sample clusters
samclus <- getdata(MDpop, sam)
samclus <- rename(samclus, c("Prob" = "p1i"))
samclus <- samclus[order(samclus$PSU),]
    # treat sample clusters as strata and select srswor of block groups from each
    # identify psu IDs for 1st instance of each ssuID
xx <- do.call("rbind",list(by(1:nrow(samclus),samclus$SSU,head,1)))
SSUs <- cbind(PSU=samclus$PSU[xx], SSU=samclus$SSU[xx])
    # select 2 SSUs per tract
n <- 2
s <- strata(data = as.data.frame(SSUs), stratanames = "PSU",
            size = rep(n,m), method="srswor")
s <- rename(s, c("Prob" = "p2i"))
    # extract the SSU data
    # s contains selection probs of SSUs, need to get those onto data file
SSUsam <- SSUs[s$ID_unit, ]
SSUsam <- cbind(SSUsam, s[, 2:3])
    # identify rows in PSU sample that correspond to sample SSUs
tmp <- samclus$SSU %in% SSUsam$SSU
SSUdat <- samclus[tmp,]
SSUdat <- merge(SSUdat, SSUsam[, c("p2i","SSU")], by="SSU")
    # select srswor from each sample SSU
n.SSU <- m*n
s <- strata(data = as.data.frame(SSUdat), stratanames = "SSU",
            size = rep(50,n.SSU), method="srswor")
s <- rename(s, c("Prob" = "p3i"))
samclus <- getdata(SSUdat, s)
del <- (1:ncol(samclus))[dimnames(samclus)[[2]] %in% c("ID_unit","Stratum")]
samclus <- samclus[, -del]
    # extract pop counts for PSUs in sample
pick <- names(Qi) %in% sort(unique(samclus$PSU))
Qi.sam <- Qi[pick]
    # extract pop counts of SSUs for PSUs in sample
pick <- names(Ni) %in% sort(unique(samclus$PSU))
Ni.sam <- Ni[pick]
    # extract pop counts for SSUs in sample
pick <- names(Qij) %in% sort(unique(samclus$SSU))
Qij.sam <- Qij[pick]
    # compute full sample weight and wts for PSUs and SSUs
wt <- 1 / samclus$p1i / samclus$p2i / samclus$p3i
w1i <- 1 / samclus$p1i
w2ij <- 1 / samclus$p1i / samclus$p2i
samdat <- data.frame(psuID = samclus$PSU, ssuID = samclus$SSU,
                     w1i = w1i, w2ij = w2ij, w = wt,
                     samclus[, c("y1","y2","y3","ins.cov", "hosp.stay")])
BW3stagePPSe(dat=samdat, v="y1", Ni=Ni.sam, Qi=Qi.sam, Qij=Qij.sam, m,
    lonely.SSU = "mean", lonely.TSU = "mean")

Description

Compute the sample sizes that minimize the variance of the pwr-estimator of a total in a two-stage sample.

Usage

clusOpt2(C1, C2, delta, unit.rv, k=1, CV0=NULL, tot.cost=NULL, cal.sw)

Arguments

Details

clusOpt2 will compute $m_{opt}$ and $\bar{n}_{opt}$ for a two-stage sample which uses simple random sampling at each stage or ppswr at the first stage and srs at the second.

Value

List with values:

Author(s)

Richard Valliant, Jill A. Dever, Frauke Kreuter

References

Hansen,M.H., Hurwitz,W.N., and Madow,W.G. (1953, chap. 6, sect. 16). Sample Survey Methods and Theory, Vol.I. John Wiley & Sons.

Valliant, R., Dever, J., Kreuter, F. (2018, sect. 9.3.1). Practical Tools for Designing and Weighting Survey Samples, 2nd edition. New York: Springer.

See Also

clusOpt2fixedPSU, clusOpt3, clusOpt3fixedPSU

Examples

# optimum for a fixed total budget
clusOpt2(C1=750, C2=100, delta=0.05, unit.rv=1, k=1, tot.cost=100000, cal.sw=1)
clusOpt2(C1=750, C2=100, delta=seq(0.05,0.25,0.05), unit.rv=1, k=1, tot.cost=100000, cal.sw=1)
    # optimum for a target CV
clusOpt2(C1=750, C2=100, delta=0.01, unit.rv=1, k=1, CV0=0.05, cal.sw=2)

Description

Compute the optimum number of sample elements per primary sampling unit (PSU) for a fixed set of PSUs

Usage

clusOpt2fixedPSU(C1, C2, m, delta, unit.rv, k=1, CV0=NULL, tot.cost, cal.sw)

Arguments

Details

clusOpt2fixedPSU will compute $\bar{n}_{opt}$ for a two-stage sample which uses simple random sampling at each stage or ppswr at the first stage and srs at the second. The PSU sample is fixed.

Value

List with values:

Author(s)

Richard Valliant, Jill A. Dever, Frauke Kreuter

References

Valliant, R., Dever, J., Kreuter, F. (2018, sect. 9.3.3). Practical Tools for Designing and Weighting Survey Samples, 2nd edition. New York: Springer.

See Also

clusOpt2, clusOpt3, clusOpt3fixedPSU

Examples

# optima for a vector of budgets
clusOpt2fixedPSU(C1=500, C2=100, m=100, delta=0.05, unit.rv=2, k=1, CV0=NULL,
       tot.cost=c(100000, 500000, 10^6), cal.sw=1)
    # optima for a target CV and vector of PSU costs
clusOpt2fixedPSU(C1=c(500,1000,5000), C2=100, m=100, delta=0.05, unit.rv=2, k=1,
       CV0=0.05, tot.cost=NULL, cal.sw=2)

Description

Compute the sample sizes that minimize the variance of the pwr-estimator of a total in a three-stage sample.

Usage

clusOpt3(unit.cost, delta1, delta2, unit.rv, k1=1, k2=1, CV0=NULL, tot.cost=NULL, cal.sw)

Arguments

Details

clusOpt3 will compute $m_{opt}$, $\bar{n}_{opt}$, and $\bar{\bar{q}}_{opt}$ for a three-stage sample which uses simple random sampling at each stage or ppswr at the first stage and srs at the second and third stages.

Value

List with values:

Author(s)

Richard Valliant, Jill A. Dever, Frauke Kreuter

References

Hansen,M.H., Hurwitz,W.N., and Madow,W.G. (1953, p. 225). Sample Survey Methods and Theory, Vol.II. John Wiley & Sons.

Valliant, R., Dever, J., Kreuter, F. (2018, sect. 9.3.2). Practical Tools for Designing and Weighting Survey Samples, 2nd edition. New York: Springer.

See Also

clusOpt2, clusOpt2fixedPSU, clusOpt3fixedPSU

Examples

# optima for a fixed total budget
clusOpt3(unit.cost=c(500, 100, 120), delta1=0.01, delta2=0.10, unit.rv=1,
       k1=1, k2=1, tot.cost=100000,cal.sw=1)
    # optima for a target CV
clusOpt3(unit.cost=c(500, 100, 120), delta1=0.01, delta2=0.10, unit.rv=1,
       k1=1, k2=1, CV0=0.01,cal.sw=2)

Description

Compute the sample sizes that minimize the variance of the pwr-estimator of a total in a three-stage sample when the PSU sample is fixed.

Usage

clusOpt3fixedPSU(unit.cost, m, delta1, delta2, unit.rv, k1=1, k2=1, CV0=NULL,
         tot.cost=NULL, cal.sw)

Arguments

Details

clusOpt3 will compute $\bar{n}_{opt}$ and $\bar{\bar{q}}_{opt}$ for a three-stage sample which uses simple random sampling at each stage or ppswr at the first stage and srs at the second and third stages. The set of sample PSUs is assumed to be fixed. "Variable costs" in tot.cost includes the budget for all costs that vary with the number of sample PSUs, SSUs, and elements, i.e., $C_{1}m + C_{2}m\bar{n} + C_{3}m\bar{n}\bar{\bar{q}}$.

Value

List with values:

Author(s)

Richard Valliant, Jill A. Dever, Frauke Kreuter

References

Hansen,M.H., Hurwitz,W.N., and Madow,W.G. (1953, p. 225). Sample Survey Methods and Theory, Vol.II. John Wiley & Sons.

Valliant, R., Dever, J., Kreuter, F. (2018, sect. 9.3.2). Practical Tools for Designing and Weighting Survey Samples, 2nd edition. New York: Springer.

See Also

clusOpt2, clusOpt2fixedPSU, clusOpt3

Examples

# optima for a fixed total budget
clusOpt3fixedPSU(unit.cost=c(500, 100, 120), m=100, delta1=0.01, delta2=0.05, unit.rv=1,
     k1=1, k2=1, tot.cost=500000,cal.sw=1)
    # optima for a target CV
clusOpt3fixedPSU(unit.cost=c(500, 100, 120), m=100, delta1=0.01, delta2=0.05, unit.rv=1,
     k1=1, k2=1, CV0=0.05,cal.sw=2)

Description

Compute a composite measure of size variable for domain-based sampling that accounts for desired sampling rates of domain units.

Usage

CompMOS(dsn = NULL,  psuID = NULL, n.PSU = NULL, domain = NULL, domain.req.n = NULL,
   exp.domain.rr = NULL)

Arguments

Details

Two-stage samples are often selected from populations for which separate estimates are required for domains, i.e., subpopulations. Composite measures of size for selecting PSU samples with probability proportional to that size can accomplish three things:

1. Self-weighting samples from each of several domains

2. Equal workload in each PSU, i.e., same total sample size in each PSU (across all domains)

3. PSU selection probabilities that give "credit" for containing domains that are relatively rare in the population

CompMOS computes a single composite measure of size, probability of inclusion for each PSU in the sampling frame, and within-PSU sampling rates for each domain. Additional variables regarding survey operations at the PSU domain level are also provided (see Value section below).

Value

A list with four components:

Author(s)

George Zipf, Richard Valliant

References

Aldworth J., Hirsch E. L., Martin P. C., Shook-Sa B. E. (2015). 2014 National Survey on Drug Use and Health sample design report. Tech. Rep. Prepared under contract no. HHSS283201300001C by RTI International, Substance Abuse and Mental Health Services Administration, https://www. samhsa.gov/data/sites/default/files/NSDUHmrbSampleDesign2014v1.pdf

Singh, A.C. and Harter, R. (2015). Domain sample allocation within primary sampling units in designing domain-level equal probability selection methods. Survey Methodology, 41(2), 297-314.

Valliant, R., Dever, J., Kreuter, F. (2018, sec. 10.5). Practical Tools for Designing and Weighting Survey Samples, 2nd edition. New York: Springer.

Examples

psuID <- c(1:10)
D1 <- c(50, 50, 50, 50, 50, 70, 50, 50, 50, 50)
D2 <- c(50, 30, 90, 40, 25, 40, 80, 65, 30, 50)
dsn <- cbind.data.frame(psuID, D1, D2)
n.PSU <- 4
domain <- c("D1", "D2")
domain.req.n <- c(130, 50)
exp.domain.rr <- c(1, 1)

CompMOS(dsn = dsn, psuID  = psuID, n.PSU  = n.PSU, domain = domain,
        domain.req.n = domain.req.n, exp.domain.rr = exp.domain.rr)

  # MDarea.popA has multiple rows for each TRACT; need to summarize TRACT/Age totals
  # for input to CompMOS
data(MDarea.popA)
MDpop <- MDarea.popA[,1:8]
MDpop$AgeGrp <- cut(MDpop$Age, breaks = c(0, 12, 17, 23),
                    labels = c("Age.44.or.under", "Age.45-64", "Age.65+"))

xx <- by(MDpop$TRACT, INDICES=MDpop$AgeGrp, table)
  # All tracts do not contain every age group; merge tract/domain count tables, retaining all tracts
xx1 <- cbind(tract=rownames(xx$Age.44.or.under), as.data.frame(unname(xx$Age.44.or.under)))
colnames(xx1)[3] <- 'Age.44.or.under'
xx2 <- cbind(tract=rownames(xx$`Age.45-64`), as.data.frame(unname(xx$`Age.45-64`)))
colnames(xx2)[3] <- 'Age.45-64'
xx3 <- cbind(tract=rownames(xx$`Age.65+`), as.data.frame(unname(xx$`Age.65+`)))
colnames(xx3)[3] <- 'Age.65+'
pop <- merge(xx1,xx2,by='tract', all=TRUE)
pop <- merge(pop,xx3,by='tract', all=TRUE)
pop <- pop[, -c(2,4,6)]
  # recode counts for missing tract/age-groups to 0
pop[is.na(pop)] <- 0

   # Note that one tract cannot be sampled at the desired rate for the 'Age.65+' domain
MDmos <- CompMOS(dsn  = pop, psuID  = pop$tract, n.PSU  = 15,
              domain = c("Age.44.or.under", "Age.45-64", "Age.65+"),
              exp.domain.rr = c(0.60, 0.70, 0.85),
              domain.req.n  = c(100, 100, 100))

Description

Compute the coefficient of variation of an estimated total in a two-stage design. Primary sampling units (PSUs) can be selected either with probability proportional to size (pps) or with equal probability. Elements are selected via simple random sampling (srs).

Usage

CVcalc2(V=NULL, m=NULL , nbar=NULL, k=1, delta=NULL, Bsq=NULL, Wsq=NULL)

Arguments

Details

CVcalc2 computes the coefficient of variation of an estimated total for a two-stage sample. PSUs can be selected either with varying probabilities and with replacement or with equal probabilities and with replacement. Elements within PSUs are selected by simple random sampling. The $CV$ formula is appropriate for approximating the relvariance of the probability-with-replacement (pwr)-estimator of a total when the same number of elements is selected within each sample PSU. See Sections 9.2.1–9.2.3 of Valliant, Dever, and Kreuter (2013) for details of formulas.

Value

Value of the coefficient of variation of an estimated total

Author(s)

Richard Valliant, Jill A. Dever, Frauke Kreuter

References

Cochran, W.G. (1977, pp.308-310). Sampling Techniques. New York: John Wiley & Sons.

Saerndal, C.E., Swensson, B., and Wretman, J. (1992). Model Assisted Survey Sampling. New York: Springer.

Valliant, R., Dever, J., Kreuter, F. (2018, sect. 9.2.1). Practical Tools for Designing and Weighting Survey Samples, 2nd edition. New York: Springer.

See Also

CVcalc3

Examples

CVcalc2(V=1, m=20 , nbar=5, k=1, delta=0.05)
CVcalc2(V=10, m=20 , nbar=5, k=1, delta=0.5)
CVcalc2(V=2.5, m=20 , nbar=5, k=2, Bsq=1, Wsq=4)

Description

Compute the coefficient of variation of an estimated total in a three-stage design. Primary sampling units (PSUs) can be selected either with probability proportional to size (pps) or with equal probability. Secondary units and elements within SSUs are selected via simple random sampling (srs).

Usage

CVcalc3(V=NULL, m=NULL , nbar=NULL, qbar=NULL, k1=1, k2=1, delta1=NULL, delta2=NULL,
            Bsq=NULL, Wsq=NULL, W2sq=NULL, W3sq=NULL)

Arguments

Details

CVcalc3 computes the coefficient of variation of an estimated total for a three-stage sample. PSUs can be selected either with varying probabilities and with replacement or with equal probabilities and with replacement. SSUs and elements within SSUs are selected by simple random sampling. The $CV$ formula is appropriate for approximating the relvariance of the probability-with-replacement (pwr)-estimator of a total when the same number of SSUs is selected in each PSU and the same number of elements is selected within each sample SSU. See Sect. 9.2.4 of Valliant, Dever, and Kreuter (2018) for details of formulas.

Value

Value of the coefficient of variation of an estimated total

Author(s)

Richard Valliant, Jill A. Dever, Frauke Kreuter

References

Cochran, W.G. (1977, pp.308-310). Sampling Techniques. New York: John Wiley & Sons.

Saerndal, C.E., Swensson, B., and Wretman, J. (1992). Model Assisted Survey Sampling. New York: Springer.

Valliant, R., Dever, J., Kreuter, F. (2018, sect. 9.2.4). Practical Tools for Designing and Weighting Survey Samples, 2nd edition. New York: Springer.

See Also

CVcalc3

Examples

CVcalc3(V=1, m=20 , nbar=5, qbar=10, delta1=0.02, delta2=0.10)
CVcalc3(V=1, m=20 , nbar=5, qbar=10, delta1=0.02, delta2=0.09)
CVcalc3(V=2, m=20 , nbar=5, qbar=10, k1=5, k2=10, Bsq=1, Wsq=9, W2sq=2 , W3sq=18 )

Description

Compute the Kish, Henry, Spencer, or Chen-Rust design effects.

Usage

deff(w, x=NULL, y=NULL, p=NULL, strvar=NULL, clvar=NULL, Wh=NULL, nest=FALSE, type)

Arguments

Details

deff calls one of deffK, deffH, deffS, or deffCR depending on the value of the type parameter. The Kish design effect is the ratio of the variance of an estimated mean in stratified simple random sampling without replacement (stsrswor) to the variance of the estimated mean in srswor, assuming that all stratum unit variances are equal. In that case, proportional allocation with equal weighting is optimal. deffK equals 1 + relvar(w) where relvar is relvariance of the vector of survey weights. This measure is not appropriate in samples where unequal weighting is more efficient than equal weighting.

The Henry design effect is the ratio of the variance of the general regression (GREG) estimator of a total of $y$ to the variance of the estimated total in srswr. Calculations for the Henry deff are done as if the sample is selected in a single-stage and with replacement. Varying selection probabilities can be used. The model for the GREG is assumed to be $y = \alpha + \beta x + \epsilon$, i.e., the model has an intercept.

The Spencer design effect is the ratio of the variance of the pwr-estimator of the total of y, assuming that a single-stage sample is selected with replacement, to the variance of the total estimated in srswr. Varying selection probabilities can be used.

The Chen-Rust deff accounts for stratification, clustering, and unequal weights, but does not account for the use of any auxiliary data in the estimator of a mean. The Chen-Rust deff returned here is appropriate for stratified, two-stage sampling.

Value

Numeric design effect for types kish, henry, spencer. For type cr a list with components:

Author(s)

Richard Valliant, Jill A. Dever, Frauke Kreuter

References

Chen, S. and Rust, K. (2017). An Extension of Kish's Formula for Design Effects to Two- and Three-Stage Designs with Stratification. Journal of Survey Statistics and Methodology, 5(2), 111-130.

Henry, K.A., and Valliant, R. (2015). A Design Effect Measure for Calibration Weighting in Single-stage Samples. Survey Methodology, 41, 315-331.

Kish, L. (1965). Survey Sampling. New York: John Wiley & Sons.

Kish, L. (1992). Weighting for unequal Pi. Journal of Official Statistics, 8, 183-200.

Park, I., and Lee, H. (2004). Design Effects for the Weighted Mean and Total Estimators under Complex Survey Sampling. Survey Methodology, 30, 183-193.

Spencer, B. D. (2000). An Approximate Design Effect for Unequal Weighting When Measurements May Correlate With Selection Probabilities. Survey Methodology, 26, 137-138.

Valliant, R., Dever, J., Kreuter, F. (2018, chap. 14). Practical Tools for Designing and Weighting Survey Samples, 2nd edition. New York: Springer.

See Also

deffK, deffH, deffS, deffCR

Examples

require(reshape)      # has function that allows renaming variables
require(sampling)

set.seed(-500398777)
    # generate population using HMT function
pop.dat <- as.data.frame(HMT())
mos <- pop.dat$x
pop.dat$prbs.1d <- mos / sum(mos)
    # select pps sample
n <- 80
pk <- pop.dat$prbs.1d
sam <- UPrandomsystematic(pk)
sam <- sam==1

sam.dat <- pop.dat[sam, ]
dsgn.wts <- 1/pk[sam]
deff(w=dsgn.wts, type="kish")
deff(w=dsgn.wts, y=sam.dat$y, p=sam.dat$prbs.1d, type="spencer")
deff(w=dsgn.wts, x=sam.dat$x, y=sam.dat$y, type="henry")


data(MDarea.popA)
Ni <- table(MDarea.popA$TRACT)
m <- 10
probi <- m*Ni / sum(Ni)
    # select sample of clusters
set.seed(-780087528)
sam <- cluster(data=MDarea.popA, clustername="TRACT", size=m, method="systematic",
                pik=probi, description=TRUE)
    # extract data for the sample clusters
samclus <- getdata(MDarea.popA, sam)
samclus <- rename(samclus, c("Prob" = "pi1"))
    # treat sample clusters as strata and select srswor from each
nbar <- 4
s <- strata(data = as.data.frame(samclus), stratanames = "TRACT",
            size = rep(nbar,m), method="srswor")
    # extracts the observed data
samdat <- getdata(samclus,s)
samdat <- rename(samdat, c("Prob" = "pi2"))
    # add a fake stratum ID
H <- 2
nh <- m * nbar / H
stratum <- NULL
for (h in 1:H){
    stratum <- c(stratum, rep(h,nh))
}
wt <- 1/(samdat$pi1*samdat$pi2) * runif(m*nbar)
samdat <- cbind(subset(samdat, select = -c(Stratum)), stratum, wt)
deff(w = samdat$wt, y=samdat$y2, strvar = samdat$stratum, clvar = samdat$TRACT, Wh=NULL, type="cr")

Description

Chen-Rust design effect for an estimated mean from a stratified, clustered, two-stage samples

Usage

deffCR(w, strvar=NULL, clvar=NULL, Wh=NULL, nest=FALSE, y)

Arguments

Details

The Chen-Rust deff for an estimated mean accounts for stratification, clustering, and unequal weights, but does not account for the use of any auxiliary data in the estimator of a mean. The Chen-Rust deff returned here is appropriate for stratified, two-stage sampling. Note that separate deff's are produced for weighting, clustering, and stratification within each stratum. These cannot be added across strata unless the stratum values of the coefficient of variation of the weights, the sample size of clusters, and the intracluster correlation of y are equal across all strata (see Chen and Rust 2017, p.117).

Value

A list with components:

Author(s)

Richard Valliant, Jill A. Dever, Frauke Kreuter

References

Chen, S. and Rust, K. (2017). An Extension of Kish's Formula for Design Effects to Two- and Three-Stage Designs with Stratification. Journal of Survey Statistics and Methodology, 5(2), 111-130.

Valliant, R., Dever, J., Kreuter, F. (2018, chap. 14). Practical Tools for Designing and Weighting Survey Samples, 2nd edition. New York: Springer.

See Also

deff, deffH, deffK, deffS

Examples

require(sampling)
require(reshape)
data(MDarea.popA)
Ni <- table(MDarea.popA$TRACT)
m <- 20
probi <- m*Ni / sum(Ni)
    # select sample of clusters
set.seed(-780087528)
sam <- sampling::cluster(data=MDarea.popA, clustername="TRACT", size=m, method="systematic",
                pik=probi, description=TRUE)
    # extract data for the sample clusters
samclus <- getdata(MDarea.popA, sam)
samclus <- rename(samclus, c("Prob" = "pi1"))
    # treat sample clusters as strata and select srswor from each
nbar <- 8
s <- sampling::strata(data = as.data.frame(samclus), stratanames = "TRACT",
            size = rep(nbar,m), method="srswor")
    # extracts the observed data
samdat <- getdata(samclus,s)
samdat <- rename(samdat, c("Prob" = "pi2"))
    # add a fake stratum ID
H <- 2
nh <- m * nbar / H
stratum <- NULL
for (h in 1:H){
    stratum <- c(stratum, rep(h,nh))
}
wt <- 1/(samdat$pi1*samdat$pi2) * runif(m*nbar)
samdat <- cbind(subset(samdat, select = -c(stratum)), stratum, wt)
deffCR(w = samdat$wt, strvar = samdat$stratum, clvar = samdat$TRACT, Wh=NULL, y=samdat$y2)

Description

Compute the Henry design effect for single-stage samples when a general regression estimator is used for a total.

Usage

deffH(w, y, x)

Arguments

Details

The Henry design effect is the ratio of the variance of the general regression (GREG) estimator of a total of $y$ to the variance of the estimated total in srswr. Calculations for the Henry deff are done as if the sample is selected in a single-stage and with replacement. Varying selection probabilities can be used. The model for the GREG is assumed to be $y = \alpha + \beta x + \epsilon$, i.e., the model has an intercept.

Value

numeric design effect

Author(s)

Richard Valliant, Jill A. Dever, Frauke Kreuter

References

Henry, K.A., and Valliant, R. (2015). A Design Effect Measure for Calibration Weighting in Single-stage Samples. Survey Methodology, 41, 315-331.

Valliant, R., Dever, J., Kreuter, F. (2018, chap. 14). Practical Tools for Designing and Weighting Survey Samples, 2nd edition. New York: Springer.

See Also

deff, deffCR, deffK, deffS

Examples

set.seed(-500398777)
    # generate population using HMT function
pop.dat <- as.data.frame(HMT())
mos <- pop.dat$x
pop.dat$prbs.1d <- mos / sum(mos)
    # select pps sample
require(sampling)
n <- 80
pk <- n * pop.dat$prbs.1d
sam <- UPrandomsystematic(pk)
sam <- sam==1
sam.dat <- pop.dat[sam, ]
dsgn.wts <- 1/pk[sam]
deffH(w=dsgn.wts, y=sam.dat$y, x=sam.dat$x)

Description

Compute the Kish design effect due to having unequal weights.

Usage

deffK(w)

Arguments

Details

The Kish design effect is the ratio of the variance of an estimated mean in stratified simple random sampling without replacement (stsrswor) to the variance of the estimated mean in srswor, assuming that all stratum unit variances are equal. In that case, proportional allocation with equal weighting is optimal. deffK equals $1 + relvar(w)$ where $relvar$ is relvariance of the vector of survey weights. This measure is not appropriate in samples where unequal weighting is more efficient than equal weighting.

Value

numeric design effect

Author(s)

Richard Valliant, Jill A. Dever, Frauke Kreuter

References

Kish, L. (1965). Survey Sampling. New York: John Wiley & Sons.

Kish, L. (1992). Weighting for unequal Pi. Journal of Official Statistics, 8, 183-200.

Valliant, R., Dever, J., Kreuter, F. (2018, chap. 14). Practical Tools for Designing and Weighting Survey Samples, 2nd edition. New York: Springer.

See Also

deff, deffCR, deffH, deffS

Examples

data(nhis)
w <- nhis$svywt
deffK(w)

Description

Compute the Spencer design effect for single-stage samples selected with probability proportional to a measure of size.

Usage

deffS(p, w, y)

Arguments

Details

The Spencer design effect is the ratio of the variance of the pwr-estimator of the total of $y$, assuming that a single-stage sample is selected with replacement, to the variance of the total estimated in srswr. Varying selection probabilities can be used.

Value

numeric design effect

Author(s)

Richard Valliant, Jill A. Dever, Frauke Kreuter

References

Park, I., and Lee, H. (2004). Design Effects for the Weighted Mean and Total Estimators under Complex Survey Sampling. Survey Methodology, 30, 183-193.

Spencer, B. D. (2000). An Approximate Design Effect for Unequal Weighting When Measurements May Correlate With Selection Probabilities. Survey Methodology, 26, 137-138.

Valliant, R., Dever, J., Kreuter, F. (2018, chap. 14). Practical Tools for Designing and Weighting Survey Samples, 2nd edition. New York: Springer.

See Also

deff, deffCR, deffH, deffK

Examples

set.seed(-500398777)
    # generate population using HMT function
pop.dat <- as.data.frame(HMT())
mos <- pop.dat$x
pop.dat$prbs.1d <- mos / sum(mos)
    # select pps sample
require(sampling)
n <- 80
pk <- pop.dat$prbs.1d
sam <- UPrandomsystematic(pk)
sam <- sam==1
sam.dat <- pop.dat[sam, ]
dsgn.wts <- 1/pk[sam]
deffS(p=sam.dat$prbs.1d, w=dsgn.wts, y=sam.dat$y)

Description

Domainy1y2 is a small data file used for an exercise in sample size calculations.

Usage

data(Domainy1y2)

Format

A data frame with 30 observations on 2 variables.

y1

an artificial variable

y2

an artificial variable

References

Valliant, R., Dever, J., Kreuter, F. (2018, chap. 3). Practical Tools for Designing and Weighting Survey Samples, 2nd edition. New York: Springer.

Examples

data(Domainy1y2)
str(Domainy1y2)
summary(Domainy1y2)

Description

Compute samples sizes at each phase of a two-phase design where strata are created using the first phase.

Usage

dub(c1, c2, Ctot, Nh, Sh, Yh.bar)

Arguments

Details

Compute the first and second phase sample sizes for a double sampling design. A first phase sample is selected by simple random sampling (srs). Strata are formed based on information collected in the first phase. The Neyman allocation to strata of the second phase sample is computed ignoring costs. Optimal total sample sizes are computed for the first and second phases, given per-unit costs for the first and second phases and a fixed total budget for both phases combined.

Value

A list object with elements:

Author(s)

Richard Valliant, Jill A. Dever, Frauke Kreuter

References

Cochran W (1977, sect. 12.3) Sampling Techniques. New York: John Wiley & Sons, Inc.

Neyman J (1938) Contribution to the theory of sampling human populations. Journal of the American Statistical Association, 33(201), 101-116.

Valliant, R., Dever, J., Kreuter, F. (2018, sect. 17.5.2). Practical Tools for Designing and Weighting Survey Samples, 2nd edition. New York: Springer.

Examples

Wh <- rep(0.25,4)
Ph <- c(0.02,0.12,0.37,0.54)
Sh <- sqrt(Ph*(1-Ph))
c1 <- 10
c2 <- 50
Ctot <- 20000
dub(c1, c2, Ctot, Nh=Wh, Sh, Yh.bar=Ph)

Description

Regresses a y on a set of covariates X where $Var_M(y)=\sigma^2x^\gamma$ and then regresses the squared residuals on $log(x)$ to estimate $\gamma$.

Usage

gamEst(X1, x1, y1, v1)

Arguments

Details

The function gamEst estimates the power $\gamma$ in a model where the variance of the errors is proportional to $x^\gamma$ for some covariate x. Values of $\gamma$ are typically in [0,2]. The function is iteratively called by gammaFit, which is normally the function that an analyst should use.

Value

The estimate of $\gamma$.

Author(s)

Richard Valliant, Jill A. Dever, Frauke Kreuter

References

Valliant, R., Dever, J., Kreuter, F. (2018, chap. 3). Practical Tools for Designing and Weighting Survey Samples, 2nd edition. New York: Springer.

See Also

gammaFit

Examples

data(hospital)
x <- hospital$x
y <- hospital$y

X <- cbind(sqrt(x), x)
gamEst(X1 = X, x1 = x, y1 = y, v1 = x)

Description

Iteratively computes estimate of $\gamma$ in a model with $E_M(y)=x^T\beta$ and $Var_M(y)=\sigma^2x^\gamma$.

Usage

gammaFit(X, x, y, maxiter = 100, show.iter = FALSE, tol = 0.001)

Arguments

Details

The function gammaFit estimates the power $\gamma$ in a model where the variance of the errors is proportional to $x^\gamma$ for some covariate x. Values of $\gamma$ are typically in [0,2]. The function calls gamEst.

Value

A list with the components:

Author(s)

Richard Valliant, Jill A. Dever, Frauke Kreuter

References

Valliant, R., Dever, J., Kreuter, F. (2018, chap. 3). Practical Tools for Designing and Weighting Survey Samples, 2nd edition. New York: Springer.

See Also

gamEst

Examples

data(hospital)
x <- hospital$x
y <- hospital$y

X <- cbind(sqrt(x), x)
gammaFit(X = X, x = x, y = y, maxiter=100, tol=0.002)

Description

Split geographic PSUs into new geographically contiguous PSUs based on a maximum measure of size for each PSU

Usage

GeoDistMOS(lat, long, psuID, n, MOS.var, MOS.takeall = 1, Input.ID = NULL)

Arguments

Details

GeoDistMOS splits geographic primary sampling units (PSUs) in the input object based on a variable which is used to create the measure of size for each PSU (MOS.var). The goal is to create PSUs of similarly sized MOS. The input file should have one row for each geographic unit, i.e. secondary sampling unit (SSU), with a PSU ID assigned. The latitude and longitude input vectors define the centroid of each input SSU. The complete linkage method for clustering is used. Accordingly, PSUs are split on a distance metric and not on the MOS threshold value. GeoDistMOS calls the function inclusionprobabilities from the sampling package to calculate the inclusion probability for each SSU within a PSU and distHaversine from the geosphere package to calculate the distances between centroids.

Value

A list with two components:

Author(s)

George Zipf, Richard Valliant

See Also

GeoDistPSU, GeoMinMOS

Examples

data(Test_Data_US)

   # Create PSU ID with GeoDistPSU
g <- GeoDistPSU(Test_Data_US$lat,
                Test_Data_US$long,
                "miles",
                100,
                Input.ID = Test_Data_US$ID)
   # Append PSU ID to input file
library(dplyr)
Test_Data_US <- dplyr::inner_join(Test_Data_US, g$PSU.ID, by=c("ID" = "Input.file.ID"))

   # Split PSUs with MOS above 0.80
m <- GeoDistMOS(lat         = Test_Data_US$lat,
                long        = Test_Data_US$long,
                psuID       = Test_Data_US$psuID,
                n           = 15,
                MOS.var     = Test_Data_US$Amount,
                MOS.takeall = 0.80,
                Input.ID    = Test_Data_US$ID)

   # Create histogram of Measure of Size Values
hist(m$PSU.Max.MOS.Info$psuID.prob,
     breaks = seq(0, 1, 0.1),
     main = "Histogram of PSU Inclusion Probabilities (Certainties = 1)",
     xlab = "Inclusion Probability",
     ylab = "Frequency")

Description

Combine geographic areas into primary sampling units to limit travel distances

Usage

GeoDistPSU(lat, long, dist.sw, max.dist, Input.ID = NULL)

Arguments

Details

GeoDistPSU combines geographic secondary sampling units (SSUs), like cities or census block groups, into primary sampling units (PSUs) given a maximum distance allowed between the centroids of the SSUs within each grouped PSU. The input file must have one row for each geographic unit. If the input file does not have an ID field, the function will create a sequential ID that is appended to the output. The latitude and longitude input vectors define the centroid of each input SSU. The complete linkage method for clustering is used. GeoDistPSU calls the functions distm and distHaversine from the geosphere package to calculate the distances between centroids.

Value

A list with two components:

.

Author(s)

George Zipf, Richard Valliant

See Also

GeoDistMOS, GeoMinMOS

Examples

data(Test_Data_US)
g <- GeoDistPSU(Test_Data_US$lat,
                Test_Data_US$long,
                "miles", 100,
                Input.ID = Test_Data_US$ID)
    # Plot GeoDistPSU output
plot(g$PSU.Info$PSU.Mean.Longitude,
     g$PSU.Info$PSU.Mean.Latitude,
     col  = 1:nrow(g$PSU.Info),
     pch  = 19,
     main = "Plot of PSU Centers",
     xlab = "Longitude",
     ylab = "Latitude")
grid(col = "grey40")

    # Plot GeoDistPSU output with map
## Not run: 
  # install package sf to run usmap_transform
library(ggplot2)
library(sp)
library(usmap)
    # Transform PSUs into usmap projection
g.map  <- cbind(long = g$PSU.Info$PSU.Mean.Longitude,
                lat  = g$PSU.Info$PSU.Mean.Latitude)
g.map  <- as.data.frame(g.map)
g.proj <- usmap::usmap_transform(g.map,
                          input_names  = c("long", "lat"),
                          output_names = c("Long", "Lat"))
usmap::plot_usmap(color = "gray") +
  geom_point(data = g.proj,
             aes(x = Long,
                 y = Lat))
    # Create histogram of maximum distance
hist(g$PSU.Info$PSU.Max.Dist,
     main = "Histogram of Maximum Within-PSU Distance",
     xlab = "Distance",
     ylab = "Frequency")

## End(Not run)

Description

Identify geographic PSUs whose measure of size is below a specified minimum and combine those PSUs with others

Usage

GeoMinMOS(lat, long, geo.var, MOS.var, MOS.min)

Arguments

Details

GeoMinMOS is a utility function that should be run after using GeoDistMOS or GeoDistPSU. GeoMinMOS identifies each PSU whose measure of size, (MOS.var), is below the minimum specified by MOS.min. Distances to the latitude/longitude centroids of other PSUs are calculated. The undersized PSUs are then combined with the nearest PSUs in proximity order until the minimum MOS is met or exceeded. In some cases, this can result in the same input PSU being assigned to more than one combined PSU. Also, the distances between the centroids of the PSUs in a combination may be impractically large. Thus, the new combinations generated by GeoMinMOS should be treated as suggestions that should be manually reviewed and adjusted if desired.

Value

A list with four components:

Author(s)

George Zipf, Richard Valliant

See Also

GeoDistPSU, GeoDistMOS

Examples

library(PracTools)
library(dplyr)
g <- GeoDistPSU(Test_Data_US$lat,
                Test_Data_US$long,
                "miles",
                100,
                Input.ID = Test_Data_US$ID)
Test_Data_US <- inner_join(Test_Data_US, g$PSU.ID, by=c("ID" = "Input.file.ID"))
GeoMinMOS(lat      = Test_Data_US$lat,
          long     = Test_Data_US$long,
          geo.var  = Test_Data_US$psuID,
          MOS.var  = Test_Data_US$Amount,
          MOS.min  = 200000)

Description

Generate a population that follows the model in Hansen, Madow, and Tepping (1983)

Usage

HMT(N=5000, H=10)

Arguments

Details

HMT generates a population based on the model: $E(y)= \alpha + \beta x$, $Var(y)=\sigma^2x^{3/2}$. Both x and y have gamma distributions. Strata are formed to have approximately the same total of $x$.

Value

N x 3 matrix with columns:

Author(s)

Richard Valliant, Jill A. Dever, Frauke Kreuter

References

Hansen,M.H., Madow,W.G., and Tepping,B.J. (1983). An evaluation of model-dependent and probability sampling inferences in sample surveys. Journal of the American Statistical Association, 78, 776-793.

Examples

# generate HMT population with 1000 units and 5 strata and plot results
pop <- HMT(N=1000, H=5)
plot(pop[,"x"],pop[,"y"])

Description

The hospital data file is a national sample of short-stay hospitals with fewer than 1000 beds.

Usage

data(hospital)

Format

A data frame with 393 observations on the following 2 variables.

y

Number of patients discharged by the hospital in January 1968

x

Number of inpatient beds in the hospital

Details

The hospital data are from the National Hospital Discharge Survey conducted by the U.S. National Center for Health Statistics. The survey collects characteristics of inpatients discharged from non-Federal short-stay hospitals in the United States. This population is from the January 1968 survey and contains observations on 393 hospitals.

Source

National Center for Health Statistics Hospital Discharge Survey of 1968.

References

Herson, J. (1976). An Investigation of Relative Efficiency of Least-Squares Prediction to Conventional Probability Sampling Plans. Journal of the American Statistical Association, 71, 700-703.

Examples

data(hospital)
str(hospital)

Description

A clustered population of persons extracted from the September 1976 Current Population Survey (CPS)

Usage

data(labor)

Format

A data frame with 478 persons on the following variables:

h

stratum

cluster

cluster (or segment) number

person

person number

age

age of person

agecat

age category (1 = 19 years and under; 2 = 20-24; 3 = 25-34; 4 = 35-64; 5 = 65 years and over)

race

race (1 = non-Black; 2 = Black)

sex

Gender (1=Male; 2=Female)

HoursPerWk

Usual number of hours worked per week

WklyWage

Usual amount of weekly wages (in 1976 U.S. dollars)

y

An artificial variable generated to follow a model with a common mean. Persons in the same cluster are correlated. Persons in different clusters are uncorrelated under the model.

Details

This population is a clustered population of 478 persons extracted from the September 1976 Current Population Survey (CPS) in the United States. The clusters are compact geographic areas used as one of the stages of sampling in the CPS and are typically composed of about 4 nearby households. The elements within clusters for this illustrative population are individual persons.

Source

Current Population Survey, https://www.census.gov/programs-surveys/cps.html

Examples

data(labor)
str(labor)
table(labor$h)
hist(labor$WklyWage)

Description

An artificial population of census tracts, block groups, and persons

Usage

data(MDarea.popA)

Format

A data frame with 343,398 persons on the following variables:

PSU

A grouping of block groups (BLKGROUP) which has about 4290 persons

SSU

A grouping of block groups which has about 1010 persons

TRACT

A geographic area defined by the Census Bureau. Tracts generally have between 1,500 and 8,000 people but have a much wider range in Anne Arundel county.

BLKGROUP

Block group. A geographic area defined by the Census Bureau. Block groups generally have between 600 and 3,000 people.

Hispanic

Hispanic ethnicity (1=Hispanic; 2=Non-Hispanic)

Gender

Gender (1=Male; 2=Female)

Age

23 level age category (1 = Under 5 years; 2 = 5 to 9 years; 3 = 10 to 14 years; 4 = 15 to 17 years; 5 = 18 and 19 years; 6 = 20 years; 7 = 21 years; 8 = 22 to 24 years; 9 = 25 to 29 years; 10 = 30 to 34 years; 11 = 35 to 39 years; 12 = 40 to 44 years; 13 = 45 to 49 years; 14 = 50 to 54 years; 15 = 55 to 59 years; 16 = 60 and 61 years; 17 = 62 to 64 years; 18 = 65 and 66 years; 19 = 67 to 69 years; 20 = 70 to 74 years; 21 = 75 to 79 years; 22 = 80 to 84 years; 23 = 85 years and over)

person

Counter for person within tract/block group/Hispanic/Gender/Age combination

y1

Artificial continuous variable

y2

Artificial continuous variable

y3

Artificial continuous variable

ins.cov

Medical coverage (0 = person does not have medical insurance coverage; 1 = person has medical insurance coverage)

hosp.stay

Overnight hospital stay (0 = person did not have an overnight hospital stay in last 12 months; 1 = person did have an overnight hospital stay in last 12 months)

Details

A dataset of 343,398 persons based on the 2000 decennial U.S. Census for Anne Arundel County in the US state of Maryland. Person records were generated based on counts from the 2000 census. Individual values for each person were generated using models. Groupings to form the variables PSU and SSU were done after sorting the census file by tract and block group within tract.

Note that MDarea.popA is different from the dataset, MDarea.pop, that is used in the book by Valliant, Dever, and Kreuter (2018). MDarea.pop is larger with 403,997 persons. MDarea.popA was created by taking an equal probability, systematic subsample from MDarea.pop. MDarea.popA does have the same numbers of TRACTs, PSUs, and SSUs as MDarea.pop. The smaller data set was created to meet the CRAN size limit on installed packages. The full population, MDarea.pop, can be downloaded from https://umd.app.box.com/v/PracTools2ndEdition.

Source

2000 U.S. decennial census, http://www.census.gov/main/www/cen2000.html

References

Valliant, R., Dever, J., Kreuter, F. (2018). Practical Tools for Designing and Weighting Survey Samples, 2nd edition. New York: Springer.

Examples

data(MDarea.popA)
str(MDarea.popA)
table(MDarea.popA$TRACT)
table(MDarea.popA$TRACT, MDarea.popA$Hispanic)

Description

Demographic and health related variables from a U.S. household survey in the state of Michigan

Usage

data(mibrfss)

Format

A data frame with 2485 observations on persons for the following 21 variables.

SMOKE100

Smoked 100 or more cigarettes in lifetime (1 = Yes; 2 = No)

BMICAT3

Body mass index category (1 = Neither overweight nor obese (BMI < 25); 2 = Overweight (25 <= BMI <= 30); 3 = Obese (BMI > 30) )

AGECAT

Age group (1 = 18-24 years; 2 = 25-34 years; 3 = 35-44 years; 4 = 45-54 years; 5 = 55-64 years; 6 = 65+)

GENHLTH

General health (self-reported) (1 = Excellent; 2 = Very good; 3 = Good; 4 = Fair; 5 = Poor)

PHYSACT

Physical activity: In last month participated in activities such as running, calisthenics, golf, gardening, or walking for exercise (1 = Yes; 2 = No)

HIGHBP

High blood pressure: Have you ever been told by a doctor, nurse, or other health professional that you have high blood pressure? (1 = Yes; 2 = No)

ASTHMA

Asthma: Have you ever been told by a doctor, nurse, or other health professional that you have asthma? (1 = Yes; 2 = No)

HISPANIC

Hispanic ethnicity (1 = Yes; 2 = No; 7 = Missing)

WEIGHT

Body weight in pounds

GENDER

Gender (1 = Male; 2 = Female)

CELLPHON

Has a wireless phone (1 = Yes; 2 = No)

INETHOME

Has access to the Internet at home (1 = Yes; 2 = No)

WEBUSE

How often do you use the Internet at home? Would you say, at least once a day, five to six times a week, two to four times a week, about once a week, less than once a week, or have you not used the Internet in the last month? (1 = At least once a day; 2 = 5-6 times a week; 3 = 2-4 times a week; 4 = About once a week; 5 = Less than once a week; 6 = Not in the last month)

RACECAT

Race (1 = White; 2 = African American; 3 = Other)

EDCAT

Education level (1 = Did not graduate high school; 2 = Graduated high school; 3 = Attended college or technical school; 4 = Graduated from college or technical school)

INCOMC3

Income category (1 = Less than $15000; 2 = $15000 to less than $25000; 3 = $25000 to less than $35000; 4 = $35000 to less than $50000; 5 = $50000 or more)

DIABETE2

Diabetes: Have you ever been told by a doctor, nurse, or other health professional that you have diabetes? (1 = Yes; 2 = No)

CHOLCHK

Cholesterol check: Blood cholesterol is a fatty substance found in the blood. Have you ever had your blood cholesterol checked? (1 = Yes; 2 = No)

BMI

Body mass index (continuous)

BINGE2

Binge drinking: At risk for binge drinking based on alcohol consumption responses (1 = Yes; 2 = No)

ARTHRIT

Arthritis: Have you ever been told by a doctor, nurse, or other health professional that you have some form of arthritis, rheumatoid arthritis, gout, lupus, or fibromyalgia, or have joint symptoms of arthritis? (1 = Yes; 2 = No; 3 = Don't know, not sure, or refused)

Details

The Michigan Behavioral Risk Factor Surveillance Survey (MIBRFSS) is part of a national state-by-state system of surveys used to monitor health conditions in the U.S. Data are collected through telephone household interviews. Demographic variables and a few health related variables are included in this subset. The mibrfss data set contains observations on 2845 persons and is extracted from the 2003 U.S. survey. The file contains only persons 18 years and older.

Source

Michigan Behavioral Risk Factor Surveillance Survey of 2003 sponsored by the U.S. Center for Disease Control. https://www.cdc.gov/brfss/

See Also

nhis, nhis.large

Examples

data(mibrfss)
str(mibrfss)
table(mibrfss$SMOKE100, useNA = "always")
table(mibrfss$BMICAT3, useNA="always")

Description

Compute a sample size for an audit where the goal is to control the probability of observing only a small number of errors given an underlying error rate in the population. Auditors refer to this as an attribute sample.

Usage

nAuditAttr(TolRate=0.05, AccDev, CL, N=5000)

Arguments

Details

nAuditAttr computes the minimum sample size required so that the probability, 1-CL of detecting less than or equal to a specified number of errors in the sample, is controlled. The sample is assumed to be selected with equal probabilities. AccDev is the largest number of errors in the sample that will be considered as meeting the audit standards. TolRate is the underlying population error rate, which is typically set to be larger than AccDev/N. The sample size is computed in two ways: (1) using the hypergeometric distribution, which accounts for the size of the population and (2) with the binomial distribution, which will be appropriate if the population is very large. When N is large and the sampling fraction is small, both sample sizes will be approximately the same.

Value

List object with values:

Author(s)

George Zipf, Richard Valliant

References

GAO (2020). Financial Audit Manual, Volume 1, section 450.08. Washington DC; https://www.gao.gov/assets/gao-18-601g.pdf

Stewart, Trevor R. (2012). Technical Notes on the AICPA Audit Guide: Audit Sampling. American Institute of Certified Public Accountants, Inc. New York, NY 10036-8775; https://us.aicpa.org/content/dam/aicpa/publications/accountingauditing/keytopics/downloadabledocuments/sampling_guide_technical_notes.pdf

Examples

# Examples from the US GAO Financial Audit Manual (2020), Figure 450.1, Table 1
nAuditAttr(AccDev = 0, CL = .90)
nAuditAttr(AccDev = 1, CL = .90)
nAuditAttr(AccDev = 2, CL = .90)
nAuditAttr(AccDev = 3, CL = .90)
nAuditAttr(AccDev = 4, CL = .90)

Description

Compute a sample size for an audit where the goal is to control the probability of observing only a small number of errors given an underlying error rate in the population. The sample will be selected with probabilities proportional to a measure of size (MOS). When the MOS of each record is a monetary unit, auditors refer to this as an monetary unit sampling or dollar unit sampling.

Usage

nAuditMUS(MUSVar, Value.sw, CL = 0.90, Error.sw, Tol.Error, Exp.Error = 0)

Arguments

Details

nAuditMUS computes the minimum sample size required for a given population, tolerable error rate or misstatement, and desired confidence level. If the expected error or misstatement is 0, (i.e. Exp.Error = 0), then the sample size is computed using the hypergeometric distribution where the acceptable number of deviations is 0. If the expected error is greater than 0, then sample size is computed by first calculating the maximum sample size where the number of deviations divided by the sample size is less than the expected error, then calculating the minimum sample size where the number of deviations divided by the sample size is greater than the expected error, and finally performing a straight line interpolation between these two values where the interpolated value is the specified expected error. The returned sample size calculation is the ceiling of that interpolated sample size.

Value

List object with values:

Author(s)

George Zipf, Richard Valliant

References

GAO (2020). Financial Audit Manual, Volume 1, section 480.21-480.26. Washington DC; https://www.gao.gov/assets/gao-18-601g.pdf

See Also

nAuditAttr

Examples

# generate an artificial population with some negative monetary amounts
EX <- 1000
relvar <- 2
alpha <- 1/relvar
sigma <- EX * relvar
lowval <- 100                   # minimum positive X's allowed
prop.neg <- 0.05                # proportion of pop with negative values
N.neg <- floor(1000 * prop.neg)    # number of negative X's allowed
X <- rgamma(n=1000, shape=alpha, scale=sigma)
Xlow <- sort(X)[1:N.neg]
xneg <- -Xlow - lowval
xpos <- X[N.neg:length(X)]
X <- c(xneg, xpos)

nAuditMUS(X, Value.sw = "Pos", Error.sw = "Amount", Tol.Error = 180000, Exp.Error = 10000)
nAuditMUS(X, Value.sw = "Pos", Error.sw = "Pct", Tol.Error = 18, Exp.Error = 3)
nAuditMUS(X, Value.sw = "Abs", Error.sw = "Amount", Tol.Error = 180000, Exp.Error = 10000)

Description

Compute a simple random sample size using either a target coefficient of variation, $CV_0$, or target variance, $V_0$, for an estimated mean.

Usage

nCont(CV0=NULL, V0=NULL, S2=NULL, ybarU=NULL, N=Inf, CVpop=NULL)

Arguments

Details

If $CV_0$ is the desired target, then the unit CV, CVpop, or the population mean and variance, ybarU and S2, must also be provided. If $V_0$ is the constrained value, then S2 must be also be included in the function call.

Value

numeric sample size

Author(s)

Richard Valliant, Jill A. Dever, Frauke Kreuter

References

Valliant, R., Dever, J., Kreuter, F. (2018, chap. 3). Practical Tools for Designing and Weighting Survey Samples, 2nd edition. New York: Springer.

See Also

nLogOdds, nProp, nPropMoe, nWilson

Examples

nCont(CV0=0.05, CVpop=2)
nCont(CV0=0.05, CVpop=2, N=500)
nCont(CV0=0.10/1.645, CVpop=1)

    # Compute sample size for a ratio estimator in smho98 population
    # Identify large units to select with certainty first
data(smho98)
cert <- smho98[,"BEDS"] > 2000
tmp <- smho98[!cert, ]
tmp <- tmp[tmp[, "BEDS"] > 0, ]

x <- tmp[,"BEDS"]
y <- tmp[, "EXPTOTAL"]
m <- lm(y ~ 0 + x, weights = 1/x)
ybarU <- mean(y)
S2R <- sum(m$residuals^2/(length(x)-1))
nCont(CV0=0.15, S2=S2R, ybarU=ybarU)

Description

Compute a simple random sample size using a margin of error specified as the half-width of a normal approximation confidence interval or the half-width relative to the population mean.

Usage

nContMoe(moe.sw, e, alpha=0.05, CVpop=NULL, S2=NULL, ybarU=NULL, N=Inf)

Arguments

Details

If moe.sw=1, then S2 must be provided. If moe.sw=2, then either (i) CVpop or (ii) S2 and ybarU must be provided.

Value

numeric sample size

Author(s)

Richard Valliant, Jill A. Dever, Frauke Kreuter

References

Valliant, R., Dever, J., Kreuter, F. (2018, chap. 3). Practical Tools for Designing and Weighting Survey Samples, 2nd edition. New York: Springer.

See Also

nCont, nLogOdds, nProp, nPropMoe, nWilson

Examples

nContMoe(moe.sw=1, e=0.05, alpha=0.05, S2=2)
nContMoe(moe.sw=1, e=0.05, alpha=0.05, S2=2, N=200)
nContMoe(moe.sw=2, e=0.05, alpha=0.05, CVpop=2)
nContMoe(moe.sw=2, e=0.05, alpha=0.05, CVpop=2, N=200)
nContMoe(moe.sw=2, e=0.05, alpha=0.05, S2=4, ybarU=2)

Description

Compute a sample size required to achieve a precision target for an estimated mean, $\hat{\bar{y}}_s$, based on splitting the sample between take-alls and non-take-alls. The sample design for non-take-alls can be either simple random sampling or probability proportional to size sampling.

Usage

nContOpt(X, Y = NULL, CV0 = NULL, V0 = NULL, design = NULL)

Arguments

Details

Compute a sample size based on splitting the sample between take-alls and non-take-alls in a way that achieves either a target coefficient of variation or a target variance for an estimated mean. The function sorts the file in descending order by X and then systematically designates units as take-alls (certainty selections) starting from largest to smallest, and computes the sample size of non-take-alls needed to achieve the precision target. Initially, no unit in the ordered list is a certainty, and if design = "SRS", the first value in nContOpt.curve is the same as nCont produces under identical inputs. In each pass, the algorithm increases the number of certainties. In the second pass, the first value is taken as a certainty and the non-take-all sample size is based on units 2:N, where N is the population size. On the third pass, the first two values are taken as certainties and the non-take-all sample size is based on units 3:N. The function cycles through units 1:(N-1) with take-alls increasing by 1 each cycle, and determines the minimum total sample size needed to achieve the specified precision target. The optimum sample size nContOpt.n combines certainties and non-certainties for its value.

The sample design can be either simple random sampling or probability proportional to size sampling. When design = "SRS", calculations are based only on X. The SRS variance formula is for without replacement sampling so that a finite population correction factor (fpc) is included. When design = "PPS", X is used for the measure of size and Y is the variable for computing the variance used to determine the sample size. The PPS variance is computed for a with-replacement design, but an ad hoc fpc is included. Either CV0 or V0 must be provided but not both.

Value

A list with five components:

Author(s)

George Zipf, Richard Valliant

See Also

nCont, nContMoe

Examples

nContOpt(X = TPV$Total.Pot.Value, CV0 = 0.05, design = "SRS")
nContOpt(X = TPV$Total.Pot.Value, V0  = 5e+14, design = "SRS")
g <- nContOpt(X = TPV$Total.Pot.Value, CV0 = 0.05, design = "SRS")
plot(g$nContOpt.Curve,
     type = "o",
     main = "Sample Size Curve",
     xlab = "Take-all / Sample Split Starting Value",
     ylab = "Total sample size (take-alls + non-tale-alls)" )
nContOpt(X = TPV$Total.Pot.Value, Y = TPV$Y, CV0 = 0.05, design = "PPS")

Description

Compute a simple random sample size for estimating the difference in means when samples overlap

Usage

nDep2sam(S2x, S2y, g, r, rho, alt, del, sig.level=0.05, pow=0.80)

Arguments

Details

nDep2sam computes sample sizes in two groups that are required for testing whether the difference in group means is significant. The power of the test is one of the input parameters. The samples have a specified proportion of units in common. Both samples are assumed to be selected via simple random sampling.

Value

List with values:

Author(s)

Richard Valliant, Jill A. Dever, Frauke Kreuter

References

Valliant, R., Dever, J., Kreuter, F. (2018, chap. 4). Practical Tools for Designing and Weighting Survey Samples, 2nd edition. New York: Springer.

Woodward, M. (1992). Formulas for Sample Size, Power, and Minimum Detectable Relative Risk in Medical Studies. The Statistician, 41, 185-196.

See Also

nProp2sam

Examples

nDep2sam(S2x=200, S2y=200,
            g=0.75, r=1, rho=0.9,
            alt="one.sided", del=5,
            sig.level=0.05, pow=0.80)

Description

Compute a simple random sample size using either a target coefficient of variation, $CV_{0}(d)$, or target variance, $V_{0}(d)$, for an estimated mean or total for a domain.