SampStop: Stopping rule for surveys

In PracTools: Designing and Weighting Survey Samples

Stopping rule for surveys

Description

Compute the probability that continuing data collection will lead to a change in the value of an estimated mean.

Usage

SampStop(lm.obj, formula, n1.data, yvar, n2.data, p = NULL, delta = NULL, seed = NULL)

Arguments

lm.obj	object of class lm from a regression predicting y based on n1.data
formula	righthand side of the formula in lm.obj; it excludes the dependent variable y; no quotes are used.
n1.data	data frame containing units in the part of the sample that has been completed; includes y and the covariates in formula.
yvar	name or number of column in n1.data containing y.
n2.data	data frame containing units in the part of the sample that is yet to be completed; includes only covariates in formula.
p	Vector of anticipated response probabilities for the n2 sample; 0 < p < 1.
delta	vector of potential differences in the estimated means for the n1 and n2 samples.
seed	random number seed for selecting sample from incomplete cases.

Details

SampStop allows an evaluation to be made of whether data collection can be stopped, without substantially affecting the value of an estimated mean, prior to completing collection for all units. Suppose that a sample of size n is divided between the n_1 units whose collection has been completed and the remaining n_2 = n - n_1 units that are yet to be completed. The function computes Pr(|e_1 - e_2| < \delta) where e_1 - e_2 is the potential difference (delta) between the estimated mean based on the completed sample and the estimated mean for the full sample if all units were to be completed. For e_1 the mean is estimated after imputing the y's for the n_2 incomplete units. The estimated mean e_2 is computed assuming that an additional n_2 * p units are completed, and the y's for the remaining n_2 - n_2*p incomplete units are imputed. Estimating the variance of e_1 - e_2 involves selecting a sample from n2.data using the random number seed in seed.

The parameter p is the response rate that is anticipated for the n_2 uncompleted units. The usual situation is that there is some uncertainty about p which can be accounted for by inputting a vector of p's. \delta is a difference in estimates that, if not exceeded, would lead to stopping data collection. For an acceptably small value of delta, if Pr(|e_1 - e_2| < \delta) is large enough, the decision can be made to stop data collection. The variable y in yvar is assumed to follow the linear model in lm.obj. A model with independent errors (or a simple random sample) is assumed for calculations.

Value

Matrix with length(p)*length{delta} rows and columns:

Pr(response)	Probability of response by each of the remaining n_2 cases
Exp no. resps	Expected number of respondents among the remaining n_2 cases

, i.e. n_2*p

y1 mean	Mean of the n_1 respondents
diff in means	Value of the input parameter delta
se of diff	Standard error of the difference delta
z-score	Z-score for computing Pr(|e_1 - e_2| < \delta)
Pr(smaller diff)	Pr(|e_1 - e_2| < \delta) for the inputs of p and delta

Author(s)

George Zipf, Richard Valliant

References

Wagner, J. and Raghunathan, T. (2010). A new stopping rule for surveys. Statistics in Medicine, 29(9), 1014-1024.

Examples

library(PracTools)
    # Model with quantitative covariates
data(hospital)
HOSP <- hospital
HOSP$sqrt.x <- sqrt(HOSP$x)
sam   <- sample(nrow(HOSP), 50)
N1       <- HOSP[sam, ]
N2       <- HOSP[-sam, ]
    ## Create lm object using "known" data; no intercept model
lm.obj  <- lm(y ~ 0 + sqrt.x + x, data = N1)
del <- mean(HOSP$y) - mean(HOSP$y) * seq(.6, 1, by=0.05)
SampStop(lm.obj  = lm.obj,
                    formula = ~ 0 + sqrt.x + x,
                    n1.data = N1,
                    yvar    = "y",
                    n2.data = N2,
                    p       = seq(0.2, 0.6, by=0.05),
                    delta   = del,
                    seed = .Random.seed[413]) 
    # Model with factors
data(labor)
sam   <- sample(nrow(labor), 50)
n1.vars <- c("WklyWage", "HoursPerWk", "agecat", "sex")
n2.vars <- c("HoursPerWk", "agecat", "sex")
N1       <- labor[sam, n1.vars]
N2       <- labor[-sam, n2.vars]
lm.obj  <- lm(WklyWage ~ HoursPerWk + as.factor(agecat) + as.factor(sex), data = labor)
del <- mean(N1$WklyWage) - mean(N1$WklyWage) * seq(.75, .95, by=0.05)
result <- SampStop(lm.obj  = lm.obj,
                    formula = ~ HoursPerWk + as.factor(agecat) + as.factor(sex),
                    n1.data = N1,
                    yvar    = "WklyWage",
                    n2.data = N2,
                    p       = seq(0.2, 0.4, by=0.05),
                    delta   = del,
                    seed = .Random.seed[78]) 

p.nresp <- paste(result[,1], result[,2], sep=", ")
library(ggplot2)
ggplot2::ggplot(result, aes(result[,4], result[,7], colour = factor(p.nresp) )) +
  geom_point() +
  geom_line(linewidth=1.1) +
  labs(x = "delta", y = "Pr(|e1-e2|<= delta)", colour = "Pr(resp), n.resp")                      

PracTools documentation built on June 8, 2025, 10:12 a.m.