CalSF {Frames2} | R Documentation |
SF calibration estimator
Description
Produces estimates for population totals and means using the SF calibration estimator from survey data obtained from a dual frame sampling design. Confidence intervals are also computed, if required.
Usage
CalSF(ysA, ysB, pi_A, pi_B, pik_ab_B, pik_ba_A, domains_A, domains_B, N_A = NULL,
N_B = NULL, N_ab = NULL, xsAFrameA = NULL, xsBFrameA = NULL, xsAFrameB = NULL,
xsBFrameB = NULL, xsT = NULL, XA = NULL, XB = NULL, X = NULL, met = "linear",
conf_level = NULL)
Arguments
ysA |
A numeric vector of length |
ysB |
A numeric vector of length |
pi_A |
A numeric vector of length |
pi_B |
A numeric vector of length |
pik_ab_B |
A numeric vector of size |
pik_ba_A |
A numeric vector of size |
domains_A |
A character vector of size |
domains_B |
A character vector of size |
N_A |
(Optional) A numeric value indicating the size of frame A |
N_B |
(Optional) A numeric value indicating the size of frame B |
N_ab |
(Optional) A numeric value indicating the size of the overlap domain |
xsAFrameA |
(Optional) A numeric vector of length |
xsBFrameA |
(Optional) A numeric vector of length |
xsAFrameB |
(Optional) A numeric vector of length |
xsBFrameB |
(Optional) A numeric vector of length |
xsT |
(Optional) A numeric vector of length |
XA |
(Optional) A numeric value or vector of length |
XB |
(Optional) A numeric value or vector of length |
X |
(Optional) A numeric value or vector of length |
met |
(Optional) A character vector indicating the distance that must be used in calibration process. Possible values are "linear", "raking" and "logit". Default is "linear". |
conf_level |
(Optional) A numeric value indicating the confidence level for the confidence intervals, if desired. |
Details
SF calibration estimator of population total is given by
\hat{Y}_{CalSF} = \hat{Y}_a + \hat{Y}_{ab} + \hat{Y}_b
where \hat{Y}_a = \sum_{i \in s_a}\tilde{d}_i y_i, \hat{Y}_{ab} = \sum_{i \in (s_{ab} \cup s_{ba})}\tilde{d}_i y_i
and \hat{Y}_b = \sum_{i \in s_b} \tilde{d}_i y_i
, with \tilde{d}_i
calibration weights which are calculated
having into account a different set of constraints, depending on the case. For instance, if N_A, N_B
and N_{ab}
are known and no other auxiliary information is available, calibration constraints are
\sum_{i \in s_a}\tilde{d}_i = N_a, \sum_{i \in s_{ab} \cup s_{ba}}\tilde{d}_i = N_{ab}, \sum_{i \in s_{ba}}\tilde{d}_i = N_{ba}
Function covers following scenarios:
There is not any additional auxiliary variable
-
N_A, N_B
andN_{ab}
unknown -
N_{ab}
known andN_A
andN_B
unknown -
N_A
andN_B
known andN_{ab}
unknown -
N_A, N_B
andN_{ab}
known
-
At least, information about one additional auxiliary variable is available
-
N_{ab}
known andN_A
andN_B
unknown -
N_A
andN_B
known andN_{ab}
unknown -
N_A, N_B
andN_{ab}
known
-
To obtain an estimator of the variance for this estimator, one can use Deville's expression
\hat{V}(\hat{Y}_{CalSF}) = \frac{1}{1-\sum_{k\in s} a_k^2}\sum_{k\in s}(1-\pi_k)\left(\frac{e_k}{\pi_k} - \sum_{l\in s} a_{l} \frac{e_l}{\pi_l}\right)^2
where a_k=(1-\pi_k)/\sum_{l\in s} (1-\pi_l)
and e_k
are the residuals of the regression with auxiliary variables as regressors.
Value
CalSF
returns an object of class "EstimatorDF" which is a list with, at least, the following components:
Call |
the matched call. |
Est |
total and mean estimation for main variable(s). |
VarEst |
variance estimation for main variable(s). |
If parameter conf_level
is different from NULL
, object includes component
ConfInt |
total and mean estimation and confidence intervals for main variables(s). |
In addition, components TotDomEst
and MeanDomEst
are available when estimator is based on estimators of the domains. Component Param
shows value of parameters involded in calculation of the estimator (if any).
By default, only Est
component (or ConfInt
component, if parameter conf_level
is different from NULL
) is shown. It is possible to access to all the components of the objects by using function summary
.
References
Ranalli, M. G., Arcos, A., Rueda, M. and Teodoro, A. (2013) Calibration estimation in dual frame surveys. arXiv:1312.0761 [stat.ME]
Deville, J. C., Sarndal, C. E. (1992) Calibration estimators in survey sampling. Journal of the American Statistical Association, 87, 376 - 382
See Also
Examples
data(DatA)
data(DatB)
data(PiklA)
data(PiklB)
#Let calculate SF calibration estimator for variable Clothing, without
#considering any auxiliary information
CalSF(DatA$Clo, DatB$Clo, PiklA, PiklB, DatA$ProbB, DatB$ProbA,
DatA$Domain, DatB$Domain)
#Now, let calculate SF calibration estimator for variable Leisure when the frame
#sizes and the overlap domain size are known
CalSF(DatA$Lei, DatB$Lei, PiklA, PiklB, DatA$ProbB, DatB$ProbA, DatA$Domain,
DatB$Domain, N_A = 1735, N_B = 1191, N_ab = 601)
#Finally, let calculate SF calibration estimator and a 90% confidence interval
#for population total for variable Feeding, considering Income and Metres2 as auxiliary
#variables and with frame sizes and overlap domain size known.
CalSF(DatA$Feed, DatB$Feed, PiklA, PiklB, DatA$ProbB, DatB$ProbA, DatA$Domain,
DatB$Domain, N_A = 1735, N_B = 1191, N_ab = 601, xsAFrameA = DatA$Inc,
xsBFrameA = DatB$Inc, xsAFrameB = DatA$M2, xsBFrameB = DatB$M2,
XA = 4300260, XB = 176553, conf_level = 0.90)