WeightsCalSF: g-weights for the SF calibration estimator
In Frames2: Estimation in Dual Frame Surveys

Description Usage Arguments Details Value References Examples

Computes the g-weights for the SF calibration estimator.

WeightsCalSF(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")

`ysA`	A numeric vector of length n_A or a numeric matrix or data frame of dimensions n_A x c containing information about variable(s) of interest from s_A.
`ysB`	A numeric vector of length n_B or a numeric matrix or data frame of dimensions n_B x c containing information about variable(s) of interest from s_A.
`pi_A`	A numeric vector of length n_A or a square numeric matrix of dimension n_A containing first order or first and second order inclusion probabilities for units included in s_A.
`pi_B`	A numeric vector of length n_B or a square numeric matrix of dimension n_B containing first order or first and second order inclusion probabilities for units included in s_B.
`pik_ab_B`	A numeric vector of size n_A containing first order inclusion probabilities according to sampling desing in frame B for units belonging to overlap domain that have been selected in s_A.
`pik_ba_A`	A numeric vector of size n_B containing first order inclusion probabilities according to sampling desing in frame A for units belonging to overlap domain that have been selected in s_B.
`domains_A`	A character vector of size n_A indicating the domain each unit from s_A belongs to. Possible values are "a" and "ab".
`domains_B`	A character vector of size n_B indicating the domain each unit from s_B belongs to. Possible values are "b" and "ba".
`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 n_A or a numeric matrix or data frame of dimensions n_A x m_A, with m_A the number of auxiliary variables in frame A, containing auxiliary information in frame A for units included in s_A.
`xsBFrameA`	(Optional) A numeric vector of length n_B or a numeric matrix or data frame of dimensions n_B x m_A, with m_A the number of auxiliary variables in frame A, containing auxiliary information in frame A for units included in s_B. For units in domain b, these values are 0.
`xsAFrameB`	(Optional) A numeric vector of length n_A or a numeric matrix or data frame of dimensions n_A x m_B, with m_B the number of auxiliary variables in frame B, containing auxiliary information in frame B for units included in s_A. For units in domain a, these values are 0.
`xsBFrameB`	(Optional) A numeric vector of length n_B or a numeric matrix or data frame of dimensions n_B x m_B, with m_B the number of auxiliary variables in frame B, containing auxiliary information in frame B for units included in s_B.
`xsT`	(Optional) A numeric vector of length n or a numeric matrix or data frame of dimensions n x m_T, with m_T the number of auxiliary variables in both frames, containing auxiliary information for all units in the entire sample s = s_A \cup s_B.
`XA`	(Optional) A numeric value or vector of length m_A, with m_A the number of auxiliary variables in frame A, indicating the population totals for the auxiliary variables considered in frame A.
`XB`	(Optional) A numeric value or vector of length m_B, with m_B the number of auxiliary variables in frame B, indicating the population totals for the auxiliary variables considered in frame B.
`X`	(Optional) A numeric value or vector of length m_T, with m_T the number of auxiliary variables in both frames, indicating the population totals for the auxiliary variables considered in both frames.
`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".

Function provides g-weights in following scenarios:

There is not any additional auxiliary variable
- N_A, N_B and N_{ab} unknown
- N_{ab} known and N_A and N_B unknown
- N_A and N_B known and N_{ab} unknown
- N_A, N_B and N_{ab} known
At least, one additional auxiliary variable is available
- N_{ab} known and N_A and N_B unknown
- N_A and N_B known and N_{ab} unknown
- N_A, N_B and N_{ab} known

A numeric vector containing the g-weights for the SF calibration estimator.

Ranalli, M. G., Arcos, A., Rueda, M. and Teodoro, A. (2013) Calibration estimationn in dual frame surveys. arXiv:1312.0761 [stat.ME]

Deville, J. C., S\"arndal, C. E. (1992) Calibration estimators in survey sampling. Journal of the American Statistical Association, 87, 376 - 382

data(DatA)
data(DatB)
data(PiklA)
data(PiklB)

#Let calculate g-weights for the SF calibration estimator for variable Clothing,
#without considering any auxiliary information
WeightsCalSF(DatA$Clo, DatB$Clo, PiklA, PiklB, DatA$ProbB, DatB$ProbA, 
DatA$Domain, DatB$Domain)

#Now, let calculate g-weights for the SF calibration estimator for variable Leisure
#when the frame sizes and the overlap domain size are known
WeightsCalSF(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 g-weights for the SF calibration estimator
#for variable Feeding, considering Income and Metres2 as auxiliary 
#variables and with frame sizes and overlap domain size known.
WeightsCalSF(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)