MLCSW {Frames2}

Multinomial logistic calibration estimator under single frame approach with auxiliary information from the whole population

Description

Produces estimates for class totals and proportions using multinomial logistic regression from survey data obtained from a dual frame sampling design using a model calibrated single frame approach with auxiliary information from the whole population. Confidence intervals are also computed, if required.

Usage

MLCSW (ysA, ysB, pik_A, pik_B, pik_ab_B, pik_ba_A, domains_A, domains_B, xsA, xsB,
 x, ind_sam, N_A, N_B, N_ab = NULL, met = "linear", conf_level = NULL)

Arguments

ysA

A data frame containing information about one or more factors, each one of dimension n_A, collected from s_A.

ysB

A data frame containing information about one or more factors, each one of dimension n_B, collected from s_B.

pik_A

A numeric vector of length n_A containing first order inclusion probabilities for units included in s_A.

pik_B

A numeric vector of length n_B containing first 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 design 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 design 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".

xsA

A numeric vector of length n_A or a numeric matrix or data frame of dimensions n_A x m, with m the number of auxiliary variables, containing auxiliary information in frame A for units included in s_A.

xsB

A numeric vector of length n_B or a numeric matrix or data frame of dimensions n_B x m, with m the number of auxiliary variables, containing auxiliary information in frame B for units included in s_B.

x

A numeric vector or length N or a numeric matrix or data frame of dimensions N x m, with m the number of auxiliary variables, containing auxiliary information for every unit in the population.

ind_sam

A numeric vector of length n = n_A + n_B containing the identificators of units of the population (from 1 to N) that belongs to s_A or s_B

N_A

A numeric value indicating the size of frame A

N_B

A numeric value indicating the size of frame B

N_ab

(Optional) A numeric value indicating the size of the overlap domain

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

Multinomial logistic calibration estimator in single frame using auxiliary information from the whole population for a proportion is given by

\hat{P}_{MLCi}^{SW} = \frac{1}{N} \left(\sum_{k \in s_A \cup s_B} \tilde{w}_k z_{ki}\right) \hspace{0.3cm} i = 1,...,m

with m the number of categories of the response variable, z_i the indicator variable for the i-th category of the response variable, and \tilde{w} 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, calibration constraints are

\sum_{k \in s_a}\tilde{w}_k = N_a, \sum_{k \in s_{ab} \cup s_{ba}}\tilde{w}_k = N_{ab}, \sum_{k \in s_{ba}}\tilde{w}_k = N_{ba}

and

\sum_{k \in s_A \cup s_B}\tilde{w}_k \tilde{p}_{ki} = \sum_{k \in U} \tilde{p}_{ki}

with

\tilde{p}_{ki} = \frac{exp(x_k^{'}\tilde{\beta_i})}{\sum_{r=1}^m exp(x_k^{'}\tilde{\beta_r})},

being \tilde{\beta_i} the maximum likelihood parameters of the multinomial logistic model considering weights \tilde{d}_k =\left\{\begin{array}{lcc} d_k^A & \textrm{if } k \in a\\ (1/d_k^A + 1/d_k^B)^{-1} & \textrm{if } k \in ab \cup ba \\ d_k^B & \textrm{if } k \in b \end{array} \right..

Value

MLCSW returns an object of class "MultEstimatorDF" which is a list with, at least, the following components:

Call

the matched call.

Est

class frequencies and proportions estimations for main variable(s).

References

Molina, D., Rueda, M., Arcos, A. and Ranalli, M. G. (2015) Multinomial logistic estimation in dual frame surveys Statistics and Operations Research Transactions (SORT). To be printed.

See Also

JackMLCSW

Examples

data(DatMA)
data(DatMB)
data(DatPopM) 

IndSample <- c(DatMA$Id_Pop, DatMB$Id_Pop)
N_FrameA <- nrow(DatPopM[DatPopM$Domain == "a" | DatPopM$Domain == "ab",])
N_FrameB <- nrow(DatPopM[DatPopM$Domain == "b" | DatPopM$Domain == "ab",])
N_Domainab <- nrow(DatPopM[DatPopM$Domain == "ab",])
#Let calculate proportions of categories of variable Prog using MLCSW estimator
#using Read as auxiliary variable
MLCSW(DatMA$Prog, DatMB$Prog, DatMA$ProbA, DatMB$ProbB, DatMA$ProbB, DatMB$ProbA,
DatMA$Domain, DatMB$Domain, DatMA$Read, DatMB$Read, DatPopM$Read, IndSample, N_FrameA, 
N_FrameB)

#Now, let suppose that the overlap domian size is known
MLCSW(DatMA$Prog, DatMB$Prog, DatMA$ProbA, DatMB$ProbB, DatMA$ProbB, DatMB$ProbA,
DatMA$Domain, DatMB$Domain, DatMA$Read, DatMB$Read, DatPopM$Read, IndSample, N_FrameA, 
N_FrameB, N_Domainab)

#Let obtain 95% confidence intervals together with the estimations
MLCSW(DatMA$Prog, DatMB$Prog, DatMA$ProbA, DatMB$ProbB, DatMA$ProbB, DatMB$ProbA,
DatMA$Domain, DatMB$Domain, DatMA$Read, DatMB$Read, DatPopM$Read, IndSample, N_FrameA, 
N_FrameB, N_Domainab, conf_level = 0.95)