MLSW {Frames2}

Multinomial logistic 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 with the same set of auxiliary variables for the whole population. Confidence intervals are also computed, if required.

Usage

MLSW (ysA, ysB, pik_A, pik_B, pik_ab_B, pik_ba_A, domains_A, domains_B, xsA, xsB, 
x, ind_sam, 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

conf_level

(Optional) A numeric value indicating the confidence level for the confidence intervals, if desired.

Details

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

\hat{P}_{MLi}^{SW} = \frac{1}{N} \left(\sum_{k \in U} \tilde{p}_{ki} + \sum_{k \in s} \tilde{d}_k (z_{ki} - \tilde{p}_{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, \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. and

\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}.

Value

PMLSW 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.

Lehtonen, R. and Veijanen, A. (1998) On multinomial logistic generalizaed regression estimators Technical report 22, Department of Statistics, University of Jyvaskyla.

See Also

JackMLSW

Examples

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

IndSample <- c(DatMA$Id_Pop, DatMB$Id_Pop)
#Let calculate proportions of categories of variable Prog using MLSW estimator
#using Read as auxiliary variable
MLSW(DatMA$Prog, DatMB$Prog, DatMA$ProbA, DatMB$ProbB, DatMA$ProbB, DatMB$ProbA,
DatMA$Domain, DatMB$Domain, DatMA$Read, DatMB$Read, DatPopM$Read, IndSample)

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