MLDF {Frames2}

Multinomial logistic estimator under dual frame approach with auxiliary information from each frame

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 assisted approach with a possibly different set of auxiliary variables for each frame. Confidence intervals are also computed, if required.

Usage

MLDF (ysA, ysB, pik_A, pik_B, domains_A, domains_B, xsA, xsB, xA, xB, ind_samA, 
 ind_samB, ind_domA, ind_domB, N, 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.

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_A, with m_A the number of auxiliary variables in frame A, 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_B, with m_B the number of auxiliary variables in frame B, containing auxiliary information in frame B for units included in s_B.

xA

A numeric vector or 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 for the units in frame A.

xB

A numeric vector or 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 for the units in frame B.

ind_samA

A numeric vector of length n_A containing the identificators of units of the frame A (from 1 to N_A) that belongs to s_A.

ind_samB

A numeric vector of length n_B containing the identificators of units of the frame B (from 1 to N_B) that belongs to s_B.

ind_domA

A character vector of length N_A indicating the domain each unit from frame A belongs to. Possible values are "a" and "ab".

ind_domB

A character vector of length N_B indicating the domain each unit from frame B belongs to. Possible values are "b" and "ba".

N

A numeric value indicating the size of the population.

conf_level

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

Details

Multinomial logistic estimator in dual frame using auxiliary information from each frame for a proportion is given by

\hat{P}_{MLi}^{DF} = \frac{1}{N} \left(\sum_{k \in U_a} p_{ki}^A + \eta \sum_{k \in U_{ab}} p_{ki}^A + (1 - \eta) \sum_{k \in U_{ba}} p_{ki}^B + \sum_{k \in U_b} p_{ki}^B \right.

+ \sum_{k \in s_a} d_k^A (z_{ki} - p_{ki}^A) + \eta \sum_{k \in s_{ab}} d_k^A (z_{ki} - p_{ki}^A)

\left. + (1 - \eta) \sum_{k \in s_{ba}} d_k^B (z_{ki} - p_{ki}^B) + \sum_{k \in s_b} d_k^B (z_{ki} - p_{ki}^B)\right), \hspace{0.3cm} i = 1,...,m

with \eta \in (0,1), m the number of categories of the response variable, z_i the indicator variable for the i-th category of the response variable, d^A and d^B the design weights for each frame, defined as the inverse of the first order inclusion probabilities and

p_{ki}^A = \frac{exp(x_k^{'}\beta_i^A)}{\sum_{r=1}^m exp(x_k^{'}\beta_r^A)},

being \beta_i^A the maximum likelihood parameters of the multinomial logistic model considering weights d^A. p_{ki}^B can be defined similarly.

Value

MLDF 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

JackMLDF

Examples

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

N <- nrow(DatPopM)
levels(DatPopM$Domain) <- c(levels(DatPopM$Domain), "ba")
DatPopMA <- subset(DatPopM, DatPopM$Domain == "a" | DatPopM$Domain == "ab", stringAsFactors = FALSE)
DatPopMB <- subset(DatPopM, DatPopM$Domain == "b" | DatPopM$Domain == "ab", stringAsFactors = FALSE)
DatPopMB[DatPopMB$Domain == "ab",]$Domain <- "ba"

#Let calculate proportions of categories of variable Prog using MLDF estimator
#using Read as auxiliary variable
MLDF(DatMA$Prog, DatMB$Prog, DatMA$ProbA, DatMB$ProbB, DatMA$Domain, DatMB$Domain, 
DatMA$Read, DatMB$Read, DatPopMA$Read, DatPopMB$Read, DatMA$Id_Frame, DatMB$Id_Frame, 
DatPopMA$Domain, DatPopMB$Domain, N)

#Let obtain 95% confidence intervals together with the estimations
MLDF(DatMA$Prog, DatMB$Prog, DatMA$ProbA, DatMB$ProbB, DatMA$Domain, DatMB$Domain, 
DatMA$Read, DatMB$Read, DatPopMA$Read, DatPopMB$Read, DatMA$Id_Frame, DatMB$Id_Frame, 
DatPopMA$Domain, DatPopMB$Domain, N, conf_level = 0.95)