MLDW: Multinomial logistic estimator under dual frame approach with...
In Frames2: Estimation in Dual Frame Surveys

Description Usage Arguments Details Value References See Also Examples

Produces estimates for class totals and proportions using multinomial logistic regression from survey data obtained from a dual frame sampling design using a dual frame model assisted approach. Confidence intervals are also computed, if required.

1 2	MLDW (ysA, ysB, pik_A, pik_B, domains_A, domains_B, xsA, xsB, x, ind_sam, conf_level = NULL)

`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, 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.

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

\hat{P}_{MLi}^{DW} = \frac{1}{N} (∑_{k \in U} p_{ki}^{\circ} + ∑_{k \in s} {d}_k^{\circ} (z_{ki} - p_{ki}^{\circ})) \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, d_k^{\circ} =≤ft\{\begin{array}{lcc} d_k^A & \textrm{if } k \in a\\ η d_k^A & \textrm{if } k \in ab\\ (1 - η) d_k^B & \textrm{if } k \in ba \\ d_k^B & \textrm{if } k \in b \end{array} \right. with η \in (0,1) and

p_{ki}^\circ = \frac{exp(x_k^{'}β_i^{\circ})}{∑_{r=1}^m exp(x_k^{'}β_r^{\circ})},

being β_i^{\circ} the maximum likelihood parameters of the multinomial logistic model considering the weights d^{\circ}.

MLDW 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).

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.

JackMLDW

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

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

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