MLCDW {Frames2} | R Documentation |
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 dual frame approach with auxiliary information from the whole population. Confidence intervals are also computed, if required.
MLCDW (ysA, ysB, pik_A, pik_B, domains_A, domains_B, xsA, xsB, x, ind_sam, N_A,
N_B, N_ab = NULL, met = "linear", conf_level = NULL)
ysA |
A data frame containing information about one or more factors, each one of dimension |
ysB |
A data frame containing information about one or more factors, each one of dimension |
pik_A |
A numeric vector of length |
pik_B |
A numeric vector of length |
domains_A |
A character vector of size |
domains_B |
A character vector of size |
xsA |
A numeric vector of length |
xsB |
A numeric vector of length |
x |
A numeric vector or length |
ind_sam |
A numeric vector of length |
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. |
Multinomial logistic calibration estimator in dual frame using auxiliary information from the whole population for a proportion is given by
\hat{P}_{MLCi}^{DW} = \frac{1}{N} \left(\sum_{k \in s_A \cup s_B} w_k^{\circ} 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 w^{\circ}
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}w_k^{\circ} = N_a, \sum_{k \in s_{ab}}w_k^{\circ} = \eta N_{ab}, \sum_{k \in s_{ba}}w_k^{\circ} = (1 - \eta) N_{ab}, \sum_{k \in s_{b}}w_k^{\circ} = N_{b}
and
\sum_{k \in s_A \cup s_B}w_k^\circ p_{ki}^{\circ} = \sum_{k \in U} p_{ki}^\circ
with \eta \in (0,1)
and
p_{ki}^{\circ} = \frac{exp(x_k^{'}\beta_i^{\circ})}{\sum_{r=1}^m exp(x_k^{'}\beta_r^{\circ})},
being \beta_i^\circ
the maximum likelihood parameters of the multinomial logistic model considering weights d_k^{\circ} =\left\{\begin{array}{lcc}
d_k^A & \textrm{if } k \in a\\
\eta d_k^A & \textrm{if } k \in ab\\
(1 - \eta) d_k^B & \textrm{if } k \in ba \\
d_k^B & \textrm{if } k \in b
\end{array}
\right.
.
MLCDW
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.
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$Domain == "ab",])
#Let calculate proportions of categories of variable Prog using MLCDW estimator
#using Read as auxiliary variable
MLCDW(DatMA$Prog, DatMB$Prog, DatMA$ProbA, DatMB$ProbB, DatMA$Domain, DatMB$Domain,
DatMA$Read, DatMB$Read, DatPopM$Read, IndSample, N_FrameA, N_FrameB)
#Now, let suppose that the overlap domian size is known
MLCDW(DatMA$Prog, DatMB$Prog, DatMA$ProbA, DatMB$ProbB, DatMA$Domain, DatMB$Domain,
DatMA$Read, DatMB$Read, DatPopM$Read, IndSample, N_FrameA, N_FrameB, N_Domainab)
#Let obtain 95% confidence intervals together with the estimations
MLCDW(DatMA$Prog, DatMB$Prog, DatMA$ProbA, DatMB$ProbB, DatMA$Domain, DatMB$Domain,
DatMA$Read, DatMB$Read, DatPopM$Read, IndSample, N_FrameA, N_FrameB, N_Domainab,
conf_level = 0.95)