MLCSW {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 single frame approach with auxiliary information from the whole population. Confidence intervals are also computed, if required.
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)
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 |
pik_ab_B |
A numeric vector of size |
pik_ba_A |
A numeric vector of size |
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 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.
.
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). |
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$Domain == "ab",])
#Let calculate proportions of categories of variable Prog using MLCSW estimator
#using Read as auxiliary variable
MLCSW(DatMA$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)