MLCDF {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 a possibly different set of auxiliary variables for each frame. Confidence intervals are also computed, if required.
MLCDF (ysA, ysB, pik_A, pik_B, domains_A, domains_B, xsA, xsB, xA, xB, ind_samA,
ind_samB, ind_domA, ind_domB, N, 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 |
xA |
A numeric vector or length |
xB |
A numeric vector or length |
ind_samA |
A numeric vector of length |
ind_samB |
A numeric vector of length |
ind_domA |
A character vector of length |
ind_domB |
A character vector of length |
N |
A numeric value indicating the size of the population. |
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 each frame for a proportion is given by
\hat{P}_{MLCi}^{DF} = \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},
\sum_{k \in s_A}w_k^\circ p_{ki}^A = \sum_{k \in U_a} p_{ki}^A + \eta \sum_{k \in U_{ab}} p_{ki}^A
and
\sum_{k \in s_B}w_k^\circ p_{ki}^B = \sum_{k \in U_b} p_{ki}^B + (1 - \eta) \sum_{k \in U_{ba}} p_{ki}^B
with \eta \in (0,1)
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 original design weights d^A
. p_{ki}^B
can be defined similarly.
MLCDF
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)
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 MLCDF estimator
#using Read as auxiliary variable
MLCDF(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
MLCDF(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)