Description Usage Arguments Details Value References Examples
satMarML
fits saturated models for the marginal probabilities of
categorization as well as missing at random (MAR) or missing completely at random (MCAR)
models for the missingness mechanism by maximum likelihood (ML) methodology.
It is based on input data of a readCatdata
object.
Linear, log-linear and functional linear models may be subsequently fitted,
respectively, using functions linML()
, loglinML()
and
funlinWLS()
.
1 2 |
catdataobj |
|
missing |
the covariance matrix (based on a Fisher information matrix) of the
estimates for the marginal probabilities of categorization may be computed under
|
method |
the iterative processes available are: |
start |
by default, the function uses the proportions of the complete data as starting
values in the iterative process, but the current argument allows the user to inform an
alternative starting value for all marginal probabilities except the one corresponding to the
last category of each multinomial, i.e., a vector of dimension |
zero |
when there are sampling zeros in the complete data, these frequencies are replaced
by small values just for the computation of the starting values; this avoids the use of
starting values on the boundary of the parameter space and also allows to incorporate
information from other missingness patterns in the EM iterative process; by default, the
function replaces the values by |
maxit |
the maximum number of iterations (the default is 100). |
trace |
the alternatives are: 0 for no printing (default), 1 for showing only the value of the likelihood ratio statistic at each iteration of the iterative process, and 2 for including also the parameter estimates at each iteration. |
epsilon1 |
the convergence criterion of the iterative process is attained if the
absolute difference of the values of the likelihood ratio statistic of successive iterations
is less than the value defined in |
epsilon2 |
the convergence criterion of the iterative process is attained if the
absolute differences of the values of estimates for all parameters of the marginal
probabilities of categorization in consecutive iterations are less than the value defined
in |
zeroN |
values used to replace null frequencies in the denominator of the Neyman statistic;
by default, the function replaces the values by |
digits |
integer value indicating the number of decimal places to round results when shown
by |
The generic functions print
and summary
are used to print the results and to obtain a
summary thereof.
An object of the class satMarML
is a list containing most of the components of the
readCatdata
source object informed in the argument catdataobj
as well as
the following components:
theta |
vector of ML estimates for all product-multinomial probabilities under the saturated model for the marginal probabilities of categorization and an assumption of an ignorable missingness mechanism; this is the same under MAR and under MCAR. |
Vtheta |
corresponding estimated covariance matrix based on the Fisher information matrix obtained under the assumed missingness mechanism, leading to different results depending whether the assumption is MAR or MCAR). |
QvMCAR |
likelihood ratio statistic for the conditional test of MCAR given a MAR assumption. |
QpMCAR |
Pearson statistic for the conditional test of MCAR given a MAR assumption. |
QnMCAR |
Neyman statistic for the conditional test of MCAR given a MAR assumption. |
glMCAR |
degrees of freedom for the conditional tests of MCAR given a MAR assumption. |
alphast |
ML estimates for the conditional probabilities of missingness under the assumed missingness mechanism (MAR or MCAR). |
yst |
ML estimates for the augmented frequencies under the saturated model for the marginal probabilities and the assumed missingness mechanism (MAR or MCAR). |
Paulino, C.D. e Singer, J.M. (2006). Analise de dados categorizados (in Portuguese). Sao Paulo: Edgard Blucher.
Poleto, F.Z. (2006). Analise de dados categorizados com omissao (in Portuguese). Dissertacao de mestrado. IME-USP. http://www.poleto.com/missing.html.
Poleto, F.Z., Singer, J.M. e Paulino, C.D. (2007). Analyzing categorical data with complete or missing responses using the Catdata package. Unpublished vignette. http://www.poleto.com/missing.html.
Poleto, F.Z., Singer, J.M. e Paulino, C.D. (2012). A product-multinomial framework for categorical data analysis with missing responses. To appear in Brazilian Journal of Probability and Statistics. http://imstat.org/bjps/papers/BJPS198.pdf.
Singer, J. M., Poleto, F. Z. and Paulino, C. D. (2007). Catdata: software for analysis of categorical data with complete or missing responses. Actas de la XII Reunion Cientifica del Grupo Argentino de Biometria y I Encuentro Argentino-Chileno de Biometria. http://www.poleto.com/SingerPoletoPaulino2007GAB.pdf.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 | #Example 13.4 of Paulino and Singer (2006)
e134.TF<-c(12,4,5,2, 50,31, 27,12)
e134.Zp<-cbind(kronecker(diag(2),rep(1,2)),kronecker(rep(1,2),diag(2)))
e134.Rp<-c(2,2)
e134.catdata<-readCatdata(TF=e134.TF,Zp=e134.Zp,Rp=e134.Rp)
e134.satmcarml<-satMarML(e134.catdata,missing="MCAR")
e134.satmarml<-satMarML(e134.catdata,method="FS-MCAR")
e134.satmarml2<-satMarML(e134.catdata,method="NR/FS-MAR")
e134.satmcarml
#Compare the estimates of the probabilities, standard errors,
#number of iterations and augmented frequencies
summary(e134.satmcarml)
summary(e134.satmarml)
summary(e134.satmarml2)
#Example 1 of Poleto et al (2012)
smoking.TF<-rbind(c(167,17,19,10,1,3,52,10,11, 176,24,121, 28,10,12),
c(120,22,19, 8,5,1,39,12,12, 103, 3, 80, 31, 8,14))
smoking.Zp <- kronecker(t(rep(1,2)),
cbind(kronecker(diag(3),rep(1,3)),
kronecker(rep(1,3),diag(3))))
smoking.Rp<-rbind(c(3,3),c(3,3))
smoking.catdata<-readCatdata(TF=smoking.TF,Zp=smoking.Zp,Rp=smoking.Rp)
smoking.catdata
smoking.satmcarml<-satMarML(smoking.catdata,missing="MCAR")
smoking.satmarml<-satMarML(smoking.catdata,method="FS-MCAR")
smoking.satmarml2<-satMarML(smoking.catdata,method="NR/FS-MAR")
smoking.satmarml
summary(smoking.satmcarml)
summary(smoking.satmarml)
summary(smoking.satmarml2)
|
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