Fitting Saturated Models for the Marginal Probabilities of Categorization via Weighted Least Squares under MCAR assumption

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Description

satMcarWLS fits saturated structural models for the marginal probabilities of categorization under a missing completely at random (MCAR) assumption for the missingness mechanism by weighted least squares (WLS) methodology. It is based on input data of a readCatdata object. Functional linear models may be subsequently fitted using function funlinWLS().

Usage

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satMcarWLS(catdataobj, zeroN)

Arguments

catdataobj

readCatdata object.

zeroN

values used to replace null frequencies in the denominator of the Neyman statistic; by default, the function replaces the values by

1/(R*nst)

, where nst is the sample size of the missingness pattern associated to the corresponding subpopulation; the user may indicate alternative values in a matrix with S rows and an additional column relatively to the number of columns of Rp; the first column relates to the completely categorized "missingness" patterns, and the remaining columns to the other missingness patterns as they appear in Rp; the values must be non-negative and less or equal to 0.5.

Details

The generic functions print and summary are used to print the results and to obtain a summary thereof.

Value

An object of the class satMcarWLS is a list containing most of the components of the readCatdata source object informed in the argument

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catdataobj

as well as the following components:

theta

vector of WLS estimates for all product-multinomial probabilities under the saturated model for the marginal probabilities of categorization and a MCAR assumption.

Vtheta

corresponding estimated covariance matrix.

QnMCAR

the Neyman statistic for the conditional test of MCAR given a MAR assumption.

glMCAR

degrees of freedom for the conditional test of MCAR given a MAR assumption.

yst

WLS estimates for the augmented frequencies under the saturated model for the marginal probabilities and the MCAR mechanism.

Author(s)

Frederico Zanqueta Poleto(frederico@poleto.com)
Julio da Motta Singer (jmsinger@ime.usp.br)
Carlos Daniel Paulino (daniel.paulino@math.ist.utl.pt)
with the collaboration of
Fabio Mathias Correa (fmcorrea@uesc.br)
Enio Galinkin Jelihovschi (eniojelihovs@gmail.com)

References

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.

Examples

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	#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.satmcarwls<-satMcarWLS(e134.catdata)
	e134.satmcarwls
	
	#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<-t(rep(1,2))%x%cbind(diag(3)%x%rep(1,3), rep(1,3)%x%diag(3))
	smoking.Rp<-rbind(c(3,3),c(3,3))
	smoking.catdata<-readCatdata(TF=smoking.TF,Zp=smoking.Zp,Rp=smoking.Rp)
	smoking.satmcarwls<-satMcarWLS(smoking.catdata)
	smoking.satmcarwls