ACD (version 1.5.3)

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

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

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.

Value

An object of the class satMcarWLS 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 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.

Details

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

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 Unpublished vignette.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

	#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