readCatdata: Reads Categorical Data

Description

readCatdata inputs the categorical data, accommodating complete or missing observations. This corresponds to objects of the classes vector or matrix which represent a table of frequencies assumed to follow a product-multinomial distribution. For complete data, only the argument TF is required. Linear, log-linear and functional linear models may be subsequently fitted, respectively, using the functions linML(), loglinML() and funlinWLS(). For missing data, all arguments TF, Zp and Rp are required. Before proceeding to model fitting, inferences for the saturated product-multinomial parameters are conducted using either the function satMarML() or satMcarWLS().

Usage

readCatdata(TF, Zp, Rp)

Arguments

a matrix including the table of frequencies (see details).

a matrix with indicators of the partially classified data (see details).

a matrix with the number of response classes corresponding to the missingness patterns (see details).

Value

R: number of response categories.
S: number of subpopulations.
Tt: number of missingness patterns of each subpopulation.
Nst: frequencies under each missingness pattern of each subpopulation.
nstm: sample size of each missingness pattern of each subpopulation.
nsmm: sample size of each subpopulation.
pst: vectors of proportions computed under each missingness pattern of each subpopulation.
Vpst: covariance matrices of the proportions.
theta: vector of estimates for all product-multinomial probabilities under the saturated model (for complete data only).
Vtheta: corresponding covariance matrix (only for complete data).

Details

Whenever TF is a vector it represents one population assumed to follow a multinomial distribution. Whenever TF is a matrix, each row represents a subpopulation, the set of which is assumed to follow a product-multinomial distribution. For complete data, TF is usually a simple matrix (table of frequencies) with S rows (subpopulations) and R columns (response categories). For missing categorical data, each row of TF is assumed to have first the R frequencies associated to the response categories of the fully classified data, and thereafter the frequencies associated to the response classes of the partially classified data. The term response class is used to indicate that the corresponding observed data may only be classified into a set of response categories and not to the individual categories within this set. This is informed via indicator vectors with R rows, the elements of which are equal to 1 for the positions corresponding to the response categories in the response class and to 0 otherwise. For computational simplicity, it is assumed that the response classes corresponding to each missingness pattern belong to a partition of the response categories. Zp contains all the indicator vectors, which were first combined columnwise within subpopulations (without mixing different missingness patterns) and then between subpopulations. As Rp is a matrix that contains the number of response classes of each missingness pattern (column) of each subpopulation (row), Zp is a matrix with R rows and sum(Rp) columns. If the subpopulations do not have the same number of missingness patterns and/or response classes, the matrices TF and Rp shall be completed with "0". The generic functions print and summary are used to print the results and to obtain a summary thereof. The latter is particularly useful for checking whether the missing categorical data input was conducted in the right way.

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

Run this code

#Example 1.5 of Paulino and Singer (2006)
#S=4 subpopulations, R=4 response categories, with complete data
e15.TF<-rbind(c(19, 5, 4, 2),
			  c( 5, 8, 0,17),
			  c(11, 6, 7, 6),
			  c( 2, 5, 1,22))
e15.catdata<-readCatdata(TF=e15.TF)

e15.catdata #shows proportions and standard errors

#Example 13.4 of Paulino and Singer (2006)
#S=1 subpopulation, R=4 response categories, with missing data
#2 missingness patterns with 2 response classes each
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.catdata #Proportions of the complete data
summary(e134.catdata) #A more detailed analysis of the missing data input

#Example 13.2 of Paulino and Singer (2006)
#S=1 subpopulation, R=9 response categories, with missing data
#2 missingness patterns with 4 response classes each
e132.TF<-c(7,11,2,3,9,5,0,10,4, 8,7,3,0, 0,7,14,7)
e132.Zp<-cbind(rbind(cbind(kronecker(rep(1,2),diag(3)),rep(0,6)),
		 cbind(matrix(0,3,3),rep(1,3)) ),
	     rbind(cbind(rep(1,3),matrix(0,3,3)),
		 cbind(rep(0,6),kronecker(rep(1,2),diag(3)))))

e132.Rp<-c(4,4)

e132.catdata<-readCatdata(TF=e132.TF,Zp=e132.Zp,Rp=e132.Rp)
summary(e132.catdata)

#Example 1 of Poleto et al (2012)
#S=2 subpopulation, R=9 response categories, with missing data
#in each subpopulation: 2 missingness patterns with 3 response classes each
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.catdata

#Example 2 of Poleto et al (2012)
#S=10 subpopulation, R=8 response categories, with missing data
#in each subpopulation: 6 missingness patterns, 3 patterns with 4 response
#classes each, and other 3 patterns with 2 response classes
obes.TF<-rbind(
	c(90, 9, 3, 7, 0,1, 1, 8,16, 5,0, 0, 9,3,0,0,129,18,6,13,32, 5,33,11,70,24),
	c(150,15, 8, 8, 8,9, 7,20,38, 3,1,11,16,6,1,3, 42, 2,3,13,45, 7,33, 4,55,14),
	c(152,11, 8,10, 7,7, 9,25,48, 6,2,14,13,5,0,3, 36, 5,4, 3,59,17,31, 9,40, 9),
	c(119, 7, 8, 3,13,4,11,16,42, 4,4,13,14,2,1,4, 18, 3,3, 1,82,24,23, 6,37,14),
	c(101, 4, 2, 7, 8,0, 6,15,82, 9,8,12, 6,1,0,1, 13, 1,2, 2,95,23,34,12,15, 3),
	c( 75, 8, 2, 4, 2,2, 1, 8,20, 0,0, 4, 7,2,0,1,109,22,7,24,23, 5,27, 5,65,19),
	c(154,14,13,19, 2,6, 6,21,25, 3,1,11,16,3,0,4, 47, 4,1, 8,47, 7,23, 5,39,13),
	c(148, 6,10, 8,12,0, 8,27,36, 0,7,17, 8,1,1,4, 39, 6,7,13,53,16,25, 9,23, 8),
	c(129, 8, 7, 9, 6,2, 7,14,36, 9,4,13,31,4,2,6, 19, 1,2, 2,58,37,21, 1,23,10),
	c(91, 9, 5, 3, 6,0, 6,15,83,15,6,23, 5,0,0,1, 11, 1,2, 3,89,32,43,15,14, 5))

obes.Zp<-t(rep(1,10))%x%cbind(diag(4)%x%rep(1,2),
		  diag(2)%x%rep(1,2)%x%diag(2), rep(1,2)%x%diag(4),
		  diag(2)%x%rep(1,4),rep(1,2)%x%diag(2)%x%rep(1,2), rep(1,4)%x%diag(2))

obes.Rp<-rep(1,10)%x%t(c(4,4,4,2,2,2))
obes.catdata<-readCatdata(TF=obes.TF,Zp=obes.Zp,Rp=obes.Rp)
obes.catdata #Proportions of the complete data

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