In this paper, the support of the joint probability distribution of categorical variables in the total population is treated as unknown. From a general total population model with unknown support, a general subpopulation model with its support equal to the set of all observed score patterns is derived. In maximum likelihood estimation of the parameters of any such subpopulation model, the evaluation of the log-likelihood function only requires the summation over a number of terms equal to at most the sample size. It is made clear that the parameters of a hypothesized total population model are consistently and asymptotically efficiently estimated by the values that maximize the log-likelihood function of the corresponding subpopulation model. Next, new likelihood ratio goodness-of-fit tests are proposed as alternatives to the Pearson chi-square goodness-of-fit test and the likelihood ratio test against the saturated model. In a simulation study, the asymptotic bias and efficiency of maximum likelihood estimators and the asymptotic performance of the goodness-of-fit tests are investigated.

The manner in which the conditional independence graph of a multiway contingency table effects the fitting and interpretation of the Goodman association model (RC) and of correspondence analysis (CA) is considered.

Estimation of the row and column scores is presented in this context by developing a unified framework that includes both models. Incorporation of the conditional independence constraints inherent in the graph may lead to equal or additive scores for the corresponding marginal tables, depending on the topology of the graph. An example of doubly additive scores in the analysis of a Burt subtable is given.

In this paper we work in the framework of a k-dimensional vector of log-linear risks. Under weak conditions on the marginal tails and the dependence structure of a vector of positive risks, we derive the asymptotic tail behaviour of the aggregated risk and present an application concerning log-normal risks with stochastic volatility.

This is the first of two papers in which we estimate transition probabilities amongst levels of disability as defined in the Australian Survey of Disability, Ageing and Carers. In this paper we describe both the main tools of our estimation and the estimation of the numbers of individuals in different disability categories at annual intervals using survey data that are available at five year intervals. In Paper II we describe our estimation procedure, followed by its implementation, discussion of results and graduation of the estimated transition probabilities.

This is the second of two papers in which we estimate transition probabilities amongst levels of disability as defined in the Australian Survey of Disability, Ageing and Carers. In this paper we describe our estimation procedure, followed by its implementation, discussion of results and graduation of the estimated transition probabilities.

The two most used instruments to assess masculinity (M) and femininity (F) are the Bem Sex Role Inventory (BSRI) and the Personality Attributes Questionnaire (PAQ). Two hypotheses will be tested: a) multidimensionality versus bidimensionality, and b) to what extent the two instruments, elaborated to measure the same constructs, classify subjects in the same way. Participants were 420 high school students, 198 women and 222 men, aged 12–15 years. Exploratory factor analysis and internal consistency analysis were carried out and log-linear models were tested. The data support a) the multidimensionality of both instruments and b) the lack of full concordance in the classification of persons according to the fourfold typology. Implications of the results are discussed regarding the supposed theory behind instrumentality/expressiveness and masculinity/femininity, as well as for the use of both instruments to classify different subjects into the four distinct types.