On Testing Sample Selection Bias Under the Multicollinearity Problem

This paper reviews and extends the literature on the finite sample behavior of tests for sample selection bias. Monte Carlo results show that, when the “multicollinearity problem” identified by Nawata (1993) is severe, (i) the t-test based on the Heckman-Greene variance estimator can be unreliable, (ii) the Likelihood Ratio test remains powerful, and (iii) nonnormality can be interpreted as severe sample selection bias by Maximum Likelihood methods, leading to negative Wald statistics. We also confirm previous findings (Leung and Yu, 1996) that the standard regression-based t-test (Heckman, 1979) and the asymptotically efficient Lagrange Multiplier test (Melino, 1982), are robust to nonnormality but have very little power.     

MML clustering of multi-state,Poisson, von Mises circular and Gaussian distributions

Minimum Message Length (MML) is an invariant Bayesian point estimation technique which is also statistically consistent and efficient. We provide a brief overview of MML inductive inference (Wallace C.S. and Boulton D.M. 1968. Computer Journal, 11: 185–194; Wallace C.S. and Freeman P.R. 1987. J. Royal Statistical Society (Series B), 49: 240–252; Wallace C.S. and Dowe D.L. (1999). Computer Journal), and how it has both an information-theoretic and a Bayesian interpretation. We then outline how MML is used for statistical parameter estimation, and how the MML mixture modelling program, Snob (Wallace C.S. and Boulton D.M. 1968. Computer Journal, 11: 185–194; Wallace C.S. 1986. In: Proceedings of the Nineteenth Australian Computer Science Conference (ACSC-9), Vol. 8, Monash University, Australia, pp. 357–366; Wallace C.S. and Dowe D.L. 1994b. In: Zhang C. et al. (Eds.), Proc. 7th Australian Joint Conf. on Artif. Intelligence. World Scientific, Singapore, pp. 37–44. See http://www.csse.monash.edu.au/-dld/Snob.html) uses the message lengths from various parameter estimates to enable it to combine parameter estimation with selection of the number of components and estimation of the relative abundances of the components. The message length is (to within a constant) the logarithm of the posterior probability (not a posterior density) of the theory. So, the MML theory can also be regarded as the theory with the highest posterior probability. Snob currently assumes that variables are uncorrelated within each component, and permits multi-variate data from Gaussian, discrete multi-category (or multi-state or multinomial), Poisson and von Mises circular distributions, as well as missing data. Additionally, Snob can do fully-parameterised mixture modelling, estimating the latent class assignments in addition to estimating the number of components, the relative abundances of the parameters and the component parameters. We also report on extensions of Snob for data which has sequential or spatial correlations between observations, or correlations between attributes.     

Exploratory method for summarizing concomitant medication data – the mean cumulative function

Concomitant Medications are medications used by patients in a clinical trial, other than the investigational drug. These data are routinely collected in clinical trials. The data are usually collected in a longitudinal manner, for the duration of patients' participation in the trial. The routine summaries of this data are incidence‐type, describing whether or not a medication was ever administered during the study. The longitudinal aspect of the data is essentially ignored. The aim of this article is to suggest exploratory methods for graphically displaying the longitudinal features of the data using a well‐established estimator called the ‘mean cumulative function’. This estimator permits summary and a graphical display of the data, and preparation of some statistical tests to compare between groups. This estimator may also incorporate information on censoring of patient data. Copyright © 2009 John Wiley & Sons, Ltd.     

Understanding Interest in the Second Year of Life

Infants (n = 24, mean age 13 months and n = 24, mean age 19 months) were tested on an extension of the method introduced by Tomasello and Haberl (2003) to examine the understanding of another person’s interest in a novel object. Four objects were presented serially. For two objects, infants played with an experimenter. The infant played with one object alone, and the experimenter played with one object alone. Finally, all four objects were presented together, and the experimenter excitedly asked for one without indicating which. Results showed that younger infants tended to chose the object that they had not yet played with, whereas older infants were significantly more likely to choose the object that the experimenter had not yet played with. These results are discussed in the context of research on the development of understanding diversity of simple object‐directed attitudes in the second year of life.     

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