A Comparison of Bayesian and Sampling Theory Inferences in a Probit Model

HE PROBIT MODEL IS A POPULAR DEVICE for explaining binary choice decisions in econometrics. It has been used to describe choices such as labor force participation, travel mode, home ownership, and type of education. These and many more examples can be found in papers by Amemiya (1981) and Maddala (1983). Given the contribution of economics towards explaining such choices, and given the nature of data that are collected, prior information on the relationship between a choice probability and several explanatory variables frequently exists. Bayesian inference is a convenient vehicle for including such prior information. Given the increasing popularity of Bayesian inference it is useful to ask whether inferences from a probit model are sensitive to a choice between Bayesian and sampling theory techniques. Of interest is the sensitivity of inference on coefficients, probabilities, and elasticities. We consider these issues in a model designed to explain choice between fixed and variable interest rate mortgages. Two Bayesian priors are employed: a uniform prior on the coefficients, designed to be noninformative for the coefficients, and an inequality restricted prior on the signs of the coefficients. We often know, a priori, whether increasing the value of a particular explanatory variable will have a positive or negative effect on a choice probability. This knowledge can be captured by using a prior probability density function (pdf) that is truncated to be positive or negative. Thus, three sets of results are compared:those from maximum likelihood (ML) estimation, those from Bayesian estimation with an unrestricted uniform prior on the coefficients, and those from Bayesian estimation with a uniform prior truncated to accommodate inequality restrictions on the coefficients.

Depositional environments for strata cored in CRP-3 (Cape Roberts Project), Victoria Land Basin, Antarctica: palaeoglaciological and palaeoclimatological inferences

Cape Roberts Project drill core 3 (CRP-3) was obtained from Roberts ridge, a sea-floor high located at 77°S, 12 km offshore from Cape Roberts in western McMurdo Sound, Antarctica. The recovered core is about 939 m long and comprises strata dated as being early Oligocene (possibly latest Eocene) in age, resting unconformably on ∼ 116 m of basement rocks consisting of Palaeozoic Beacon Supergroup sediments. The core includes ten facies commonly occuring in five major associations that are repeated in particular sequences throughout the core and which are interpreted as representing different depositional environments through time. Depositional systems inferred to be represented in the succession include: outer shelf, inner shelf, nearshore to shoreface each under iceberg influence, deltaic and/or grounding-line fan, and ice proximal-ice marginal-subglacial (mass flow/rainout diamictite/subglacial till) singly or in combination. The record is taken to represent the initial talus/alluvial fan setting of a glaciated rift margin adjacent to the block-uplifted Transantarctic Mountains. Development of a deltaic succession upcore was probably associated with the formation of palaeo-Mackay valley with temperate glaciers in its headwaters. At that stage glaciation was intense enough to support glaciers ending in the sea elsewhere along the coast, but a local glacier was fluctuating down to the sea by the time the youngest part of CRP-3 was being deposited. Changes in palaeoenvironmental interpretations in this youngest part of the core are used to estimate relative glacial proximity to the drillsite through time. These inferred glacial fluctuations are compared with the global δ18O and Mg/Ca curves to evaluate the potential of glacial fluctuations on Antarctica for influencing these records of global change. Although the comparisons are tentative at present, the records do have similarities, but there are also some differences that require further evaluation.

Bayesian inferences on the recent island colonization history by the bird Zosterops lateralis lateralis

The founding of new populations by small numbers of colonists has been considered a potentially important mechanism promoting evolutionary change in island populations. Colonizing species, such as members of the avian species complex Zosterops lateralis, have been used to support this idea. A large amount of background information on recent colonization history is available for one Zosterops subspecies, Z. lateralis lateralis, providing the opportunity to reconstruct the population dynamics of its colonization sequence. We used a Bayesian approach to combine historical and demographic information available on Z. l. lateralis with genotypic data from six microsatellite loci, and a rejection algorithm to make simultaneous inferences on the demographic parameters describing the recent colonization history of this subspecies in four southwest Pacific islands. Demographic models assuming mutation–drift equilibrium or a large number of founders were better supported than models assuming founder events for three of four recently colonized island populations. Posterior distributions of demographic parameters supported (i) a large stable effective population size of several thousands individuals with point estimates around 4000–5000; (ii) a founder event of very low intensity with a large effective number of founders around 150–200 individuals for each island in three of four islands, suggesting the colonization of those islands by one flock of large size or several flocks of average size; and (iii) a founder event of higher intensity on Norfolk Island with an effective number of founders around 20 individuals, suggesting colonization by a single flock of moderate size. Our inferences on demographic parameters, especially those on the number of founders, were relatively insensitive to the precise choice of prior distributions for microsatellite mutation processes and demographic parameters, suggesting that our analysis provides a robust description of the recent colonization history of the subspecies.

The implications of simultaneous smoking initiation for inferences about the genetics of smoking behavior from twin data

We examined early social influences across stages of smoking within the context of a twin study using an environmental exposure specific to smoking: whether twins started smoking at the same time (simultaneous smoking initiation: SSI). We expected that SSI would be a good index of shared social influences on smoking initiation. Rates of SSI were indeed significantly higher in MZ twins and in twins who shared peers and classes, as well as in male twins. With the exception of regular smoking in females, we found no significant difference in estimates of genetic and environmental parameters between SSI and non-SSI pairs for any of the smoking measures that we examined (DSM-IV and Fagerstrom HSI measures of nicotine dependence; DSM-IV nicotine withdrawal; heavy smoking; and in males, regular smoking). For regular smoking in females, allowing for additional shared environmental influences associated with SSI only modestly reduced our estimates of additive genetic variance (56% vs. 68%). These results indicate the important social influences that may occur for smoking initiation do not appear to seriously bias estimates of genetic effects on later stages of smoking.

Discourse priming of homophones in individuals with dominant subcortical lesions, cortical lesions, and Parkinson’s disease

An on-line priming experiment was used to investigate discourse-level processing in four matched groups of subjects: individuals with nonthalamic subcortical lesions (NSL) ( n =10), normal control subjects ( n =10), subjects with Parkinsons disease (PD) ( n =10), and subjects with cortical lesions ( n =10). Subjects listened to paragraphs that ended in lexical ambiguities, and then made speeded lexical decisions on visual letter strings that were: nonwords, matched control words, contextually appropriate associates of the lexical ambiguity, contextually inappropriate associates of the ambiguity, and inferences (representing information which could be drawn from the paragraphs but was not explicitly stated). Targets were presented at an interstimulus interval (ISI) of 0 or 1000ms. NSL and PD subjects demonstrated priming for appropriate and inappropriate associates at the short ISI, similar to control subjects and cortical lesion subjects, but were unable to demonstrate selective priming of the appropriate associate and inference words at the long ISI. These results imply intact automatic lexical processing and a breakdown in discourse-based meaning selection and inference development via attentional/strategic mechanisms.

Knowledge and willingness to pay for the conservation of wildlife species: Experimental results evaluating Australian tropical species

The nature of an experiment involving 204 residents is outlined and the results are reported and analysed. Two consecutive surveys of the respondents provide data about their stated knowledge of 23 wildlife species present in tropical Australia, most of which exclusively occur there. In addition, these surveys provide data about the willingness of respondents to pay for the conservation of those species belonging to three taxa; reptiles, mammals, and birds. Thus it is possible to compare the respondents’ stated knowledge of the species with their willingness to pay for their conservation, and to draw relevant inferences from this. From the initial survey and these associations, interesting relationships can be observed between those variables (knowledge and willingness to pay). The second survey was completed after the respondents’ knowledge of the species was experimentally increased and became more balanced. This is shown to result in increased dispersion (greater discrimination) in willingness to contribute to conservation of the different species in the set of wildlife species considered. Both theoretical and policy conclusions are drawn from the results.

Genetic consequences of sequential founder events by an island-colonizing bird

The importance of founder events in promoting evolutionary changes on islands has been a subject of long-running controversy. Resolution of this debate has been hindered by a lack of empirical evidence from naturally founded island populations. Here we undertake a genetic analysis of a series of historically documented, natural colonization events by the silvereye species-complex (Zosterops lateralis), a group used to illustrate the process of island colonization in the original founder effect model. Our results indicate that single founder events do not affect levels of heterozygosity or allelic diversity, nor do they result in immediate genetic differentiation between populations. Instead, four to five successive founder events are required before indices of diversity and divergence approach that seen in evolutionarily old forms. A Bayesian analysis based on computer simulation allows inferences to be made on the number of effective founders and indicates that founder effects are weak because island populations are established from relatively large flocks. Indeed, statistical support for a founder event model was not significantly higher than for a gradual-drift model for all recently colonized islands. Taken together, these results suggest that single colonization events in this species complex are rarely accompanied by severe founder effects, and multiple founder events and/or long-term genetic drift have been of greater consequence for neutral genetic diversity.

Exploring the learning potential of an artificial life simulation

CULTURE is an Artificial Life simulation that aims to provide primary school children with opportunities to become actively engaged in the high-order thinking processes of problem solving and critical thinking. A preliminary evaluation of CULTURE has found that it offers the freedom for children to take part in process-oriented learning experiences. Through providing children with opportunities to make inferences, validate results, explain discoveries and analyse situations, CULTURE encourages the development of high-order thinking skills. The evaluation found that CULTURE allows users to autonomously explore the important scientific concepts of life and living, and energy and change within a software environment that children find enjoyable and easy to use.

Young children's performance on the balance scale: The influence of relational complexity

Three experiments investigated the effect of complexity on children's understanding of a beam balance. In nonconflict problems, weights or distances varied, while the other was held constant. In conflict items, both weight and distance varied, and items were of three kinds: weight dominant, distance dominant, or balance (in which neither was dominant). In Experiment 1, 2-year-old children succeeded on nonconflict-weight and nonconflict-distance problems. This result was replicated in Experiment 2, but performance on conflict items did not exceed chance. In Experiment 3, 3- and 4-year-olds succeeded on all except conflict balance problems, while 5- and 6-year-olds succeeded on all problem types. The results were interpreted in terms of relational complexity theory. Children aged 2 to 4 years succeeded on problems that entailed binary relations, but 5- and 6-year-olds also succeeded on problems that entailed ternary relations. Ternary relations tasks from other domains-transitivity and class inclusion-accounted for 93% of the age-related variance in balance scale scores. (C) 2002 Elsevier Science (USA).

A cognitive complexity metric applied to cognitive development

Two experiments tested predictions from a theory in which processing load depends on relational complexity (RC), the number of variables related in a single decision. Tasks from six domains (transitivity, hierarchical classification, class inclusion, cardinality, relative-clause sentence comprehension, and hypothesis testing) were administered to children aged 3-8 years. Complexity analyses indicated that the domains entailed ternary relations (three variables). Simpler binary-relation (two variables) items were included for each domain. Thus RC was manipulated with other factors tightly controlled. Results indicated that (i) ternary-relation items were more difficult than comparable binary-relation items, (ii) the RC manipulation was sensitive to age-related changes, (iii) ternary relations were processed at a median age of 5 years, (iv) cross-task correlations were positive, with all tasks loading on a single factor (RC), (v) RC factor scores accounted for 80% (88%) of age-related variance in fluid intelligence (compositionality of sets), (vi) binary- and ternary-relation items formed separate complexity classes, and (vii) the RC approach to defining cognitive complexity is applicable to different content domains. (C) 2002 Elsevier Science (USA). All rights reserved.

Toward a better understanding of the influences on physical activity: The role of determinants, correlates, causal variables, mediators, moderators, and confounders

Background: For research on physical activity interventions to progress systematically, the mechanisms of action must be studied. In doing so, the research methods and their associated concepts and terminology become more complex. It is particularly important to clearly distinguish among determinants, correlates, mediators, moderators, and confounder variables used in physical activity research. This article examines the factors that are correlated with and that may have a causal relationship to physical activity. Methods and Results: We propose that the term correlate be used, instead of determinant, to describe statistical associations or correlations between measured variables and physical activity. Studies of the correlates of physical activity are reviewed. The findings of these studies can help to critique existing theories of health behavior change and can provide hypotheses to be tested in intervention studies from which it is possible to draw causal inferences. Mediator, moderator, and confounder variables can act to influence measured changes in physical activity. Intervening causal variables that are necessary to complete a cause-effect pathway between an intervention and physical activity are termed mediators. The relationship between an intervention and physical activity behaviors may vary for different groups; the strata by which they vary are levels of moderators of the relationship. Other factors may distort or affect the observed relationships between program exposure and physical activity, and are known as confounders. Conclusions: Consistent use of terms and additional research on mediators and moderators of intervention effects will improve our ability to understand and influence physical activity.

Health and demographic characteristics of respondents in an Australian national sexuality survey: comparison with population norms

Study objective: To assess the representativeness of survey participants by systematically comparing volunteers in a national health and sexuality survey with the Australian population in terms of self reported health status (including the SF-36) and a wide range of demographic characteristics. Design: A cross sectional sample of Australian residents were compared with demographic data from the 1996 Australian census and health data from the 1995 National Health Survey. Setting: The Australian population. Participants: A stratified random sample of adults aged 18-59 years drawn from the Australian electoral roll, a compulsory register of voters. Interviews were completed with 1784 people, representing 40% of those initially selected (58% of those for whom a valid telephone number could be located). Main results: Participants were of similar age and sex to the national population. Consistent with prior research, respondents had higher socioeconomic status, more education, were more likely to be employed, and less likely to be immigrants. The prevalence estimates, means, and variances of self reported mental and physical health measures (for example, SF-36 subscales, women's health indicators, current smoking status) were similar to population norms. Conclusions: These findings considerably strengthen inferences about the representativeness of data on health status from volunteer samples used in health and sexuality surveys.