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.

Commercialisation of agriculture in Kenya: Case study of urban bias on food availability in farm households

This study investigates the effect of cash cropping on food availability and examines the determinants of the proportion of income allocated for food expenditures in the Nyeri district in Kenya. Using a Tobit model, the results suggest that in general food expenditure allocations suffer due to cash cropping in Kenya as the lump-sum income flows from this may be used for purchases other than food. Food expenditure also suffers when remittances are irregular. On the other hand, earnings from outside employment for married women living with husbands are positively associated with food expenditure allocations. Amounts of non-cash food output as well as ownership of livestock are negatively associated with food expenditure allocations. These findings indicate that lump sum income may not lead to improved welfare of women and children. Thus, there may be social reasons for increasing non-cash food production especially by women, instead of over emphasizing cash cropping as now seems to be so in public policy.

Effects of sampling opportunities on preference for adults with severe disabilities

A variable that appears to affect preference development is the exposure to a variety of options. Providing opportunities for systematically sampling different options is one procedure that can facilitate the development of preference, which is indicated by the consistency of selections. The purpose of this study was to evaluate the effects of providing sampling opportunities on the preference development for two adults with severe disabilities. Opportunities for sampling a variety of drink items were presented, followed by choice opportunities for selections at the site where sampling occurred and at a non-sampling site (a grocery store). Results show that the participants developed a definite response consistency in selections at both sites. Implications for sampling practices are discussed.

Status, legitimacy and ingroup bias in the context of an organizational merger

Adopting an intergroup perspective, the research was designed to examine predictors of employee responses to an organizational merger. Data were collected from 120 employees of a newly merged scientific organization. As predicted from social identity theory, the most negative responses to the merger were apparent among the employees of the low status premerger organization. There was also evidence of ingroup bias among both groups of employees involved in the merger—as expected, the bias was most marked on the status-irrelevant dimensions for the employees of the lower status organization, but most marked on the status-relevant dimensions for the employees of the high status organization. Also, in support of social identity theory, the perceived legitimacy of the basis for the status differentiation between the groups was associated with more positive responses to the merger among employees of the low status premerger organization, but with poorer responses among employees of the high status premerger organization. There was consistent evidence that the status by legitimacy interaction was mediated through the extent to which employees of the newly merged organization perceived a common ingroup identity

Postmenopausal Hormone Use, Screening, and Breast Cancer: Characterization and Control of a Bias

Previous investigators have suggested that screening-related biases may explain associations between postmenopausal hormone use and breast cancer. To investigate these biases, we studied postmenopausal women in the Nurses' Health Study from 1988 to 1994. Hormone use is associated with increased subsequent screening. Among women not screened in the previous 2 years, the probability difference, comparing current hormone users with others, for having mammography in the following 2 years is 19.5%; among women previously screened, the difference is 4.9%. These differences persist after control for other factors. If the increase in screening is causal, screening by mammogram could be intermediate in the causal pathway to breast cancer diagnosis. To deal with this problem, we restrict attention to a subset of the cohort in which the effect of postmenopausal hormone use on screening is small (women previously screened). In this subset, the rate ratio comparing breast cancer rates among current postmenopausal hormone users with others is 1.28. In a sensitivity analysis, the bias could not by itself plausibly account for the associations in our data. Our data provide evidence of an association between postmenopausal hormone use and breast cancer that is not solely the product of a detection bias.

Comparison of measured sleeping metabolic rate and predicted basal metabolic rate during the first year of life: evidence of a bias changing with increasing metabolic rate

Objective: To compare measurements of sleeping metabolic rate (SMR) in infancy with predicted basal metabolic rate (BMR) estimated by the equations of Schofield. Methods: Some 104 serial measurements of SMR by indirect calorimetry were performed in 43 healthy infants at 1.5, 3, 6, 9 and 12 months of age. Predicted BMR was calculated using the weight only (BMR-wo) and weight and height (BMR-wh) equations of Schofield for 0-3-y-olds. Measured SMR values were compared with both predictive values by means of the Bland-Altman statistical test. Results: The mean measured SMR was 1.48 MJ/day. The mean predicted BMR values were 1.66 and 1.47 MJ/day for the weight only and weight and height equations, respectively. The Bland-Altman analysis showed that BMR-wo equation on average overestimated SMR by 0.18 MJ/day (11%) and the BMR-wh equation underestimated SMR by 0.01 MJ/day (1%). However the 95% limits of agreement were wide: - 0.64 to - 0.28MJ/day (28%) for the former equation and - 0.39 to +0.41 MJ/day (27%) for the latter equation. Moreover there was a significant correlation between the mean of the measured and predicted metabolic rate and the difference between them. Conclusions: The wide variation seen in the difference between measured and predicted metabolic rate and the bias probably with age indicates there is a need to measure actual metabolic rate for individual clinical care in this age group.

Low-density koala (Phascolarctos cinereus) populations in the mulgalands of south-west Queensland. I. Faecal pellet sampling protocol

Koala (Phascolarctos cinereus) populations in eastern Australia are threatened by land clearing for agricultural and urban development. At the same time, conservation efforts are hindered by a dearth of information about inland populations. Faecal deposits offer a source of information that is readily available and easily collected non-invasively. We detail a faecal pellet sampling protocol that was developed for use in a large rangeland biogeographic region. The method samples trees in belt transects, uses a thorough search at the tree base to quickly identify trees with koala pellets under them, then estimates the abundance of faecal pellets under those trees using 1-m(2) quadrats. There was a strong linear relationship between these estimates and a complete enumeration of pellet abundance under the same trees. We evaluated the accuracy of our method in detecting trees where pellets were present by means of a misclassification index that was weighed more heavily for missed trees that had high numbers of pellets under them. This showed acceptable accuracy in all landforms except riverine, where some trees with large numbers of pellets were missed. Here, accuracy in detecting pellet presence was improved by sampling with quadrats, rather than basal searches. Finally, we developed a method to reliably age pellets and demonstrate how this protocol could be used with the faecal-standing-crop method to derive a regional estimate of absolute koala abundance.

Two-dimensional balanced sampling plans excluding contiguous units

A balanced sampling plan excluding contiguous units (or BSEC for short) was first introduced by Hedayat, Rao and Stufken in 1988. These designs can be used for survey sampling when the units are arranged in one-dimensional ordering and the contiguous units in this ordering provide similar information. In this paper, we generalize the concept of a BSEC to the two-dimensional situation and give constructions of two-dimensional BSECs with block size 3. The existence problem is completely solved in the case where lambda = 1.

Distribution and abundance of dugongs in Moreton Bay, Queensland, Australia

Dugong abundances in Moreton Bay (south-east Queensland) were estimated during six bi- monthly aerial surveys throughout 1995. Sampling intensity ranged between 20 and 80% for different sampling zones within the Bay, with a mean intensity of 40.5%. Population estimates for dugongs were corrected for perception bias ( the proportion of animals visible in the transect that were missed by observers), and standardised for availability bias ( the proportion of animals that were invisible due to water turbidity) with survey and species-specific correction factors. Population estimates for dugongs in Moreton Bay ranged from 503 +/- 64 (s.e.) in July to 1019 +/- 166 in January. The highest uncorrected count was 857 dugongs in December. This is greater than previous population estimates, suggesting that either previous surveys have underestimated abundance and/or that this population may have increased through recruitment, immigration, or a combination of both. The high degree of variation in population estimates between surveys may be due to temporal differences in distribution and herding behaviour. In winter, dugongs were found in smaller herds and were dispersed over a wider area than in summer. The Eastern Banks region of the bay supported 80 - 98% of the dugong population at any one time. Within this region, there were several dugong 'hot spots' that were visited repeatedly by large herds. These 'hot spots' contained seagrass communities that were dominated by species that dugongs prefer to eat. The waters of Rous Channel, South Passage and nearby oceanic waters are also frequently inhabited by dugongs in the winter months. Dugongs in other parts of Moreton Bay were at much lower densities than on the Eastern Banks.

Evaluation of line-transect sampling for estimating koala abundance in the Pine Rivers Shire, south-east Queensland

Distance sampling using line transects has not been previously used or tested for estimating koala abundance. In July 2001, a pilot survey was conducted to compare the use of line transects with strip transects for estimating koala abundance. Both methods provided a similar estimate of density. On the basis of the results of the pilot survey, the distribution and abundance of koalas in the Pine Rivers Shire, south-east Queensland, was determined using line-transect sampling. In total, 134 lines (length 64 km) were used to sample bushland areas. Eighty-two independent koalas were sighted. Analysis of the frequency distribution of sighting distances using the software program DISTANCE enabled a global detection function to be estimated for survey sites in bushland areas across the Shire. Abundance in urban parts of the Shire was estimated from densities obtained from total counts at eight urban sites that ranged from 26 to 51 ha in size. Koala abundance in the Pine Rivers Shire was estimated at 4584 (95% confidence interval, 4040-5247). Line-transect sampling is a useful method for estimating koala abundance provided experienced koala observers are used when conducting surveys.

Distribution of Chlamydia pneumoniae DNA in atherosclerotic carotid arteries: significance for sampling procedures

Despite extensive efforts to confirm a direct association between Chlamydia pneumoniae and atherosclerosis, different laboratories continue to report a large variability in detection rates. In this study, we analyzed multiple sections from atherosclerotic carotid arteries from 10 endartectomy patients to determine the location of C. pneumoniae DNA and the number of sections of the plaque required for analysis to obtain a 95% confidence of detecting the bacterium. A sensitive nested PCR assay detected C. pneumoniae DNA in all patients at one or more locations within the plaque. On average, 42% (ranging from 5 to 91%) of the sections from any single patient had C. pneumoniae DNA present. A patchy distribution of C. pneumoniae in the atherosclerotic lesions was observed, with no area of the carotid having significantly more C. pneumoniae DNA present. If a single random 30-mum-thick section was tested, there was only a 35.6 to 41.6% (95% confidence interval) chance of detecting C. pneumoniae DNA in a patient with carotid artery disease. A minimum of 15 sections would therefore be required to obtain a 95% chance of detecting all true positives. The low concentration and patchy distribution of C. pneumoniae DNA in atherosclerotic plaque appear to be among the reasons for inconsistency between laboratories in the results reported.