Closed-Form Bayesian Inferences for the Logit Model via Polynomial Expansions

Articles in Marketing and choice literatures have demonstrated the need for incorporating person-level heterogeneity into behavioral models (e.g., logit models for multiple binary outcomes as studied here). However, the logit likelihood extended with a population distribution of heterogeneity doesn't yield closed-form inferences, and therefore numerical integration techniques are relied upon (e.g., MCMC methods). We present here an alternative, closed-form Bayesian inferences for the logit model, which we obtain by approximating the logit likelihood via a polynomial expansion, and then positing a distribution of heterogeneity from a flexible family that is now conjugate and integrable. For problems where the response coefficients are independent, choosing the Gamma distribution leads to rapidly convergent closed-form expansions; if there are correlations among the coefficients one can still obtain rapidly convergent closed-form expansions by positing a distribution of heterogeneity from a Multivariate Gamma distribution. The solution then comes from the moment generating function of the Multivariate Gamma distribution or in general from the multivariate heterogeneity distribution assumed. Closed-form Bayesian inferences, derivatives (useful for elasticity calculations), population distribution parameter estimates (useful for summarization) and starting values (useful for complicated algorithms) are hence directly available. Two simulation studies demonstrate the efficacy of our approach.Comment: 30 pages, 2 figures, corrected some typos. Appears in Quantitative Marketing and Economics vol 4 (2006), no. 2, 173--20

General Chemistry Student Attitudes and Success with Use of Online Homework: Traditional- Responsive versus Adaptive-Responsive

We investigated whether use of an adaptive-responsive online homework system (OHS) that tailors homework to students’ prior knowledge and periodically reassesses students to promote learning through practice retrieval has inherent advantages over traditional-responsive online homework. A quasi-experimental cohort control post-test-only design with nonequivalent groups and propensity scores with nearest neighbor matching (n = 6,114 pairs) was used. The adaptive system was found to increase the odds of a higher final letter grade for average, below average, and failing students. However, despite the learning advantages, students self-reported less favorable attitudes toward adaptive-responsive (3.15 of 5) relative to traditional-responsive OHS (3.31). Specific to the adaptive OHS, the following were found: (i) student attitudes were moderately and positively correlated (r = 0.36, p \u3c 0.01) to final letter grade, (ii) most students (95%) reported engaging in remediation of incorrect responses, (iii) a majority of students (69%) reported changes in study habits, and (iv) students recognized the benefit of using adaptive OHS by ranking its assignments and explanations or review materials as two of the top three most useful course aspects contributing to perceived learning. Instructors can use our findings to inform their choice of online homework system for formative assessment of chemistry learning by weighing the benefits, disadvantages, and learning pedagogies of traditional-responsive versus adaptive-responsive systems

Practical solutions for sampling alternatives in large-scale models

Many large-scale real-world transport applications have choice sets that are so large as to make model estimation and application computationally impractical. The ability to estimate models on subsets of the alternatives is thus of great appeal, and correction approaches have existed since the late 1970s for the simple multinomial logit (MNL) model. However, many of these models in practice rely on nested logit specifications, for example, in the context of the joint choice of mode and destination. Recent research has put forward solutions for such generalized extreme value (GEV) structures, but these structures remain difficult to apply in practice. This paper puts forward a simplification of the GEV method for use in computationally efficient implementations of nested logit. The good performance of this approach is illustrated with simulated data, and additional insights into sampling error are also provided with different sampling strategies for MNL

Utjecaj sadržaja lijeka i veličine aglomerata na tabletiranje i oslobađanje bromheksin hidroklorida iz aglomerata s talkom pripremljenih kristalokoaglomeracijom

The objective of the investigation was to study the effect of bromhexine hydrochloride (BXH) content and agglomerate size on mechanical, compressional and drug release properties of agglomerates prepared by crystallo-co-agglomeration (CCA). Studies on optimized batches of agglomerates (BXT1 and BXT2) prepared by CCA have showed adequate sphericity and strength required for efficient tabletting. Trend of strength reduction with a decrease in the size of agglomerates was noted for both batches, irrespective of drug loading. However, an increase in mean yield pressure (14.189 to 19.481) with an increase in size was observed for BXT2 having BXH-talc (1:15.7). Surprisingly, improvement in tensile strength was demonstrated by compacts prepared from BXT2, due to high BXH load, whereas BXT1, having a low amount of BXH (BXH-talc, 1:24), showed low tensile strength. Consequently, increased tensile strength was reflected in extended drug release from BXT2 compacts (Higuchi model, R2 = 0.9506 to 0.9981). Thus, it can be concluded that interparticulate bridges formed by BXH and agglomerate size affect their mechanical, compressional and drug release properties.Cilj rada bio je praćenje utjecaja sadržaja bromheksidin hidroklorida (BXH) i veličine aglomerata na mehanička svojstva, kompresivnost i oslobađanje ljekovite tvari iz aglomerata pripravljenih kristalokoaglomeracijom (CCA). Optimizirani pripravci aglomerata (BXT1 i BXT2) pripravljeni CCA metodom pokazuju adekvatnu sferičnost i čvrstoću potrebnu za učinkovito tabletiranje. U oba pripravka se smanjenjem veličine aglomerata smanjivala i čvrstoća, neovisno o količini ljekovite tvari. Međutim, povećanje prosječnog tlaka s povećanjem veličine čestica primijećeno je u pripravku BXT2 s omjerom BXH-talk 1:15,7. Iznenađuje da su kompakti pripravljeni iz BXT2, s visokim sadržajem BXH, imali veću vlačnu čvrstoću, dok su BXT1 s niskim sadržajem BXH (BXH-talk, 1:24) imali manju čvrstoću. Veća vlačna čvrstoća imala je za posljedicu produljeno oslobađanje ljekovite tvari iz BXT2 (Higuchijev model, R2 = 0,9506 do 0,9981). Može se zaključiti da mostovi među česticama BXH i veličina aglomerata utječu na njihova mehanička i kompresivna svojstva te na oslobađanje ljekovite tvari

Another Avenue for Anatomy of Income Comparisons : Evidence from Hypothetical Choice Experiments

September 2010, Revised December 2010, Secondly Revised November 2011, Thirdly Revised May 2012, Fourthly Revised March 2013

Factors influencing job preferences of health workers providing obstetric care : results from discrete choice experiments in Malawi, Mozambique and Tanzania

BACKGROUND: Task shifting from established health professionals to mid-level providers (MLPs) (professionals who undergo shorter training in specific procedures) is one key strategy for reducing maternal and neonatal deaths. This has resulted in a growth in cadre types providing obstetric care in low and middle-income countries. Little is known about the relative importance of the different factors in determining motivation and retention amongst these cadres. METHODS: This paper presents findings from large sample (1972 respondents) discrete choice experiments to examine the employment preferences of obstetric care workers across three east African countries. RESULTS: The strongest predictors of job choice were access to continuing professional development and the presence of functioning human resources management (transparent, accountable and consistent systems for staff support, supervision and appraisal). Consistent with similar works we find pay and allowances significantly positively related to utility, but financial rewards are not as fundamental a factor underlying employment preferences as many may have previously believed. Location (urban vs rural) had the smallest average effect on utility for job choice in all three countries. CONCLUSIONS: These findings are important in the context where efforts to address the human resources crisis have focused primarily on increasing salaries and incentives, as well as providing allowances to work in rural areas

"If only I had taken the other road...": Regret, risk and reinforced learning in informed route-choice

This paper presents a study of the effect of regret on route choice behavior when both descriptional information and experiential feedback on choice outcomes are provided. The relevance of Regret Theory in travel behavior has been well demonstrated in non-repeated choice environments involving decisions on the basis of descriptional information. The relation between regret and reinforced learning through experiential feedbacks is less understood. Using data obtained from a simple route-choice experiment involving different levels of travel time variability, discrete-choice models accounting for regret aversion effects are estimated. The results suggest that regret aversion is more evident when descriptional information is provided ex-ante compared to a pure learning from experience condition. Yet, the source of regret is related more strongly to experiential feedbacks rather than to the descriptional information itself. Payoff variability is negatively associated with regret. Regret aversion is more observable in choice situations that reveal risk-seeking, and less in the case of risk-aversion. These results are important for predicting the possible behavioral impacts of emerging information and communication technologies and intelligent transportation systems on travelers' behavior. © 2012 Springer Science+Business Media, LLC