Ranking Models in Conjoint Analysis

In this paper we consider the estimation of probabilisticranking models in the context of conjoint experiments. By usingapproximate rather than exact ranking probabilities, we do notneed to compute high-dimensional integrals. We extend theapproximation technique proposed by \\citet{Henery1981} in theThurstone-Mosteller-Daniels model for any Thurstone orderstatistics model and we show that our approach allows for aunified approach. Moreover, our approach also allows for theanalysis of any partial ranking. Partial rankings are essentialin practical conjoint analysis to collect data efficiently torelieve respondents' task burden.conjoint experiments;partial rankings;thurstone order statistics model

Modelling rankings in R: the PlackettLuce package

This paper presents the R package PlackettLuce, which implements a generalization of the Plackett-Luce model for rankings data. The generalization accommodates both ties (of arbitrary order) and partial rankings (complete rankings of subsets of items). By default, the implementation adds a set of pseudo-comparisons with a hypothetical item, ensuring that the underlying network of wins and losses between items is always strongly connected. In this way, the worth of each item always has a finite maximum likelihood estimate, with finite standard error. The use of pseudo-comparisons also has a regularization effect, shrinking the estimated parameters towards equal item worth. In addition to standard methods for model summary, PlackettLuce provides a method to compute quasi standard errors for the item parameters. This provides the basis for comparison intervals that do not change with the choice of identifiability constraint placed on the item parameters. Finally, the package provides a method for model-based partitioning using covariates whose values vary between rankings, enabling the identification of subgroups of judges or settings that have different item worths. The features of the package are demonstrated through application to classic and novel data sets.Comment: In v2: review of software implementing alternative models to Plackett-Luce; comparison of algorithms provided by the PlackettLuce package; further examples of rankings where the underlying win-loss network is not strongly connected. In addition, general editing to improve organisation and clarity. In v3: corrected headings Table 4, minor edit

Wages, Rents and Heterogeneous Moving Costs (second version)

The model of compensating differentials in regional labor and land markets was formalized by Roback (1982). The model interprets regional differences in constant quality wages and rents as compensating firms and residents for inter-regional differences in amenities. While the model assumes that the costs of relocating to a new city are zero, the results hold in the presence of moving costs for the marginal migrant. This paper extends the Roback model to allow for moving costs which vary among a city's residents and businesses. This modification of the model generates new interpretations of regional differences in rents and wages. The theoretical results suggests that the interpretation of inter-city rent and wage differentials as compensating is misguided, that such differentials are inappropriate as weights in QOL comparisons and stresses the importance of local housing and labor market parameters in the determination of these differentials. The importance of amenities is retained, but housing supply becomes the main other determinant of regional rents. Housing supply was ignored in the literature following on Roback's initial insight. The new perspective also provides a bridge between the neoclassical perspective implicit in Roback's approach and the newer literature on agglomeration economies. Working Paper 08-0

Are R&D subsidies provided optimally? Evidence from a simulated agency-firm stochastic dynamic game

By means of a simulated funding-agency/supported-firm stochastic dynamic game, this paper firstly shows that not only the level of R&D performed by firms is underprovided (as maintained by traditional literature on the subject), but also the level of the subsidy provided by the funding (public) agency (used to correct exactly for the corporate R&D shortage). This event is due to externalities generated by the agency-firm strategic relationship. Two versions of the model are simulated and compared: one assuming rival behaviors between companies and agency, and one associated to the Social-planner (or cooperative) strategy. Secondly, the paper looks at what “welfare” implications are associated to different degree of funding effect’s persistency. Three main conclusions are drawn: (i) the relative quota of subsidy to R&D is undersized in the rival compared to the Social-planner model; (2) the rivalry strategy generates distortions that favor the agency compared to firms; (3) when passing from less persistent to more persistent R&D additionality/crowding-out effect, the lower the bias the greater the variance is and vice versa. As for the management of R&D funding policies, all the elements favouring greater collaboration between agency and firm objectives can help current R&D support to reach its social optimum.R&D subsidies, Rivalry vs. cooperation, Dynamic-stochastic games, Simulations

Gröbner fan and universal characteristic sets of prime differential ideals

AbstractThe concepts of Gröbner cone, Gröbner fan, and universal Gröbner basis are generalized to the case of characteristic sets of prime differential ideals. It is shown that for each cone there exists a set of polynomials which is characteristic for every ranking from this cone; this set is called a strong characteristic set, and an algorithm for its construction is given. Next, it is shown that the set of all differential Gröbner cones is finite for any differential ideal. A subset of the ideal is called its universal characteristic set, if it contains a characteristic set of the ideal w.r.t. any ranking. It is shown that every prime differential ideal has a finite universal characteristic set, and an algorithm for its construction is given. The question of minimality of this set is addressed in an example. The example also suggests that construction of a universal characteristic set can help in solving a system of nonlinear PDE’s, as well as maybe providing a means for more efficient parallel computation of characteristic sets