Personalized Travel Recommendations Based on Asynchronous and Privacy-Preserving Mixed Logit Model
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Mixed logit
When one estimates discrete choice models, the mixed logit approach is commonly superior to simple conditional logit setups. Mixed logit models not only allow the researcher to implement difficult random components but also overcome the restrictive IIA assumption. Despite these theoretical advantages, the estimation of mixed logit models becomes cumbersome when the model’s complexity increases. Applied works therefore often rely on rather simple empirical specifications because this reduces the computational burden. I introduce the user-written command lslogit, which fits complex mixed logit models using maximum simulated likelihood methods. As lslogit is a d2-ML-evaluator written in Mata, the estimation is rather efficient compared with other routines. It allows the researcher to specify complicated structures of unobserved heterogeneity and to choose from a set of frequently used functional forms for the direct utility function—for example, Box-Cox transformations, which are difficult to estimate in the context of logit models. The particular focus of lslogit is on the estimation of labor supply models in the discrete choice context; therefore, it facilitates several computationally exhausting but standard tasks in this research area. However, the command can be used in many other applications of mixed logit models as well.
Mixed logit
Discrete choice
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This paper uses a multi-profile best-worst scaling dataset to compare the mixed logit model and the latent class logit model for mobile payment choice. Three non-nested tests are applied to show the comparison results. The results indicate that the mixed logit model is superior to the latent class logit model in all three tests.
Mixed logit
Nested logit
Mobile Payment
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Background: The International Classification of Disease Injury Severity Score (ICISS) and the Trauma Registry Abbreviated Injury Scale Score (TRAIS) are trauma injury severity scores based on probabilities of survival. They are widely used in logistic regression models as raw probability scores to predict the logit of mortality. The aim of this study was to evaluate whether these severity indicators would offer a more accurate prediction of mortality if they were used with a logit transformation. Methods: Analyses were based on 25,111 patients from the trauma registries of the four Level I trauma centers in the province of Quebec, Canada, abstracted between 1998 and 2005. The ICISS and TRAIS were calculated using survival proportions from the National Trauma Data Bank. The performance of the ICISS and TRAIS in their widely used form, proportions varying from 0 to 1, was compared with a logit transformation of the scores in logistic regression models predicting in-hospital mortality. Calibration was assessed with the Hosmer-Lemeshow statistic. Results: Neither the ICISS nor the TRAIS had a linear relation with the logit of mortality. A logit transformation of these scores led to a near-linear association and consequently improved model calibration. The Hosmer-Lemeshow statistic was 68 (35–192) and 69 (41–120) with the logit transformation compared with 272 (227–339) and 204 (166–266) with no transformation, for the ICISS and TRAIS, respectively. Conclusions: In logistic regression models predicting mortality, the ICISS and TRAIS should be used with a logit transformation. This study has direct implications for improving the validity of analyses requiring control for injury severity case mix.
Statistic
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Mixed logit
Simultaneity
Representation
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When estimating discrete choice models, the mixed logit approach is commonly superior to simple conditional logit setups. Mixed logit models not only allow the researcher to implement difficult random components but also overcome the restrictive IIA assumption. Despite these theoretical advantages, the estimation of mixed logit models becomes cumbersome when the model's complexity increases. Applied works therefore often rely on rather simple empirical specifications as this reduces the computational burden. I introduce the user-written command lslogit which fits complex mixed logit models using maximum simulated likelihood methods. As lslogit is a d2-ML-evaluator written in Mata, the estimation is rather efficient compared to other routines. It allows the researcher to specify complicated structures of unobserved heterogeneity and to choose from a set of frequently used functional forms for the direct utility function---e.g., including Box-Cox transformations which are difficult to estimate in the context of logit models. The particular focus of lslogit is on the estimation of labor supply models in the discrete choice context and therefore it facilitates several computational exhausting but standard tasks in this research area. However, the command can be used in many other applications of mixed logit models as well.
Mixed logit
Discrete choice
Nested logit
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This paper reports stated preferences of Dutch workers for combinations of housing, employment, and commuting. The analysis uses standard logit models as well as mixed logit models. Estimation results offer insights into the relative importance of various aspects of housing, employment, and commuting. Households dislike commuting and the value of commuting time implied by the model is high in comparison to the wage rate. Nevertheless, preferences for some housing attributes are strong enough to make substantially longer commuting acceptable to most workers. Of special interest is the strong preference for living in small‐or medium‐size cities, especially among two income households. Using a mixed logit model instead of a standard logit model results in a substantial improvement of the loglikelihood, reflecting the importance of heterogeneity among respondents. If no individual characteristics are incorporated into the model, the mixed logit implies substantially lower average monetary evaluations of most attributes. These differences are much smaller if some individual characteristics are incorporated into the model.
Mixed logit
Discrete choice
Nested logit
Value (mathematics)
Revealed preference
Value of time
Ordered logit
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A mixed logit function, also known as a random-coefficients logit function, is an integral of logit functions. The mixed logit model is one of the most widely used models in the analysis of discrete choice. Observed behavior is described by a random choice function, which associates with each choice set a probability measure over the choice set. I obtain several necessary and sufficient conditions under which a random choice function becomes a mixed logit function. One condition is easy to interpret and another condition is easy to test.
Mixed logit
Discrete choice
Choice set
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In this note we investigate the empirical differences between the Random Utility model with fixed coefficients (Conditional Logit), and the Random Utility model with random coefficients (Mixed Logit). We consider a model of household labour supply developed for a project aimed at the evaluation of alternative Basic Income mechanisms. Data are drawn from the 1998 Bank of Italy survey of household income and wealth (SHIW 1998) and choice alternatives are generated using EUROMOD. We compare the estimates of the Conditional Logit and Mixed Logit. We also compare the respective results from simulating the effects of a Flat Tax reform. Although on average the estimates of Conditional Logit and of Mixed Logit are very close, the Mixed Logit estimates reveal that there is a significant unobserved heterogeneity of preferences. We also compare the simulations of a hypothetical Flat Tax reform. Although the differences are small, yet the results would imply different policy conclusions depending on whether Conditional Logit or Mixed Logit is adopted.
Mixed logit
Discrete choice
Labour supply
Nested logit
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Spurious relationship
Logistic model tree
Mixed logit
Ordered logit
Empirical Research
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Kenneth Train . JEL #: C15, C25 Keywords: mixed logit, Halton The simulation variance in the estimation of mixed logit parameters is found, in our application, to be lower with 100 Halton draws than with 1000 random draws. This finding confirms Bhat's (1999a) results and implies significant reduction in run times for mixed logit estimation. Further investigation is needed to assure that the result is not quixotic or masking other issues. May 2000
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