Multinomial test

Abstract: This paper proposes the use of a quasi-random sequence for the estimation of the mixed multinomial logit model. The mixed multinomial structure is a flexible discrete choice formulation which accommodates general patterns of competitiveness as well as heterogeneity across individuals in sensitivity to exogenous variables. The estimation of this model has been achieved in the past using the pseudo-random maximum simulated likelihood method that evaluates the multi-dimensional integrals in the log-likelihood function by computing the integrand at a sequence of pseudo-random points and taking the average of the resulting integrand values. We suggest and implement an alternative quasi-random maximum simulated likelihood method which uses cleverly crafted non-random but more uniformly distributed sequences in place of the pseudo-random points in the estimation of the mixed logit model. Numerical experiments, in the context of intercity travel mode choice, indicate that the quasi-random method provides considerably better accuracy with much fewer draws and computational time than does the pseudo-random method. This result has the potential to dramatically influence the use of the mixed logit model in practice; specifically, given the flexibility of the mixed logit model, the use of the quasi-random estimation method should facilitate the application of behaviorally rich structures in discrete choice modeling.

Abstract: Background When the dependent variable consists of several categories that are not ordinal (i.e., they have no natural ordering), the ordinary least square estimator cannot be used. Instead, a maximum likelihood estimator like multinomial logit or probit should be used. Objectives The purpose of this article is to understand the multinomial logit model (MLM) that uses maximum likelihood estimator and its application in nursing research. Method The research on "Racial differences in use of long-term care received by the elderly" (Kwak, 2001) is used to illustrate the multinomial logit model approach. This method assumes that the data satisfy a critical assumption called the "independence of irrelevant alternatives." A diagnostic developed by Hausman is used to test the independence of irrelevant alternatives assumption. Models in which the dependent variable consists of several unordered categories can be estimated with the multinomial logit model, and these models can be easily interpreted. Conclusions This method can handle situations with several categories. There is no need to limit the analysis to pairs of categories, or to collapse the categories into two mutually exclusive groups so that the (more familiar) logit model can be used. Indeed, any strategy that eliminates observations or combines categories only leads to less efficient estimates.

Abstract: This paper evaluates a nonparametric sign test for abnormal security price performance in event studies. The sign test statistic examined here does not require a symmetrical distribution of security excess returns for correct specification. Sign test performance is compared to a parametric r-test and a nonparametric rank test. Simulations with daily security return data show that the sign test is better specified under the null hypothesis and often more powerful under the alternative hypothesis than a r-test. The performance of the sign test is dominated by the performance of a rank test, however, indicating that the rank test is preferable to the sign test in obtaining nonparametric inferences concerning abnormal security price performance in event studies.