A binary choice model with partial observability for panel data
We consider a panel model with a binary response variable that is a product of two unobservable factors, each determined by a separate binary choice equation. One of these factors is assumed to be time-invariant and may be interpreted as a latent class indicator. A simulation study shows that maximum likelihood estimates from even the shortest panel are much more reliable than those obtained from a cross-section. As an illustrative example, the model is applied to Russian Longitudinal Monitoring Survey data to estimate a proportion of the non-employed population who are participating in job search.
Recently appeared online courses rapidly gained their popularity due to the great opportunities. Absolutely different people can study any discipline for various purposes. Online courses can be useful both to children in preparing for lessons, and to adults in advanced training. Gradually, courses are becoming not only part of the additional curriculum at the university, but part of the mandatory program, too. However, not everyone supports the new way of education. Therefore, the goal of this work was to identify students' attitudes towards online education, the reasons for their preferences on online format of education and the willingness to replace traditional lectures into an online format. The study was carried out on the basis of a survey of more than 6,000 students as part of the Student Life Survey conducted every year at the HSE. The analysis was made by using various clustering methods, such as hierarchical clustering, clustering using the K-means method and analysis of latent classes, as well as analysis of variance. The students were divided into 6 clusters based on the different attitude towards the replacement of all lectures to the online format: devotees of HSE, amateurs of online courses, disciplined, social, learners for the grades, a mixed cluster.
A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.