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Regarding the issue of individual purchasing behavior in the rapid growth of electric vehicles, this article studies the diffusion model of electric vehicles considering individual choices and social effects from the perspective of the scale and quantity changes of electric vehicles. First, the neural network was used to predict the charging data of electric vehicles, and the economic effects of purchasing electric vehicles were calculated by combining the purchase cost and government subsidies. Then, the utility function for owners to purchase electric or traditional fuel vehicles was created by considering economic effects, cognitive attitudes, and social effects as factors that individuals need to consider when purchasing electric or traditional fuel vehicles. Finally, the discrete choice model was used to calculate the probability of users choosing to purchase electric or traditional fuel vehicles, and the number of electric vehicles was statistically calculated. Analysis of simulation examples shows that the growth rate of fuel vehicles decreases year by year during the simulation period, and the trend of electric vehicle growth follows an S-curve.

With the development of the social economy, people’s living standards continue to improve, and the consumer demand for environmentally friendly products also increases. At the same time, many businesses have an inaccurate grasp of consumers’ consumption concept of environmentally friendly products, and there are many problems of imbalance between supply and demand. In order to improve consumers’ consumption concepts of environmentally friendly goods and maintain a balance between supply and demand in the market for environmentally friendly goods, this article takes energy-saving appliances as an example to analyze their product consumption models and trend predictions. Based on quantifying changes in residents’ consumption, two consumption models are proposed to address consumption concepts and supply and demand issues and to analyze residents’ consumption of environmentally friendly goods. The conjoint analysis method is to score and sort the products according to the willingness of consumers to a certain product, and finally analyze consumers’ preference for environmentally friendly products according to consumption behavior. The article divides the discrete choice model into four small models. Different analyses are carried out according to the consumption in different states, and from the perspective of consumers, the consumption preferences of consumers when purchasing commodities are analyzed to determine the main factors that affect consumers’ purchase of environmentally friendly commodities. In the experimental part of the article, two consumption models are used to analyze consumers’ consumption preference for environmental protection products, the prediction accuracy of consumption preference, and consumption desire. The experimental results found that consumers of different age groups have increased their desire to purchase environmentally friendly products under the stimulation of the consumption model. Under the stimulation of the discrete choice model, the consumption of residents under the age of 18 increased by 23% compared with the original. Compared with the conjoint analysis method, the discrete choice model is 12% more effective in stimulating consumption desire, and the stimulation effect is better.

This article considers generalized linear models in the presence of many controls. We lay out a general methodology to estimate an effect of interest based on the construction of an instrument that immunizes against model selection mistakes and apply it to the case of logistic binary choice model. More specifically we propose new methods for estimating and constructing confidence regions for a regression parameter of primary interest α 0 , a parameter in front of the regressor of interest, such as the treatment variable or a policy variable. These methods allow to estimate α 0 at the root-n rate when the total number p of other regressors, called controls, potentially exceeds the sample size n using sparsity assumptions. The sparsity assumption means that there is a subset of s < n controls, which suffices to accurately approximate the nuisance part of the regression function. Importantly, the estimators and these resulting confidence regions are valid uniformly over s-sparse models satisfying s 2 log  2 p = o(n) and other technical conditions. These procedures do not rely on traditional consistent model selection arguments for their validity. In fact, they are robust with respect to moderate model selection mistakes in variable selection. Under suitable conditions, the estimators are semi-parametrically efficient in the sense of attaining the semi-parametric efficiency bounds for the class of models in this article.

When modeling demand for differentiated products, it is vital to adequately capture consumer taste heterogeneity, But there is no clearly preferred approach. Here, we compare the performance of six alternative models. Currently, the most popular are mixed logit (MIXL), particularly the version with normal mixing (N-MIXL), and latent class (LC), which assumes discrete consumer types. Recently, several alternative models have been developed. The 'generalized multinomial logit' (G-MNL) extends N-MIXL by allowing for heterogeneity in the logit scale coefficient. Scale heterogeneity logit (S-MNL) is a special case of G-MNL with scale heterogeneity only. The 'mixed-mixed' logit (MM-MNL) assumes a discrete mixture-of-normals heterogeneity distribution. Finally, one can modify N-MIXL by imposing theoretical sign constraints on vertical attributes. We call this 'T-MIXL'. We find that none of these models dominates the others, but G-MNL, MM-MNL and T-MIXL typically outperform the popular N-MIXL and LC models.

Missing data problems arise in many applied research studies. They may jeopardize statistical inference of the model of interest, if the missing mechanism is nonignorable, that is, the missing mechanism depends on the missing values themselves even conditional on the observed data. With a nonignorable missing mechanism, the model of interest is often not identifiable without imposing further assumptions. We find that even if the missing mechanism has a known parametric form, the model is not identifiable without specifying a parametric outcome distribution. Although it is fundamental for valid statistical inference, identifiability under nonignorable missing mechanisms is not established for many commonly used models. In this article, we first demonstrate identifiability of the normal distribution under monotone missing mechanisms. We then extend it to the normal mixture and t mixture models with nonmonotone missing mechanisms. We discover that models under the Logistic missing mechanism are less identifiable than those under the Probit missing mechanism. We give necessary and sufficient conditions for identifiability of models under the Logistic missing mechanism, which sometimes can be checked in real data analysis. We illustrate our methods using a series of simulations, and apply them to a real-life dataset. Supplementary materials for this article are available online.

This paper defines and analyzes a new monotonicity condition for the identification of counterfactuals and treatment effects in unordered discrete choice models with multiple treatments, heterogeneous agents, and discrete-valued instruments. Unordered monotonicity implies and is implied by additive separability of choice of treatment equations in terms of observed and unobserved variables. These results follow from properties of binary matrices developed in this paper. We investigate conditions under which unordered monotonicity arises as a consequence of choice behavior. We characterize IV estimators of counterfactuals as solutions to discrete mixture problems.

Statistical node clustering in discrete time dynamic networks is an emerging field that raises many challenges. Here, we explore statistical properties and frequentist inference in a model that combines a stochastic block model for its static part with independent Markov chains for the evolution of the nodes groups through time.We model binary data as well as weighted dynamic random graphs (with discrete or continuous edges values). Our approach, motivated by the importance of controlling for label switching issues across the different time steps, focuses on detecting groups characterized by a stable within-group connectivity behaviour. We study identifiability of the model parameters and propose an inference procedure based on a variational expectation–maximization algorithm as well as a model selection criterion to select the number of groups. We carefully discuss our initialization strategy which plays an important role in the method and we compare our procedure with existing procedures on synthetic data sets.We also illustrate our approach on dynamic contact networks: one of encounters between high school students and two others on animal interactions. An implementation of the method is available as an R package called dynsbm.

We consider estimating binary response models on an unbalanced panel, where the outcome of the dependent variable may be missing due to nonrandom selection, or there is self-selection into a treatment. In the present paper, we first consider estimation of sample selection models and treatment effects using a fully parametric approach, where the error distribution is assumed to be normal in both primary and selection equations. Arbitrary time dependence in errors is permitted. Estimation of both coefficients and partial effects, as well as tests for selection bias, are discussed. Furthermore, we consider a semiparametric estimator of binary response panel data models with sample selection that is robust to a variety of error distributions. The estimator employs a control function approach to account for endogenous selection and permits consistent estimation of scaled coefficients and relative effects.

In weighted moment condition models, we show a subtle link between identification and estimability that limits the practical usefulness of estimators based on these models. In particular, if it is necessary for (point) identification that the weights take arbitrarily large values, then the parameter of interest, though point identified, cannot be estimated at the regular (parametric) rate and is said to be irregularly identified. This rate depends on relative tail conditions and can be as slow in some examples as $n^{ - (1/4)}$ This nonstandard rate of convergence can lead to numerical instability and/or large standard errors. We examine two weighted model examples: (i) the binary response model under mean restriction introduced by Lewbel (1997) and further generalized to cover endogeneity and selection, where the estimator in this class of models is weighted by the density of a special regressor, and (ii) the treatment effect model under exogenous selection (Rosenbaum and Rubin (1983)), where the resulting estimator of the average treatment effect is one that is weighted by a variant of the propensity score. Without strong relative support conditions, these models, similar to well known \"identified at infinity\" models, lead to estimators that converge at slower than parametric rate, since essentially, to ensure point identification, one requires some variables to take values on sets with arbitrarily small probabilities, or thin sets. For the two models above, we derive some rates of convergence and propose that one conducts inference using rate adaptive procedures that are analogous to Andrews and Schafgans (1998) for the sample selection model.

Multivariate discrete response data can be found in diverse fields, including econometrics, finance, biometrics, and psychometrics. Our contribution, through this study, is to introduce a new class of models for multivariate discrete data based on pair copula constructions (PCCs) that has two major advantages. First, by deriving the conditions under which any multivariate discrete distribution can be decomposed as a PCC, we show that discrete PCCs attain highly flexible dependence structures. Second, the computational burden of evaluating the likelihood for an m -dimensional discrete PCC only grows quadratically with m . This compares favorably to existing models for which computing the likelihood either requires the evaluation of 2 ᵐ terms or slow numerical integration methods. We demonstrate the high quality of inference function for margins and maximum likelihood estimates, both under a simulated setting and for an application to a longitudinal discrete dataset on headache severity. This article has online supplementary material.