Many real-world datasets are labeled with natural orders, i.e., ordinal labels. Ordinal regression is a method to predict ordinal labels that finds a wide range of applications in data-rich science domains, such as medical, social and economic sciences. Most existing approaches work well for a single ordinal regression task. However, they ignore the task relatedness when there are multiple related tasks. Multi-task learning (MTL) provides a framework to encode task relatedness, to bridge data from all tasks, and to simultaneously learn multiple related tasks to improve the generalization performance. Even though MTL methods have been extensively studied, there is barely existing work investigating MTL for data with ordinal labels. We tackle multiple ordinal regression problems via sparse and deep multi-task approaches, i.e., two regularized multi-task ordinal regression (RMTOR) models for small datasets and two deep neural networks based multi-task ordinal regression (DMTOR) models for large-scale datasets. The performance of the proposed multi-task ordinal regression models (MTOR) is demonstrated on three real-world medical datasets for multi-stage disease diagnosis. Our experimental results indicate that our proposed MTOR models markedly improve the prediction performance comparing with single-task learning (STL) ordinal regression models.
Generalized linear models perform ordinal regression by fitting a coefficient vector and a set of thresholds, e.g., ordered logit @cite_46 @cite_23 and ordered probit @cite_17 @cite_32 . The margin functions are defined based on the cumulative probability of training instances' ordinal labels. Different link functions are then chosen for different models, i.e., logistic cumulative distribution function (CDF) for ordered logit and standard normal CDF for ordered probit. Finally, maximum likelihood principal is used for training.
@cite_46 @cite_32 @cite_23 @cite_17
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This article describes the gologit2 program for generalized ordered logit models. gologit2 is inspired by Vincent Fu’s gologit routine (Stata Technical Bulletin Reprints 8: 160–164) and is backward compatible with it but offers several additional powerful options. A major strength of gologit2 is that it can fit three special cases of the generalized model: the proportional odds parallel-lines model, the partial proportional odds model, and the logistic regression model. Hence, gologit2 can fit models that are less restrictive than the parallel-lines models fitted by ologit (whose assumptions are often violated) but more parsimonious and interpretable than those fitted by a nonordinal method, such as multinomial logistic regression (i.e., mlogit). Other key advantages of gologit2 include support for linear constraints, survey data estimation, and the computation of estimated probabilities via the predict command. There have been many studies that have documented the application of crash severity models to explore the relationship between accident severity and its contributing factors. Although a large amount of work has been done on different types of models, no research has been conducted about quantifying the sample size requirements for crash severity modeling. Similar to count data models, small data sets could significantly influence model performance. The objective of this study is therefore to examine the effects of sample size on the three most commonly used crash severity models: multinomial logit, ordered probit and mixed logit models. The study objective is accomplished via a Monte-Carlo approach using simulated and observed crash data. The results of this study are consistent with prior expectations in that small sample sizes significantly affect the development of crash severity models, no matter which type is used. Furthermore, among the three models, the mixed logit model requires the largest sample size, while the ordered probit model requires the lowest sample size. The sample size requirement for the multinomial logit model is located between these two models. The paper re-examines existing estimators for the panel data fixed effects ordered logit model, proposes a new one, and studies the sampling properties of these estimators in a series of Monte Carlo simulations. There are two main findings. First, we show that some of the estimators used in the literature are inconsistent, and provide reasons for the inconsistency. Second, the new estimator is never outperformed by the others, seems to be substantially more immune to small sample bias than other consistent estimators, and is easy to implement. The empirical relevance is illustrated in an application to the effect of unemployment on life satisfaction. This paper describes the use of ordered probit models to examine the risk of different injury levels sustained under all crash types, two-vehicle crashes, and single-vehicle crashes. The results suggest that pickups and sport utility vehicles are less safe than passenger cars under single-vehicle crash conditions. In two-vehicle crashes, however, these vehicle types are associated with less severe injuries for their drivers and more severe injuries for occupants of their collision partners. Other conclusions also are presented; for example, the results indicate that males and younger drivers in newer vehicles at lower speeds sustain less severe injuries.