Ordinal Ridge Regression with Categorical Predictors

In multi-category response models categories are often ordered. In case of ordinal response models, the usual likelihood approach becomes unstable with ill-conditioned predictor space or when the number of parameters to be estimated is large relative to the sample size. The likelihood estimates do not exist when the number of observations is less than the number of parameters. The same problem arises if constraints on the order of intercept values are not met during the iterative fitting procedure. Proportional odds models are most commonly used for ordinal responses. In this paper penalized likelihood with quadratic penalty is used to address these issues with a special focus on proportional odds models. To avoid large differences between two parameter values corresponding to the consecutive categories of an ordinal predictor, the differences between the parameters of two adjacent categories should be penalized. The considered penalized likelihood function penalizes the parameter estimates or differences between the parameters estimates according to the type of predictors. Mean squared error for parameter estimates, deviance of fitted probabilities and prediction error for ridge regression are compared with usual likelihood estimates in a simulation study and an application

Investigate waste management issue in Mexico Restaurant

Reliable data on waste management and controlling waste will be illuminated in an effective way to suggest better waste management practices in the hospitality industry in New Zealand. This research suggests effective steps to regain and minimize the waste produced in Mexico restaurant, which is located in Victoria Street, Hamilton. To obtain the data, interviews and observation were the preliminary methods used in this research to clearly understand the main cause of the problem by the organisation in terms of waste. This research has covered waste management issues faced in SMEs and steps to control food waste in restaurants. All the collected data are compared and analysed under a statistical result and these results are discussed on the basis of the current waste management practices of the business. The key findings recommend a possible method to control waste and implementing new software to monitor the waste. Further research will carry over under the same stream by influencing engineering methods and machines, which will be a positive deliverable for a sustainable environment and society

Customer acquisition and engagement in Magic Chinese Health Massage

With the development of massage business, there are more and more massage shops established in Hamilton. Magic Chinese Health Massage is one of them. To achieve a successful development, having appropriate strategies of customer acquisition and engagement is necessary. The aim of this research is to recommend effective and efficient approaches to attract and retain customers for Magic Chinese Health Massage. The research is implemented in the Magic Chinese Health Massage shop through the interview and observation. As a result, the researcher finds the massage shop has a good reputation but it also has some drawbacks of services, advertising and its social media. Therefore, customer services, shop advertising and the social media of Magic Chinese Health Massage should be improved. To achieve the improvement, advertising is recommended to have more detail to attract customers and customer services can be more flexible. Similarly, its social media, such as Facebook, should be updated frequently

Location analysis to suggest new warehouse for Best Furniture shop

Best Furniture operates as a retail furniture outlet in Hamilton, established in 2015, selling furniture manufactured in China and distributed to New Zealand through a network operated from Australia. While the business has tremendous opportunities to grow and outlast its competition, it does not have enough retail space to store its inventory to effectively service all the customer requests it receives. This research aims at identifying and recommending a location to situate a new warehouse for the business such that its operational capacities can be fully utilized. Qualitative research in the form of interview of business manager, and observation, were used to identify a new location and also to provide guidelines on warehouse management. Based on the research conducted, it is recommended that the business operates it new warehouse from a location proximal to Auckland port. It is also recommended that the business creates and implements a warehouse management process and policy document and utilizes available warehouse management software for efficient management of inventory and to streamline the supply chain after the centre is established

Everpresent Lambda - II: Structural Stability

Ideas from causal set theory lead to a fluctuating, time dependent cosmological-constant of the right order of magnitude to match currently quoted "dark energy" values. Although such a term was predicted some time ago, a more detailed analysis of the resulting class of phenomenological models was begun only recently (based on numerical simulation of the cosmological equations with such a fluctuating term). In this paper we continue the investigation by studying the sensitivity of the scheme to some of the ad hoc choices made in setting it up.Comment: 15 pages, 6 figures, Thoroughly rewritte

Ridge Estimation for Multinomial Logit Models with Symmetric Side Constraints

In multinomial logit models, the identifiability of parameter estimates is typically obtained by side constraints that specify one of the response categories as reference category. When parameters are penalized, shrinkage of estimates should not depend on the reference category. In this paper we investigate ridge regression for the multinomial logit model with symmetric side constraints, which yields parameter estimates that are independent of the reference category. In simulation studies the results are compared with the usual maximum likelihood estimates and an application to real data is given

Local market development for Shan Yuan Chinese Restaurant

Shan Yuan Chinese Restaurant (SYCR) is a Chinese restaurant located at 228 Victoria Street, Hamilton. As the most sinological Chinese restaurants in Hamilton, SYCR has always tried to provide customers with the best service and food. Despite this, SYCR restaurant is now facing a crisis in the market because of the turbulent New Zealand food industry. The purpose of this report is to enable the investigator to gain experience in finding and solving problems through individual research. The investigator accomplished data collection through observation, interviews and questionnaire. The researcher found that the problems that SYCR was facing were mainly reflected in four aspects: cultural differences, market competition, online marketing strategic, political factors. The researcher provided four different suggestions in each of these aspects, which can be summarised as website operation, university cooperation, social media strategic, and political study

Regularized Proportional Odds Models

The proportional odds model is commonly used in regression analysis to predict the outcome for an ordinal response variable. The maximum likelihood approach becomes unstable or even fails in small samples with relatively large number of predictors. The ML estimates also do not exist with complete separation in the data. An estimation method is developed to address these problems with MLE. The proposed method uses pseudo observations to regularize the observed responses by sharpening them so that they become close to the underlying probabilities. The estimates can be computed easily with all commonly used statistical packages supporting the fitting of proportional odds models with weights. Estimates are compared with MLE in a simulation study and two real life data sets

Proportional Odds Models with High-dimensional Data Structure

The proportional odds model (POM) is the most widely used model when the response has ordered categories. In the case of high-dimensional predictor structure the common maximum likelihood approach typically fails when all predictors are included. A boosting technique pomBoost is proposed that fits the model by implicitly selecting the influential predictors. The approach distinguishes between metric and categorical predictors. In the case of categorical predictors, where each predictor relates to a set of parameters, the objective is to select simultaneously all the associated parameters. In addition the approach distinguishes between nominal and ordinal predictors. In the case of ordinal predictors, the proposed technique uses the ordering of the ordinal predictors by penalizing the difference between the parameters of adjacent categories. The technique has also a provision to consider some mandatory predictors (if any) which must be part of the final sparse model. The performance of the proposed boosting algorithm is evaluated in a simulation study and applications with respect to mean squared error and prediction error. Hit rates and false alarm rates are used to judge the performance of pomBoost for selection of the relevant predictors

Multinomial Logit Models with Implicit Variable Selection

Multinomial logit models which are most commonly used for the modeling of unordered multi-category responses are typically restricted to the use of few predictors. In the high-dimensional case maximum likelihood estimates frequently do not exist. In this paper we are developing a boosting technique called multinomBoost that performs variable selection and fits the multinomial logit model also when predictors are high-dimensional. Since in multicategory models the effect of one predictor variable is represented by several parameters one has to distinguish between variable selection and parameter selection. A special feature of the approach is that, in contrast to existing approaches, it selects variables not parameters. The method can distinguish between mandatory predictors and optional predictors. Moreover, it adapts to metric, binary, nominal and ordinal predictors. Regularization within the algorithm allows to include nominal and ordinal variables which have many categories. In the case of ordinal predictors the order information is used. The performance of the boosting technique with respect to mean squared error, prediction error and the identification of relevant variables is investigated in a simulation study. For two real life data sets the results are also compared with the Lasso approach which selects parameters