Analysis of multivariate longitudinal substance use outcomes using multivariate mixed cumulative logit model

Background Longitudinal assessments of usage are often conducted for multiple substances (e.g., cigarettes, alcohol and marijuana) and research interests are often focused on the inter-substance association. We propose a multivariate longitudinal modeling approach for jointly analyzing the ordinal multivariate substance use data. Methods We describe how the binary random slope logistic regression model can be extended to the multi-category ordinal outcomes. We also describe how the proportional odds assumption can be relaxed by allowing differential covariate effects on different cumulative logits for multiple outcomes. Data are analyzed from a P01 study that evaluates the usage levels of cigarettes, alcohol and marijuana repeatedly across 8 measurement waves during 7 consecutive years. Results 1263 subjects participated in the study with informed consent, among whom 56.6% are females. Males and females show significant differences in terms of the time trend for substance use. Specifically, males showed steeper trends on cigarette and marijuana use over time compared to females, while less so for alcohol. For all three substances, age effects appear to be different for different cumulative logits, indicating the violation of proportional odds assumption. Conclusions The multivariate mixed cumulative logit model offers the most flexibility and allows one to examine the inter-substance association when proportional odds assumption is violated.

Smoothing in Ordinal Regression: An Application to Sensory Data

The so-called proportional odds assumption is popular in cumulative, ordinal regression. In practice, however, such an assumption is sometimes too restrictive. For instance, when modeling the perception of boar taint on an individual level, it turns out that, at least for some subjects, the effects of predictors (androstenone and skatole) vary between response categories. For more flexible modeling, we consider the use of a ‘smooth-effects-on-response penalty’ (SERP) as a connecting link between proportional and fully non-proportional odds models, assuming that parameters of the latter vary smoothly over response categories. The usefulness of SERP is further demonstrated through a simulation study. Besides flexible and accurate modeling, SERP also enables fitting of parameters in cases where the pure, unpenalized non-proportional odds model fails to converge.

A COMPARISON OF POLYTOMOUS MODEL WITH PROPORTIONAL ODDS AND NON-PROPORTIONAL ODDS MODEL ON BIRTH SIZE CASE IN INDONESIA

The proportional odds model (POM) and the non-proportional odds model (NPOM) are very useful in ordinal modeling. However, the proportional odds assumption is often violated in practice. In this paper, the non-proportional odds model is chosen as an alternative model when the proportional odds assumption is not violated. This paper aims to compare Proportional Odds Model (POM) and Non-Proportional Odds Model (NPOM) in cases of birth size in Indonesia based on the 2017 Indonesian Demographic and Health Survey (IDHS) data. The results showed that in the POM there was a violation of the proportional odds assumption, so the alternative NPOM model was used. NPOM had better use than POM. The goodness of fit shows that the deviance test failed to reject H0, and the value of Mac Fadden R2 is higher than POM. The risk factors that have a significant influence on all categories of birth size are the residence and gender of the child.

How to Interpret the Effect of Covariates on the Extreme Categories in Ordinal Data Models

This contribution deals with effect measures for covariates in ordinal data models to address the interpretation of the results on the extreme categories of the scales, evaluate possible response styles, and motivate collapsing of extreme categories. It provides a simpler interpretation of the influence of the covariates on the probability of the response categories both in standard cumulative link models under the proportional odds assumption and in the recent extension of the Combination of Uncertainty and Preference of the respondents models, the mixture models introduced to account for uncertainty in rating systems. The article shows by means of marginal effect measures that the effects of the covariates are underestimated when the uncertainty component is neglected. Visualization tools for the effect of covariates are proposed, and measures of relative size and partial effect based on rates of change are evaluated by the use of real data sets.

Using a General Ordered Logit Model to Explain the Influence of Hotel Facilities, General and Sustainability-Related, on Customer Ratings

The hotel market has become extremely competitive over the past years. Hotels try to differentiate themselves through their services and facilities. To make the best choice when searching for accommodation, guests increasingly use rating systems of booking sites. Using an ordered logit model (OLM), we identify, in our study, a sample that comprises of 635 hotels from Romania. These are the hotel facilities that significantly influence customer review scores (as an expression of customer satisfaction) on booking.com, the most widespread rating system. We also identify whether their impact on intervals of satisfaction levels vary. Some explanatory variables invalidate the Brant test for proportional odds assumption. Thus, for the final estimates, we use a generalized ordered logit model (GOLOGIT). The results show that food-related facilities, restaurants, and complimentary breakfasts, are very significant for customer ratings. Relevant hotel common facilities are the pool and parking spaces, while for the room—the flat-screen TV. It is interesting to note the negative influence of pets, which seem to disturb other tourists. In the sustainability category, only facilities for disabled people and electric vehicle charging stations are relevant.

Development of a Partial Proportional Odds Model for Pedestrian Injury Severity at Intersections

Pedestrian injury in crashes at intersections often results from complex interaction among various factors. The factor identification is a critical task for understanding the causes and improving the pedestrian safety. A total of 2,614 crash records at signalized and non-signalized intersections were applied. A Partial Proportional Odds (PPO) model was developed to examine the factors influencing Pedestrian Injury Severity (PIS) because it can accommodate the ordered response nature of injury severity. An elasticity analysis was conducted to quantify the marginal effects of contributing factors on the likelihood of PIS. For signalized intersections, seven explanatory variables significantly affect the likelihood of PIS, in which five explanatory variables violate the Proportional Odds Assumption (POA). Local driver, truck, holiday, clear weather, and hit-and-run lead to higher likelihood of severer PIS. For non-signalized intersections, six explanatory variables were found significant to the PIS, in which three explanatory variables violate the POA. Young and adult drivers, senior pedestrian, bus/van, divided road, holiday, and darkness tend to increase the likelihood of severer PIS. The vehicles of large size and heavy weight (e.g. truck, bus/van) are significant factors to the PIS at both signalized and non-signalized intersections. The proposed PPO model has demonstrated its effectiveness in identifying the effects of contributing factors on the PIS.

A Bayesian Adaptive Design in Cancer Phase I Trials Using Dose Combinations with Ordinal Toxicity Grades

We propose a Bayesian adaptive design for early phase drug combination cancer trials incorporating ordinal grade of toxicities. Parametric models are used to describe the relationship between the dose combinations and the probabilities of the ordinal toxicities under the proportional odds assumption. Trial design proceeds by treating cohorts of two patients simultaneously receiving different dose combinations. Specifically, at each stage of the trial, we seek the dose of one agent by minimizing the Bayes risk with respect to a loss function given the current dose of the other agent. We consider two types of loss functions corresponding to the Continual Reassessment Method (CRM) and Escalation with Overdose Control (EWOC). At the end of the trial, we estimate the MTD curve as a function of Bayes estimates of the model parameters. We evaluate design operating characteristics in terms of safety of the trial and percent of dose recommendation at dose combination neighborhoods around the true MTD by comparing this design to the one that uses a binary indicator of DLT. The methodology is further adapted to the case of a pre-specified discrete set of dose combinations.

Partial Ordered Logit Analysis of Confidence Levels in Financial Institutions in Ghana. The Case of Asante Mampong Municipality

In recent times the financial sector (FS) of Ghana has been saddled with liquidity and operational challenges leading to several financial policies put in place by the Central Bank. The financial crisis and its resultant stringent measures affected public confidence as many customers lost their investments/savings while some financial institutions were consolidated or collapsed. Noting the critical role of public confidence in the financial sector, this paper assessed the confidence levels in FS of Ghana, using Asante Mampong Municipality as a case study. A random sample of 384 respondents was used. Due to the ordinal nature of the dependent variable (confidence levels), the Partial Proportional Odds (PPO) model was used when the ordered logit model failed to pass the proportional odds assumption. About 46.4% of the respondents reported having ‘no confidence’ in the financial institutions of the country, while 37% indicated having ‘somehow confident’ in the sector. Less than 20% of the respondents expressed ‘confident’ (13.3%) or ‘very confident’ (3.4%) in the FS. Duration of engagement with a financial institution, loss of investment, awareness of crisis/reforms of the financial sector and income levels affected the confidence levels in the financial sector. Financial institutions are recommended to strengthen their relationship with customers by providing improved services and policy measures that secure customers investment/savings to ensure sustained and increased levels of confidence.