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This work deals with the analysis of longitudinal ordinal responses. The novelty of the proposed approach is in modeling simultaneously the temporal dynamics of a latent trait of interest, measured via the observed ordinal responses, and the answering behaviors influenced by response styles, through hidden Markov models (HMMs) with two latent components. This approach enables the modeling of (i) the substantive latent trait, controlling for response styles; (ii) the change over time of latent trait and answering behavior, allowing also dependence on individual characteristics. For the proposed HMMs, estimation procedures, methods for standard errors calculation, measures of goodness of fit and classification, and full-conditional residuals are discussed. The proposed model is fitted to ordinal longitudinal data from the Survey on Household Income and Wealth (Bank of Italy) to give insights on the evolution of households financial capability.

Introduction Chronic and highly contagious, trachoma is a condition characterized by recurrent bacterial infection with ocular strains of Mycoplasma trachoma. It spreads through fingers, flies, and fomites, especially in situations where there is overcrowding. If untreated, the illness may result in blindness. Trachoma is an ancient disease and has previously been a significant public health problem in many areas of the world, including parts of Europe and North America. There are at least 400 million cases of active trachoma in the world, 8 million of which have resulted in blindness. Trachoma is a serious public health issue that is very common in Ethiopia. Therefore, the objective of this study is to identify the determinants of active trachoma among rural children aged 1–9 years old in Aw-bare woreda, Somali region of Ethiopia. Method A cross-sectional community-based study involving children aged 1–9 who lived in six selected rural kebeles in the Awbare woreda Somali region and carried out using an ordinal logistic regression model. The study comprised 377 children in total. Our sample youngsters were chosen through a two-stage cluster sampling procedure. Then also chose our sample kebeles by simple random sampling. The main environmental, personal, and demographic factors that influenced the outcomes of active trachoma status were modeled using partial proportional odds modeling and descriptive statistics. Result The study showed that the prevalence of active trachoma was found to be 47.7%. The covariate secondary level of education of mother OR = 1.357; 95% CI (1.051, 1.75), P-value = 0.0192, Inside house cooking place of children family OR = 0.789:95% CI (0.687, 0.927), P-value = 0.0031, children stay at home OR = 2.203:95%CI (1.526, 3.473), P-value = 0.0057,rich income family OR = 1.335:95%CI(1.166,1.528),P-value = 0.0001,Amount of water fetched per day OR = 2.129,95%CI(1.780,2.547),P-Vaue = 0.0001 were significant effect on active trachoma. PPOM represents the best fit as it has the smallest AIC and BIC. It is also more parsimonious. Conclusion The mother’s educational level, the location where the children spent the majority of their time indoors cooking, the fly density during the interview, the family’s income, the child’s age in years, the distance to the water source, the quantity of water fetched daily, and the number of people sharing a room have all been found to be significant predictors of the child’s active trachoma status. Thus, increasing maternal education, access to clean water, and socioeconomic position are all crucial measures in preventing trachoma. Preventing trachoma also involves reducing the number of kids in a room and enhancing activities linked to personal cleanliness, such as giving kids a thorough facial wash to remove debris and discharge from their eyes.

Objectives This paper explores the association of body mass index (BMI) with socioeconomic and demographic factors using data from the 6th wave of the Household, Income and Labour Dynamics in Australia (HILDA) Survey. Methods This study applies a stereotype logit model (SLM) to assess 10,875 individuals on the relationship between BMI and socioeconomic and demographic indicators. Results Aggregate results from the SLM show a positive (and concave) association between age and higher BMI. Further, males are more likely than females to have higher BMI. Higher BMI is positively associated with long-term health problems, reduced prosperity, being married, and being born in Australia and negatively associated with possessing a diploma or above. Conclusions Results show that there is a positive and concave relationship between age and higher BMI. Further, males tend to have higher BMI as compared to females. Higher BMI is also positively related to long-term health problems, reduced prosperity, being married and being born in Australia. Negative association with BMI is observed on those possessing a diploma and above.

Ordinal variables are very often objects of study in health sciences. However, due to the lack of dissemination of models suited for ordinal variables, users often adopt other practices that result in the loss of statistical power. In this tutorial, different models from the family of logistic regression models are introduced as alternatives to handle and interpret ordinal outcomes. The models that were considered include: ordinal regression model (ORM), continuation ratio model (CRM), adjacent category model (ACM), generalised ordered logit model, sequential model, multinomial logit model, partial proportional odds model, partial continuation ratio model and stereotype ordered regression model. By using the relationship of hospital length of stay in a public hospital in Mexico with patient characteristics as an example, the models were used to describe the nature of such relationship and to predict the length of stay category to which a patient is most likely to belong. After an initial analysis, the ORM, CRM and ACM proved to be unsuitable for our data due to the transgression of the parallel regression assumption. The rest of the models were estimated in STATA. The results suggested analogous directionality of the parameter estimates between models, although the interpretation of the odds ratios varied from one model to another. Performance measurements indicated that the models had similar prediction performance. Therefore, when there is an interest in exploiting the ordinal nature of an outcome, there is no reason to maintain practices that ignore such nature since the models discussed here proved to be computationally inexpensive and easy to estimate, analyse and interpret.

Reduced-rank regression is a method with great potential for dimension reduction but has found few applications in applied statistics. To address this, reduced-rank regression is proposed for the class of vector generalized linear models (VGLMs), which is very large. The resulting class, which we call reduced-rank VGLMs (RR-VGLMs), enables the benefits of reduced-rank regression to be conveyed to a wide range of data types, including categorical data. RR-VGLMs are illustrated by focussing on models for categorical data, and especially the multinomial logit model. General algorithmic details are provided and software written by the first author is described. The reduced-rank multinomial logit model is illustrated with real data in two contexts: a regression analysis of workforce data and a classification problem.

The human immunodeficiency virus type 1 (HIV-1) is extremely diverse. In assessing the utility of an HIV-1 vaccine, an important issue is the possibility of differential protection. We discuss statistical methods of inferring how the vaccine efficacy may vary with viral type from data that would be collected from a randomized, double-blind, placebo-controlled preventive vaccine efficacy trial. Detailed characterization of virus isolated from individuals infected during the trial will be available. We focus on the highly simplified case in which the viral characteristics are summarized by a single feature, which may be nominal, or a scalar quantity that represents distance between the isolate and the prototype virus or viruses used in the vaccine preparation. We consider discrete categorical and continuous response models for this quantity and identify models whose parameters can be interpreted as log ratios of strain-specific relative risks of infection in a prospective model for HIV-1 exposure and transmission. Methods of inference are described for the multinomial logistic regression (MLR) model for discrete categorical response, and a new semiparametric model which can be viewed as a continuous analog of the MLR model is introduced. The methods are illustrated by application to HIV-1 and hepatitis B vaccine trial data.

Although ordinal data are not rare in ecology, ecological studies have, until now, seriously neglected the use of specific ordinal regression models. Here, we present three models – the Proportional Odds, the Continuation Ratio and the Stereotype models – that can be successfully applied to ordinal data. Their differences and respective fields of application are discussed. Finally, as an example of application, PO models are used to predict spatial abundance of plant species in a Geographical Information System. It shows that ordinal models give as good a result as binary logistic models for predicting presence‐absence, but are additionally able to predict abundance satisfactorily.