The absence of a significant finding may be related to an insufficient number of observations rather than as a result of the statistical approaches applied; however the number of observations involving six expert readers and 66 CT data sets pre and post optimisation aligns with similar observer studies and exceeds several [46–49]. Additionally, as the CT images were of the brain, the variability in subject matter was minimal with respect to anatomical criteria due to patient size differences com- pared to studies that have looked at other anatomical regions such as the chest or abdomen. It is therefore suggested that the findings are representative of the sta- tistical tool employed. Currently research incorporating both VGC and **ordinal** **regression** **analysis** in review of clinical images and anatomical criteria is limited and Table 2 AUC VGC results of one-paired sample t-test

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In this article, we defined causal measures that indicate whether a biomarker is prognostic and/or predictive. Our measure for prediction is the causal measure version of the interaction term used in **ordinal** **regression** **analysis**. However, we do not use the term for the biomarker in an **ordinal** **regression** model, which uses dummy variables set to 0 or 1, as our measure for prognosis. The measure is not calculated by comparing the outcomes of biomarker-positive and -negative subjects in the control group. Our measure takes both the treatment and control conditions into account instead of only the control condition. Specifically, on the difference scale for a binary outcome, this measure can be expressed as a func- tion of only always- and never-responders. The outcomes for these subjects do not depend on which treatment group they are assigned to. Hence, our causal measure is a plausible measure for prognosis.

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In this study, Likert scale with 5 dependent variables (1: strongly disagree, 2: disagree, 3: undecided, 4: agree, 5: strongly agree) were used. A ranking of the small size (by participation level) was also obtained, which is also appropriate for the proposal for **ordinal** **regression** measures. In **ordinal** **regression** **analysis**, the dependent variable must be measured at **ordinal** level. Two separate dependent variables tested in the study were measured using the Likert type scale. Some re- searchers describe the Likert-type scale as an ordered scale (Hox, 2010: 141). In this study, the data obtained from the questionnaire using Stata 13.0 computer package program were analyzed with the help of logistic **regression** **analysis** and **ordinal** logistic **regression** model. **Ordinal** **regression** **analysis** is a method used when the categories of the dependent variable are measured on a **ordinal** scale. Model-selected variables are used in cases where the dependent variable has more than two categories and sequenced.

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Table 6 displays score distributions in demographic sub- groups. Age was positively correlated with the impact of OA on QoL, reflected by higher scores in all instruments in the group aged over 60, despite the "affect" and "social" scale of the AIMS2-SF. Patients with lower education level achieved higher values in most scores. Women obtained higher values in most scores except for the "role" scale of AIMS2-SF. 111 patients were already retired from work, therefore numbers for the "role" scale were smaller. Table 7 displays the results of the polytomous **ordinal** **regression** **analysis** that mirrors the dependence of the GP score on age, gender, education, on the AIMS2-SF scales "physical", "affect", "symptoms", "social" and on the WOMAC scales "function", "stiffness", "pain" as well as on the radiological grading according to Kellgren and Lawrence. Interestingly, in contrast to our bivariate com- parisons, only "symptoms" and "Kellgren score" emerged as significant influence variables:

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The main contribution of this work is a learning-based method for subpixel estimation which falls under the cat- egory of supervised learning problems where the attributes are given by novel **regression** coe ﬃ cient features represent- ing two patches, and their corresponding label is the subpixel shift between them. Traditionally, the standard approach to solve such supervised learning problems which corresponds to learning the function mapping between the attributes and the label (subpixel shift) is to pose it as a multiclass classifica- tion problem or a **regression** problem. However, in our prob- lem setting, there is a certain ordering present in the class la- bels, namely, the fractional shifts, which will not be captured by a classification or a **regression** approach. In this work, we exploit e ﬃ cient learning algorithms that we proposed in our earlier work on ranking/**ordinal** **regression** [5] to per- form subpixel shift estimation. The contribution of our ear- lier work was a set of eﬃcient algorithms which learn ranking functions eﬃciently while explicitly capturing the inherent ordering present in the class labels. An elaborate description of the ranking algorithms is provided later.

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In this method, the **ordinal** data labels are mapped to certain real numbers [1]. The data labels are now real numbers and hence standardized **regression**-based algorithms and techniques are utilized for further classification. However, this technique is not devoid of shortcomings. Firstly, in **ordinal** data, the distance between the classes is unknown due to which it is difficult to convert **ordinal** numbers into a real valued entity. Secondly, the usage of these real values might hamper the **regression** algorithm’s performance. Thirdly, **regression** algorithms are more concerned about the absolute weight of the label rather than the relative positioning of a particular label with respect to other labels [2]. Hence, applying **regression** techniques do not give correct results. Monedero [3] has proposed a method in which real numbers are chosen by observing inter-class distances of all pairs of data labels, and not randomly.

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may exacerbate depressive symptoms. Our findings chal- lenge the theory that individuals with greater pain at night had disturbed sleep quality and subsequent exacer- bation of depressive symptoms. However, this result should be interpreted with caution. This exploratory study did not perform pre-study sample size calcula- tions, although we initially checked the maximum num- ber of independent variables included in the **ordinal** logistic **regression** model. Therefore, a lack of statistical power due to a small number of included patients may explain this absence. Indeed, post-hoc power calculation detected by the Power and Sample Size Program, PS (version 3.1.2) [52] revealed that we have only 69.0% power to detect a standardized mean difference of at least 0.51, at the 5% alpha level. The lower 95% CI of proportional OR for the presence of night pain is close to 1, suggesting that further studies with larger sample sizes would be warranted to confirm the relationship between depressive symptom and night pain.

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Abstract: Although Ethiopia is a young country with 46 per cent of the population under the age of 14, over five per cent of the 81 million Ethiopians are aged 60 years or more. This proportion of older persons is anticipated to nearly double to nine per cent by 2050. There are several factors that could hinder old people access to food such as income, health status, household size, disability and others (HAIE, 2011). This objective of this study was to assess the old people access to food and its determinants in Dire Dawa city. Total samples of 947 old people were taken by using cluster sampling over proportional allocation to each kebele. Quantitative and qualitative data has been collected from aged persons in Dawit Aid for Aged persons Association, Asegedech Association and other appropriate enumeration areas. The descriptive **analysis** resulted that 72.76% were members of the associations. Most (74.3%) members of the organization have medium and above food access. Additionally their life have been improved in terms of obtaining medical, clothing and counseling service after they joined the organizations. The **ordinal** logistic **regression** identified income source, occupation, owning a house and type of membership organization as determinants of daily food access for the elderly.

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Results: **Ordinal** logistic **regression** with number of injuries in the past year as **ordinal** dependent variable and dental caries and/or gum problems, age and player position as covariates, showed that participants who reported dental caries and/or gum problems and never had had a FOA reported significant more injuries in the past year compared to the reference group of participants who reported no oral health problems and never had had a FOA (adjusted OR = 2.45; 95% CI, 1.19 – 5.05; p = 0.015). A 2 (temporomandibular joint problems) × 2 (FOA) × 2 (age) ANOVA with postural stabilities as dependent variables, showed a significant FOA x age interaction for the non-dominant (standing) leg. Post-hoc t-tests showed a significant better postural stability for the non-dominant leg (and a trend for the dominant leg) for the older compared with the younger participants in the non-FOA group ( p = .002, ES = 0.61), while no age differences were found in the FOA-group.

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Many proposed methods for analyzing clustered **ordinal** data focus on the **regression** model and consider the association structure within a cluster as a nuisance. However, often the association structure is of equal interest, for example, temporal association in longitudinal studies and association between responses to similar questions in a survey. We discuss the use, appropriateness and interpretability of various latent variable and Markov models for the association structure and propose a new structure that exploits the ordinality of the response. The models are illustrated with a study concerning opin- ions regarding government spending and an **analysis** of stability and change in teenage marijuana use over time, where we reveal different behavioral patterns for boys and girls through a comprehensive investigation of individual response profiles.

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Independence among data is a common assumption in **regression** **analysis**. Neverthe- less, in reality, data can be dependent in various ways. Generally speaking, there are two types of dependency in data. Firstly, subjects could be dependent on each other in the sample. For example, a researcher wants to estimate the average base salary of all employees in a company. Instead of doing random sampling, he collects data from one particular research group. Conditioning on that they are from this group, the employees’ data could be treated as independent. However, marginally, the data are highly correlated because they are from the same group. The second type of dependency is within subjects. For instance, a patient takes a hearing test on a series of tone frequencies for both left and right ears. Test results of each sub- ject are naturally correlated. This is called repeated measures. In particular, if the measurements are taken over time, it is so-called longitudinal data. For example, a patient’s blood pressure is tested repeatedly over a period of time during treatment. Another type of dependence is when one subject is measured on diﬀerent outcomes. For example, a person may fill out a survey asking about her exercise behavior which includes information about both exercise duration and frequency.

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Classification and **regression** are essential parts of many fields of studies such as engineering, agriculture, biomedical science, social science and business where the objectives of classifying units into one of several categories and/or prediction of a continuous target variable arise. An ample understanding of the influence of predic- tors on different quantiles of the response variable is also an integral part of business decisions and scientific studies that have of late depended heavily on insights obtained from data. Moreover, technological advancements in data collection and storage have resulted in the need to analyze large data sets, and hence the need for statistical pro- cedures that can be used to analyze them. This dissertation proposes the modeling of multinomial choice, multiclass classification, **ordinal** **regression** and quantile regres- sion problems using ensemble of Bayesian **regression** trees. The proposed models are amenable to large data sets in which the number of predictors may be larger than the number of observations.

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We have proposed a new word embedding model, which is based on **ordinal** **regression**. The input to our model consists of a number of rankings, cap- turing how strongly each word is related to each context word in a purely **ordinal** way. Word vec- tors are then obtained by embedding these rank- ings in a low-dimensional vector space. Despite the fact that all quantitative information is disre- garded by our model (except for constructing the rankings), it is competitive with standard methods such as Skip-gram, and in fact outperforms them in several tasks. An important advantage of our model is that it can be used to learn region repre- sentations for words, by using a quadratic kernel. Our experimental results suggest that these regions can be useful for modeling hypernymy.

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At post-exposure day 14, Dunnett’s multiple comparison following ANOVA or Kruskal Wallis nonparametric test showed that exposure to ZnO-NPs increased significantly total cell, macrophage and lymphocyte at 30 μg per mouse in both genotypes, while it significantly increased neutro- phils at 30 μg per mouse only in Nrf2 −/− mice (Table 2). Exposure to ZnO-NPs increased eosinophils at 10 and 30 μg per mouse in Nrf2 −/− mice but increased eosinophils only at 30 μg per mouse in wild type mice (Table 2). Mul- tiple **regression** analyses or multiple **ordinal** logistic re- gression **analysis** did not show significant interaction of ZnO-NPs exposure level and Nrf2 deletion for the above parameters, thus multiple **regression** model without the interaction was applied for them, although marginally sig- nificant interaction is noted for neutrophils (p = 0.06) as it indicates different effect of ZnO-NP exposure level de- pending on the genotype. The results showed significant positive effect of ZnO-NP exposure level on total cells, macrophages, lymphocytes, neutrophils and eosinophils as well as significant positive effect of Nrf2 deletion on total cells, macrophages and eosinophils. Single **regression** ana- lyses showed significant positive trend with exposure level of ZnO-NPs for all of total cells, macrophages, lympho- cytes, neutrophils and eosinophils in both of genotypes. There was no significant effect of ZnO-NP exposure level or Nrf2 deletion on total protein level.

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Legal Aid Service (LAS) intervention is considered to have an influence on women empowerment through raising awareness of women towards their rights. Using Kongwa and Morogoro Rural districts as study areas, a study was conducted involving 240 women (120 beneficiaries and 120 non-beneficiaries of LAS). A cross-sectional research design was used, whereby random selection of respondents was done. Statistical Package for the Social Sciences (SPSS) was used to analyze the data. A Composite Empowerment Index (CEI) was used to measure the extent of women empowerment among beneficiaries and non-beneficiaries of LAS interventions. Women in the study areas were categorized at medium level of empowerment. Beneficiaries of LAS interventions were found to be more empowered relative to their counterparts. **Ordinal** logistic **regression** **analysis** results showed that involvement of women in LAS interventions, awareness of women legal rights, marital status and age at first marriage were the most determinant factors that influence women empowerment in Morogoro Rural and Kongwa district. Hence persistent sensitization of women about their rights is critical for reducing violence against them and ultimately achieving high levels of empowerment. Also, rigorous enforcement of existing laws and policies is required to discourage and ultimately eliminate the practice of early marriage.

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The interactions between variables, which were not expected during the data collection process, were identi- fied during data **analysis**. The cause for these interaction occurrences was not detected and explained. Adherence to HAART, which was one of the response variables, was measured in pill count technique. This technique had a disadvantage that include patients’ switching of medicines between bottles and discarding pills before visits [27]. Despite its limitations, pill count technique has strong linear relationship with viral load [39]. The result in this **analysis** is true only for adult patients; that is, it may have different outcomes when patients with all ages are consid- ered. This could be a potential area for further investigation.

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Abstract: Our study is to investigate the relationships between the metabolic syndrome (MS) components and the risks of the prostate cancer (PCa) in Chinese Han male population. We studied 186 PCa patients with or without MS and 107 healthy controls. Clinical data including age, body mass index (BMI), systolic blood pressure (SBP), diastolic blood pressure (DBP), fasting blood glucose (FBG), triglyceride (TG), total cholesterol (TCHO), high density lipoprotein (HDL), low density lipoprotein (LDL) and other related indicators were collected. The relationships between cases of PCa and controls were analyzed by t-test. The relationships between high-risk cases, low-risk cases and controls were analyzed by the **analysis** of variance (ANOVA) and **ordinal** logistic **regression** with SPSS 18.0. The age, BMI, DBP, TCHO and HDL were statistically significant between PCa patients and controls (P<0.05), but the age, DBP, TG, TCHO and HDL were statistically significant between high-risk cases, low-risk cases of PCa and controls these three groups (P<0.05). Among them, the age and TCHO were statistically significant not only between high-risk cases and controls but also between low-risk cases and controls. The DBP and HDL were statistically significant between high-risk cases and controls only. As mentioned, BMI is statistically significant between PCa cases and controls, but it is not statistically significant between high-risk cases, low-risk cases and controls these three groups and TG is just the opposite. It means that BMI is associated with the risks of PCa occurrence, which is not associated with high or low risks of occurred PCa. TG is associated with the high-risk of occurred PCa, which is not with the risks of PCa occurrence. The age, DBP, TCHO and HDL were associated with the risks of PCa occurrence and the degree of occurred PCa risks. BMI is associated with the risks of PCa occurrence and TG is associated with the high-risk of occurred PCa only.

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moderately malnourished and severely malnourished. When the researchers are interested to find the determi- nants of malnutrition and severe malnutrition, two sepa- rate binary logistic **regression** (BLR) models are required to develop by grouping the response variable into two categories [7]. This task is tedious and cumbersome due to estimation and interpretation of more parameters. However, the researcher may consider the response vari- able as **ordinal** and may apply **ordinal** logistic **regression** model for the same purpose. A few studies have been done using **ordinal** logistic **regression** model (OLR) to identify the predictors of child undernutrition [11]. In many epidemiological and medical studies, OLR model is frequently used when the response variable is **ordinal** in nature [12-17]. The study has made an effort to iden- tify the predictors of child malnutrition as well as severe malnutrition for under five Bangladeshi children by developing an **ordinal** logistic **regression** model.

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We collected nine benchmark data sets (Set I in Table 1) that were used for metric **regression** prob- lems. The target values were discretized into **ordinal** quantities using equal-length binning. These bins divide the range of target values into a given number of intervals that are of same length. The resulting rank values are ordered, representing these intervals of the original metric quantities. For each data set, we generated two versions by discretizing the target values into five and ten intervals respectively. We randomly partitioned each data set into training/test splits as specified in Table 1. The partition was repeated 20 times independently. The Gaussian kernel (1) was used in these three algorithms. The test results are recorded in Tables 2 and 3. The performance of the MAP and EP approaches are closely matching. Our Gaussian process algorithms often yield better results than

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All the text specificity **analysis** work in NLP has modeled the task as classification or regres- sion. As the 7-step pledge specificity levels used in this research (Pomper and Lederman, 1980) do not form a single real-valued scale, we model it as an **ordinal** **regression** task. Some examples of ordi- nal **regression** tasks include sentiment rating pre- diction (Rosenthal et al., 2017), stages of disease prediction (Gentry et al., 2015), and age prediction (Eidinger et al., 2014). Recent work has shown that adding a distributional (auxiliary) loss along- side a **regression** loss, and using expectation to ob- tain the predicted value (Imani and White, 2018), provides label smoothing and improves **regression** performance (Gao et al., 2017). Approaches based on a uni-modal probability distribution (e.g., Pois- son) as output (da Costa et al., 2008; Beckham and Pal, 2017) can be seen as related to the former ap- proach (Imani and White, 2018) where the discrete probability mass function replaces the histogram density. We propose to use a uni-modal distri- butional loss-based **ordinal** **regression** for pledge specificity prediction.

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