Flexible Bayesian Models for Inferences From Coarsened, Group-Level Achievement Data

2018 ◽  
Vol 43 (6) ◽  
pp. 663-692 ◽  
Author(s):  
J. R. Lockwood ◽  
Katherine E. Castellano ◽  
Benjamin R. Shear
Keyword(s):  
Exponential Family ◽  
Ordered Probit ◽  
School Level ◽  
Group Level ◽  
Modeling Framework ◽  
Achievement Data ◽  
Constrained Bayes ◽  
Level Data ◽  
Exponential Family Of Distributions ◽  
Math Proficiency

This article proposes a flexible extension of the Fay–Herriot model for making inferences from coarsened, group-level achievement data, for example, school-level data consisting of numbers of students falling into various ordinal performance categories. The model builds on the heteroskedastic ordered probit (HETOP) framework advocated by Reardon, Shear, Castellano, and Ho by allowing group parameters to be modeled with regressions on group-level covariates, and residuals modeled using the flexible exponential family of distributions recommended by Efron. We demonstrate that the alternative modeling framework, termed the “Fay–Herriot heteroskedastic ordered probit” (FH-HETOP) model, is useful for mitigating some of the challenges with direct maximum likelihood estimators from the HETOP model. We conduct a simulation study to compare the costs and benefits of several methods for using the FH-HETOP model to estimate group parameters and functions of them, including posterior means, constrained Bayes estimators, and the “triple goal” estimators of Shen and Louis. We also provide an application of the FH-HETOP model to math proficiency data from the Early Childhood Longitudinal Study. Code for estimating the FH-HETOP model and conducting supporting calculations is provided in a new package for the R environment.

scholarly journals Primary schools and the amplification of social differences in child mental health: a population-based cohort study

2017 ◽  
Vol 72 (1) ◽  
pp. 27-33 ◽  
Author(s):  
Louise Marryat ◽  
Lucy Thompson ◽  
Helen Minnis ◽  
Philip Wilson
Keyword(s):  
Mental Health ◽  
Primary Schools ◽  
Demographic Data ◽  
Population Based ◽  
School Level ◽  
Social Emotional ◽  
Level Data ◽  
Mental Health Difficulties ◽  
Early Primary ◽  
Additional Support

BackgroundThis paper examines socioeconomic inequalities in mental health at school entry and explores changes in these inequalities over the first 3 years of school.MethodsThe study utilises routinely collected mental health data from education records and demographic data at ages 4 and 7 years, along with administrative school-level data. The study was set in preschool establishments and schools in Glasgow City, Scotland. Data were available on 4011 children (59.4%)at age 4 years, and 3166 of these children were followed at age 7 years (46.9% of the population). The main outcome measure was the teacher-rated Goodman’s Strengths and Difficulties Questionnaire (4–16 version) at age 7 years, which measures social, emotional and behavioural difficulties.ResultsChildren living in the most deprived area had higher levels of mental health difficulties at age 4 years, compared with their most affluent counterparts (7.3%vs4.1% with abnormal range scores). There was a more than threefold widening of this disparity over time, so that by the age of 7 years, children from the most deprived area quintile had rates of difficulties 3.5 times higher than their more affluent peers. Children’s demographic backgrounds strongly predicted their age 7 scores, although schools appeared to make a significant contribution to mental health trajectories.ConclusionsAdditional support to help children from disadvantaged backgrounds at preschool and in early primary school may help narrow inequalities. Children from disadvantaged backgrounds started school with a higher prevalence of mental health difficulties, compared with their more advantaged peers, and this disparity widened markedly over the first 3 years of school.

scholarly journals Penguatan Konsep Kombinatorika Siswa SMAN 1 Muara Batu Kabupaten Aceh Utara dalam Menghadapi KSN-K Bidang Matematika 2021

2021 ◽  
Vol 2 (2) ◽  
pp. 174
Author(s):  
Herizal Herizal
Keyword(s):  
Data Analysis ◽  
Community Service ◽  
Direct Observation ◽  
Learning Process ◽  
School Level ◽  
Level Data ◽  
National Science ◽  
Service Activity ◽  
The Subject

This community service activity aimed to strengthen students’ understanding of  the combinatorics concepts in facing the regency-level of National Science Competition (KSN) in field of mathematics in 2021. The activity was carried out in March-April 2021 for six meetings in the form of training/coaching. The training used both discovery and drilling methods. The location of the activity was at SMAN 1 Muara Batu, North Aceh Regency with four students as the subject who have been selected at the school level and selected to participate in the KSN at the regency level. Data analysis was carried out qualitatively by direct observation to observe the improvement of the students’ comprehension during the learning process. The result obtained was an improvement of the students’ understanding of combinatorics topic. It can be seen in solving problems, the students are able to determine what concepts will be used and able to solve several KSN questions on combinatorics topic.

scholarly journals The closer to the Europe Union headquarters, the higher risk of COVID-19? Cautions regarding ecological studies of COVID-19

2020 ◽  
Author(s):  
Shuai Li ◽  
Xinyang Hua
Keyword(s):  
European Country ◽  
Ecological Study ◽  
Ecological Fallacy ◽  
Group Level ◽  
Ecological Studies ◽  
Public Concern ◽  
Individual Level ◽  
The Public ◽  
Country Level ◽  
Level Data

AbstractSeveral ecological studies of the coronavirus disease 2019 (COVID-19) have reported correlations between group-level aggregated exposures and COVID-19 outcomes. While some studies might be helpful in generating new hypotheses related to COVID-19, results of such type of studies should be interpreted with cautions. To illustrate how ecological studies and results could be biased, we conducted an ecological study of COVID-19 outcomes and the distance to Brussels using European country-level data. We found that, the distance was negatively correlated with COVID-19 outcomes; every 100 km away from Brussels was associated with approximately 6% to 17% reductions (all P<0.01) in COVID-19 cases and deaths in Europe. Without cautions, such results could be interpreted as the closer to the Europe Union headquarters, the higher risk of COVID-19 in Europe. However, these results are more likely to reflect the differences in the timing of and the responding to the outbreak, etc. between European countries, rather than the ‘effect’ of the distance to Brussels itself. Associations observed at the group level have limitations to reflect individual-level associations – the so-called ecological fallacy. Given the public concern over COVID-19, ecological studies should be conducted and interpreted with great cautions, in case the results would be mistakenly understood.

scholarly journals Form-Invariance of the Non-Regular Exponential Family of Distributions

2018 ◽  
Vol 41 (2) ◽  
pp. 157-172
Author(s):  
Samereh Ghorbanpour ◽  
Rahim Chinipardaz ◽  
Seyed Mohammad Reza Alavi
Keyword(s):  
Exponential Family ◽  
Information Matrix ◽  
Likelihood Estimation ◽  
Weight Functions ◽  
Weighted Distribution ◽  
Weighted Distributions ◽  
Original Distribution ◽  
Special Cases ◽  
Exponential Family Of Distributions ◽  
Regular Family

The weighted distributions are used when the sampling mechanism records observations according to a nonnegative weight function. Sometimes the form of the weighted distribution is the same as the original distribution except possibly for a change in the parameters that is called the form-invariant weighted distribution. In this paper, by identifying a general class of weight functions, we introduce an extended class of form-invariant weighted distributions belonging to the non-regular exponential family which included two common families of distribution: exponential family and non-regular family as special cases. Some properties of this class of distributions such as the sufficient and minimal sufficient statistics, maximum likelihood estimation and the Fisher information matrix are studied.

scholarly journals Asymptotic approximations to the Bayes posterior risk

1990 ◽  
Vol 3 (2) ◽  
pp. 99-116
Author(s):  
Toufik Zoubeidi
Keyword(s):  
Parameter Space ◽  
Exponential Family ◽  
Distribution Functions ◽  
Independent Random Variables ◽  
Asymptotic Approximations ◽  
Prior Density ◽  
Posterior Probabilities ◽  
Exponential Family Of Distributions ◽  
Family Of Distributions ◽  
Convex Subsets

Suppose that, given ω=(ω1,ω2)∈ℜ2, X1,X2,… and Y1,Y2,… are independent random variables and their respective distribution functions Gω1 and Gω2 belong to a one parameter exponential family of distributions. We derive approximations to the posterior probabilities of ω lying in closed convex subsets of the parameter space under a general prior density. Using this, we then approximate the Bayes posterior risk for testing the hypotheses H0:ω∈Ω1 versus H1:ω∈Ω2 using a zero-one loss function, where Ω1 and Ω2 are disjoint closed convex subsets of the parameter space.

Spatial analysis of child labour in India

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Lokender Prashad ◽  
Mili Dutta ◽  
Bishnu Mohan Dash
Keyword(s):  
Spatial Analysis ◽  
Census Data ◽  
Hot Spot ◽  
Labour Force ◽  
Child Labour ◽  
District Level ◽  
School Level ◽  
Population Census ◽  
Content Type ◽  
Level Data

Purpose This study on spatial analysis of child labour in India is a macro level analysis on child labour using the census data, 2011 of Government of India. The population census which is conducted once in 10 years only provides district level data on work-force distribution. The study has spatial analysis of child labour in the age group of 5–14 years in India. To assess the magnitude of the children in the labour force, district level data of Census 2011 has been used in the study. The study has made an attempt to identify the districts where there is high level of children in the labour force. This paper aims to estimate the magnitude and trends of children’s workforce participation using the census data as it is the only data base, which is available at the district level since 1961 onwards. The study has made an attempt to identify the clustering of child labour across districts in India and how child labour is clustered by different background characteristics. Design/methodology/approach The study has used ArcGIS software package, GeoDa software and local indicator of spatial association test. Findings The findings of study reveal that the proportion of rural, total fertility rate (TFR) and poverty headcount ratio is positively associated, whereas female literacy and the pupil-teacher ratio are negatively associated with child labour. It suggests that in the hot-spot areas and areas where there is a high prevalence of child labour, there is need to increase the teacher's number at the school level to improve the teacher-pupil ratio and also suggested to promote the female education, promote family planning practices to reduce TFR in those areas for reducing the incidences of child labour. Research limitations/implications The study also recommends that the incidences of child labour can be controlled by a comprehensive holistic action plan with the active participation of social workers. Practical implications The promulgation of effective legislation, active involvement of judiciary and police, political will, effective poverty alleviation and income generation programmes, sensitisation of parents, corporates and media can play effective role in mitigating the incidences of child labour in India. To achieve the sustainable development goals (SDGs) adopted by world leaders in 2015 to eradicate child labour in all its forms by 2025. Social implications The study aims to achieve the SDGs adopted by world leaders in 2015 to eradicate child labour in all its forms by 2025. Originality/value The study is purely original and there are no such studies in Indian context by using the latest software.

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