Graphics (and numerics) for comparison

Most statistical data analysis, and thus most graphical data analysis, is directed towards modelling of relationships, but many statistical problems have a different flavour: their focus is comparison, and the key question is assessing agreement or disagreement between two or more data sets or subsets with variables measured in the same units. I survey the range of official and user-written graphical programs available in Stata 8 for such problems, with emphasis on making use of all the information in the data. Recurrent themes include (1) the use of reference lines, especially horizontal reference lines, indicating benchmark cases; (2) the relative merits of superimposition and juxtaposition; (3) how far methods work well at a range of sample sizes; ( 4) standing on giant's shoulders by writing wrappers around existing Stata commands; (5) use (and abuse) of summary statistics appropriate for such problems.

Implementing the multimodel generalized beta estimator in stata and its application

The multimodel generalized beta estimator (MGBE) described by von Hippel, Scarpino and Hola (2014) provides researchers with an improved way to estimate inequality from binned incomes. To extend the application of MGBE, the mgbe command is developed in Stata. In this report, the implementation and performance of mgbe are discussed.Statistic

The substantive and practical significance of citation impact differences between institutions: Guidelines for the analysis of percentiles using effect sizes and confidence intervals

In our chapter we address the statistical analysis of percentiles: How should the citation impact of institutions be compared? In educational and psychological testing, percentiles are already used widely as a standard to evaluate an individual's test scores - intelligence tests for example - by comparing them with the percentiles of a calibrated sample. Percentiles, or percentile rank classes, are also a very suitable method for bibliometrics to normalize citations of publications in terms of the subject category and the publication year and, unlike the mean-based indicators (the relative citation rates), percentiles are scarcely affected by skewed distributions of citations. The percentile of a certain publication provides information about the citation impact this publication has achieved in comparison to other similar publications in the same subject category and publication year. Analyses of percentiles, however, have not always been presented in the most effective and meaningful way. New APA guidelines (American Psychological Association, 2010) suggest a lesser emphasis on significance tests and a greater emphasis on the substantive and practical significance of findings. Drawing on work by Cumming (2012) we show how examinations of effect sizes (e.g. Cohen's d statistic) and confidence intervals can lead to a clear understanding of citation impact differences

Multiple imputation and selection of ordinal level 2 predictors in multilevel models. An analysis of the relationship between student ratings and teacher beliefs and practices

The paper is motivated by the analysis of the relationship between ratings and teacher practices and beliefs, which are measured via a set of binary and ordinal items collected by a specific survey with nearly half missing respondents. The analysis, which is based on a two-level random effect model, must face two about the items measuring teacher practices and beliefs: (i) these items level 2 predictors severely affected by missingness; (ii) there is redundancy in the number of items and the number of categories of their measurement scale. tackle the first issue by considering a multiple imputation strategy based on information at both level 1 and level 2. For the second issue, we consider regularization techniques for ordinal predictors, also accounting for the multilevel data structure. The proposed solution combines existing methods in an original way to solve specific problem at hand, but it is generally applicable to settings requiring to select predictors affected by missing values. The results obtained with the final model out that some teacher practices and beliefs are significantly related to ratings about teacher ability to motivate students.Comment: Presented at the 12th International Multilevel Conference is held April 9-10, 2019 , Utrech

Heterogeneous Effects in Education: The Promise and Challenge of Incorporating Intersectionality into Quantitative Methodological Approaches

To date, the theory of intersectionality has largely guided qualitative efforts in social science and education research. Translating the construct to new methodological approaches is inherently complex and challenging, but offers the possibility of breaking down silos that keep education researchers with similar interests—but different methodological approaches—from sharing knowledge. Quantitative approaches that emphasize the varied impacts of individual identities on educational outcomes move beyond singular dimensions capturing individual characteristics, drawing a parallel to intersectionality. Scholars interested in heterogeneous effects recognize the shortcomings of focusing on the effect of a single social identity. This integrative review explores techniques used in quantitative research to examine heterogeneous effects across individual background, drawing on methodological literature from the social sciences and education. I examine the goals and challenges of the quantitative techniques and explore how they relate to intersectionality. I conclude by discussing what education researchers can learn from other applied fields that are working to develop a crosswalk across the two disparate, but interconnected, literatures.Educational Leadership and Polic

Better estimates from binned income data: Interpolated CDFs and mean-matching

Researchers often estimate income statistics from summaries that report the number of incomes in bins such as \$0-10,000, \$10,001-20,000,...,\$200,000+. Some analysts assign incomes to bin midpoints, but this treats income as discrete. Other analysts fit a continuous parametric distribution, but the distribution may not fit well. We fit nonparametric continuous distributions that reproduce the bin counts perfectly by interpolating the cumulative distribution function (CDF). We also show how both midpoints and interpolated CDFs can be constrained to reproduce the mean of income when it is known. We compare the methods' accuracy in estimating the Gini coefficients of all 3,221 US counties. Fitting parametric distributions is very slow. Fitting interpolated CDFs is much faster and slightly more accurate. Both interpolated CDFs and midpoints give dramatically better estimates if constrained to match a known mean. We have implemented interpolated CDFs in the binsmooth package for R. We have implemented the midpoint method in the rpme command for Stata. Both implementations can be constrained to match a known mean.Comment: 20 pages (including Appendix), 3 tables, 2 figures (+2 in Appendix

The Relationship Between Annual GDP Growth and Income Inequality: Developed and Undeveloped Countries

The hypothesis is that there exists a linear relationship between income inequality and annual GDP growth rate. When the GDP growth rate decreases, the income inequality also decreases. The researchers measured this across two major categories of countries: the developed and the undeveloped countries to see if there exists an optimal range of GDP growth that results in the lowest level of income inequality